From bf3e4965021f6dd541173318bbf463470172fbee Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Wed, 17 Jan 2024 13:10:19 +0100
Subject: [PATCH 01/12] put the mappers in separate files for clarity

---
 .../transformations/datacube_mappers.py       | 4426 +----------------
 .../transformations/mappers/healpix.py        |  123 +
 .../transformations/mappers/octahedral.py     | 2752 ++++++++++
 .../transformations/mappers/reduced_ll.py     | 1504 ++++++
 .../transformations/mappers/regular.py        |   56 +
 tests/test_ecmwf_oper_data_fdb.py             |    2 +-
 tests/test_fdb_datacube.py                    |    3 +-
 tests/test_mappers.py                         |    2 +-
 tests/test_slice_date_range_fdb.py            |    4 +-
 tests/test_slice_date_range_fdb_v2.py         |    2 +-
 10 files changed, 4441 insertions(+), 4433 deletions(-)
 create mode 100644 polytope/datacube/transformations/mappers/healpix.py
 create mode 100644 polytope/datacube/transformations/mappers/octahedral.py
 create mode 100644 polytope/datacube/transformations/mappers/reduced_ll.py
 create mode 100644 polytope/datacube/transformations/mappers/regular.py

diff --git a/polytope/datacube/transformations/datacube_mappers.py b/polytope/datacube/transformations/datacube_mappers.py
index 0a7a3f5e..2e94c649 100644
--- a/polytope/datacube/transformations/datacube_mappers.py
+++ b/polytope/datacube/transformations/datacube_mappers.py
@@ -1,9 +1,6 @@
-import bisect
-import math
 from copy import deepcopy
 from importlib import import_module
 
-from ...utility.list_tools import bisect_left_cmp, bisect_right_cmp
 from .datacube_transformations import DatacubeAxisTransformation
 
 
@@ -22,7 +19,7 @@ def __init__(self, name, mapper_options):
 
     def generate_final_transformation(self):
         map_type = _type_to_datacube_mapper_lookup[self.grid_type]
-        module = import_module("polytope.datacube.transformations.datacube_mappers")
+        module = import_module("polytope.datacube.transformations.mappers." + self.grid_type)
         constructor = getattr(module, map_type)
         transformation = deepcopy(constructor(self.old_axis, self.grid_axes, self.grid_resolution))
         return transformation
@@ -76,4427 +73,6 @@ def unmap(self, first_val, second_val):
         return self._final_transformation.unmap(first_val, second_val)
 
 
-class RegularGridMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
-        self._mapped_axes = mapped_axes
-        self._base_axis = base_axis
-        self._resolution = resolution
-        self.deg_increment = 90 / self._resolution
-        self._axis_reversed = {mapped_axes[0]: True, mapped_axes[1]: False}
-        self._first_axis_vals = self.first_axis_vals()
-
-    def first_axis_vals(self):
-        first_ax_vals = [90 - i * self.deg_increment for i in range(2 * self._resolution)]
-        return first_ax_vals
-
-    def map_first_axis(self, lower, upper):
-        axis_lines = self._first_axis_vals
-        return_vals = [val for val in axis_lines if lower <= val <= upper]
-        return return_vals
-
-    def second_axis_vals(self, first_val):
-        second_ax_vals = [i * self.deg_increment for i in range(4 * self._resolution)]
-        return second_ax_vals
-
-    def map_second_axis(self, first_val, lower, upper):
-        axis_lines = self.second_axis_vals(first_val)
-        return_vals = [val for val in axis_lines if lower <= val <= upper]
-        return return_vals
-
-    def axes_idx_to_regular_idx(self, first_idx, second_idx):
-        final_idx = first_idx * 4 * self._resolution + second_idx
-        return final_idx
-
-    def find_second_idx(self, first_val, second_val):
-        tol = 1e-10
-        second_axis_vals = self.second_axis_vals(first_val)
-        second_idx = bisect.bisect_left(second_axis_vals, second_val - tol)
-        return second_idx
-
-    def unmap_first_val_to_start_line_idx(self, first_val):
-        tol = 1e-8
-        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
-        first_idx = self._first_axis_vals.index(first_val)
-        return first_idx * 4 * self._resolution
-
-    def unmap(self, first_val, second_val):
-        tol = 1e-8
-        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
-        first_idx = self._first_axis_vals.index(first_val)
-        second_val = [i for i in self.second_axis_vals(first_val) if second_val - tol <= i <= second_val + tol][0]
-        second_idx = self.second_axis_vals(first_val).index(second_val)
-        final_index = self.axes_idx_to_regular_idx(first_idx, second_idx)
-        return final_index
-
-
-class ReducedLatLonMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
-        self._mapped_axes = mapped_axes
-        self._base_axis = base_axis
-        self._resolution = resolution
-        self._axis_reversed = {mapped_axes[0]: False, mapped_axes[1]: False}
-        self._first_axis_vals = self.first_axis_vals()
-
-    def first_axis_vals(self):
-        resolution = 180 / (self._resolution - 1)
-        vals = [-90 + i * resolution for i in range(self._resolution)]
-        return vals
-
-    def map_first_axis(self, lower, upper):
-        axis_lines = self._first_axis_vals
-        return_vals = [val for val in axis_lines if lower <= val <= upper]
-        return return_vals
-
-    def lon_spacing(self):
-        if self._resolution == 1441:
-            return [
-                2,
-                6,
-                14,
-                20,
-                26,
-                32,
-                38,
-                44,
-                50,
-                58,
-                64,
-                70,
-                76,
-                82,
-                88,
-                94,
-                102,
-                108,
-                114,
-                120,
-                126,
-                132,
-                138,
-                144,
-                152,
-                158,
-                164,
-                170,
-                176,
-                182,
-                188,
-                196,
-                202,
-                208,
-                214,
-                220,
-                226,
-                232,
-                238,
-                246,
-                252,
-                258,
-                264,
-                270,
-                276,
-                282,
-                290,
-                296,
-                302,
-                308,
-                314,
-                320,
-                326,
-                332,
-                340,
-                346,
-                352,
-                358,
-                364,
-                370,
-                376,
-                382,
-                388,
-                396,
-                402,
-                408,
-                414,
-                420,
-                426,
-                432,
-                438,
-                444,
-                452,
-                458,
-                464,
-                470,
-                476,
-                482,
-                488,
-                494,
-                500,
-                506,
-                512,
-                520,
-                526,
-                532,
-                538,
-                544,
-                550,
-                556,
-                562,
-                568,
-                574,
-                580,
-                586,
-                594,
-                600,
-                606,
-                612,
-                618,
-                624,
-                630,
-                636,
-                642,
-                648,
-                654,
-                660,
-                666,
-                672,
-                678,
-                686,
-                692,
-                698,
-                704,
-                710,
-                716,
-                722,
-                728,
-                734,
-                740,
-                746,
-                752,
-                758,
-                764,
-                770,
-                776,
-                782,
-                788,
-                794,
-                800,
-                806,
-                812,
-                818,
-                824,
-                830,
-                836,
-                842,
-                848,
-                854,
-                860,
-                866,
-                872,
-                878,
-                884,
-                890,
-                896,
-                902,
-                908,
-                914,
-                920,
-                926,
-                932,
-                938,
-                944,
-                950,
-                956,
-                962,
-                968,
-                974,
-                980,
-                986,
-                992,
-                998,
-                1004,
-                1010,
-                1014,
-                1020,
-                1026,
-                1032,
-                1038,
-                1044,
-                1050,
-                1056,
-                1062,
-                1068,
-                1074,
-                1080,
-                1086,
-                1092,
-                1096,
-                1102,
-                1108,
-                1114,
-                1120,
-                1126,
-                1132,
-                1138,
-                1144,
-                1148,
-                1154,
-                1160,
-                1166,
-                1172,
-                1178,
-                1184,
-                1190,
-                1194,
-                1200,
-                1206,
-                1212,
-                1218,
-                1224,
-                1230,
-                1234,
-                1240,
-                1246,
-                1252,
-                1258,
-                1264,
-                1268,
-                1274,
-                1280,
-                1286,
-                1292,
-                1296,
-                1302,
-                1308,
-                1314,
-                1320,
-                1324,
-                1330,
-                1336,
-                1342,
-                1348,
-                1352,
-                1358,
-                1364,
-                1370,
-                1374,
-                1380,
-                1386,
-                1392,
-                1396,
-                1402,
-                1408,
-                1414,
-                1418,
-                1424,
-                1430,
-                1436,
-                1440,
-                1446,
-                1452,
-                1456,
-                1462,
-                1468,
-                1474,
-                1478,
-                1484,
-                1490,
-                1494,
-                1500,
-                1506,
-                1510,
-                1516,
-                1522,
-                1526,
-                1532,
-                1538,
-                1542,
-                1548,
-                1554,
-                1558,
-                1564,
-                1570,
-                1574,
-                1580,
-                1584,
-                1590,
-                1596,
-                1600,
-                1606,
-                1610,
-                1616,
-                1622,
-                1626,
-                1632,
-                1636,
-                1642,
-                1648,
-                1652,
-                1658,
-                1662,
-                1668,
-                1672,
-                1678,
-                1684,
-                1688,
-                1694,
-                1698,
-                1704,
-                1708,
-                1714,
-                1718,
-                1724,
-                1728,
-                1734,
-                1738,
-                1744,
-                1748,
-                1754,
-                1758,
-                1764,
-                1768,
-                1774,
-                1778,
-                1784,
-                1788,
-                1794,
-                1798,
-                1804,
-                1808,
-                1812,
-                1818,
-                1822,
-                1828,
-                1832,
-                1838,
-                1842,
-                1846,
-                1852,
-                1856,
-                1862,
-                1866,
-                1870,
-                1876,
-                1880,
-                1886,
-                1890,
-                1894,
-                1900,
-                1904,
-                1908,
-                1914,
-                1918,
-                1922,
-                1928,
-                1932,
-                1936,
-                1942,
-                1946,
-                1950,
-                1956,
-                1960,
-                1964,
-                1970,
-                1974,
-                1978,
-                1982,
-                1988,
-                1992,
-                1996,
-                2002,
-                2006,
-                2010,
-                2014,
-                2020,
-                2024,
-                2028,
-                2032,
-                2036,
-                2042,
-                2046,
-                2050,
-                2054,
-                2060,
-                2064,
-                2068,
-                2072,
-                2076,
-                2080,
-                2086,
-                2090,
-                2094,
-                2098,
-                2102,
-                2106,
-                2112,
-                2116,
-                2120,
-                2124,
-                2128,
-                2132,
-                2136,
-                2140,
-                2144,
-                2150,
-                2154,
-                2158,
-                2162,
-                2166,
-                2170,
-                2174,
-                2178,
-                2182,
-                2186,
-                2190,
-                2194,
-                2198,
-                2202,
-                2206,
-                2210,
-                2214,
-                2218,
-                2222,
-                2226,
-                2230,
-                2234,
-                2238,
-                2242,
-                2246,
-                2250,
-                2254,
-                2258,
-                2262,
-                2266,
-                2270,
-                2274,
-                2278,
-                2282,
-                2286,
-                2290,
-                2292,
-                2296,
-                2300,
-                2304,
-                2308,
-                2312,
-                2316,
-                2320,
-                2324,
-                2326,
-                2330,
-                2334,
-                2338,
-                2342,
-                2346,
-                2348,
-                2352,
-                2356,
-                2360,
-                2364,
-                2366,
-                2370,
-                2374,
-                2378,
-                2382,
-                2384,
-                2388,
-                2392,
-                2396,
-                2398,
-                2402,
-                2406,
-                2410,
-                2412,
-                2416,
-                2420,
-                2422,
-                2426,
-                2430,
-                2432,
-                2436,
-                2440,
-                2442,
-                2446,
-                2450,
-                2452,
-                2456,
-                2460,
-                2462,
-                2466,
-                2470,
-                2472,
-                2476,
-                2478,
-                2482,
-                2486,
-                2488,
-                2492,
-                2494,
-                2498,
-                2500,
-                2504,
-                2508,
-                2510,
-                2514,
-                2516,
-                2520,
-                2522,
-                2526,
-                2528,
-                2532,
-                2534,
-                2538,
-                2540,
-                2544,
-                2546,
-                2550,
-                2552,
-                2556,
-                2558,
-                2560,
-                2564,
-                2566,
-                2570,
-                2572,
-                2576,
-                2578,
-                2580,
-                2584,
-                2586,
-                2590,
-                2592,
-                2594,
-                2598,
-                2600,
-                2602,
-                2606,
-                2608,
-                2610,
-                2614,
-                2616,
-                2618,
-                2622,
-                2624,
-                2626,
-                2628,
-                2632,
-                2634,
-                2636,
-                2640,
-                2642,
-                2644,
-                2646,
-                2650,
-                2652,
-                2654,
-                2656,
-                2658,
-                2662,
-                2664,
-                2666,
-                2668,
-                2670,
-                2674,
-                2676,
-                2678,
-                2680,
-                2682,
-                2684,
-                2686,
-                2690,
-                2692,
-                2694,
-                2696,
-                2698,
-                2700,
-                2702,
-                2704,
-                2706,
-                2708,
-                2712,
-                2714,
-                2716,
-                2718,
-                2720,
-                2722,
-                2724,
-                2726,
-                2728,
-                2730,
-                2732,
-                2734,
-                2736,
-                2738,
-                2740,
-                2742,
-                2744,
-                2746,
-                2748,
-                2750,
-                2750,
-                2752,
-                2754,
-                2756,
-                2758,
-                2760,
-                2762,
-                2764,
-                2766,
-                2768,
-                2768,
-                2770,
-                2772,
-                2774,
-                2776,
-                2778,
-                2780,
-                2780,
-                2782,
-                2784,
-                2786,
-                2788,
-                2788,
-                2790,
-                2792,
-                2794,
-                2794,
-                2796,
-                2798,
-                2800,
-                2800,
-                2802,
-                2804,
-                2806,
-                2806,
-                2808,
-                2810,
-                2810,
-                2812,
-                2814,
-                2814,
-                2816,
-                2818,
-                2818,
-                2820,
-                2822,
-                2822,
-                2824,
-                2826,
-                2826,
-                2828,
-                2828,
-                2830,
-                2832,
-                2832,
-                2834,
-                2834,
-                2836,
-                2836,
-                2838,
-                2838,
-                2840,
-                2842,
-                2842,
-                2844,
-                2844,
-                2846,
-                2846,
-                2846,
-                2848,
-                2848,
-                2850,
-                2850,
-                2852,
-                2852,
-                2854,
-                2854,
-                2856,
-                2856,
-                2856,
-                2858,
-                2858,
-                2860,
-                2860,
-                2860,
-                2862,
-                2862,
-                2862,
-                2864,
-                2864,
-                2864,
-                2866,
-                2866,
-                2866,
-                2868,
-                2868,
-                2868,
-                2868,
-                2870,
-                2870,
-                2870,
-                2872,
-                2872,
-                2872,
-                2872,
-                2874,
-                2874,
-                2874,
-                2874,
-                2874,
-                2876,
-                2876,
-                2876,
-                2876,
-                2876,
-                2876,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2880,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2878,
-                2876,
-                2876,
-                2876,
-                2876,
-                2876,
-                2876,
-                2874,
-                2874,
-                2874,
-                2874,
-                2874,
-                2872,
-                2872,
-                2872,
-                2872,
-                2870,
-                2870,
-                2870,
-                2868,
-                2868,
-                2868,
-                2868,
-                2866,
-                2866,
-                2866,
-                2864,
-                2864,
-                2864,
-                2862,
-                2862,
-                2862,
-                2860,
-                2860,
-                2860,
-                2858,
-                2858,
-                2856,
-                2856,
-                2856,
-                2854,
-                2854,
-                2852,
-                2852,
-                2850,
-                2850,
-                2848,
-                2848,
-                2846,
-                2846,
-                2846,
-                2844,
-                2844,
-                2842,
-                2842,
-                2840,
-                2838,
-                2838,
-                2836,
-                2836,
-                2834,
-                2834,
-                2832,
-                2832,
-                2830,
-                2828,
-                2828,
-                2826,
-                2826,
-                2824,
-                2822,
-                2822,
-                2820,
-                2818,
-                2818,
-                2816,
-                2814,
-                2814,
-                2812,
-                2810,
-                2810,
-                2808,
-                2806,
-                2806,
-                2804,
-                2802,
-                2800,
-                2800,
-                2798,
-                2796,
-                2794,
-                2794,
-                2792,
-                2790,
-                2788,
-                2788,
-                2786,
-                2784,
-                2782,
-                2780,
-                2780,
-                2778,
-                2776,
-                2774,
-                2772,
-                2770,
-                2768,
-                2768,
-                2766,
-                2764,
-                2762,
-                2760,
-                2758,
-                2756,
-                2754,
-                2752,
-                2750,
-                2750,
-                2748,
-                2746,
-                2744,
-                2742,
-                2740,
-                2738,
-                2736,
-                2734,
-                2732,
-                2730,
-                2728,
-                2726,
-                2724,
-                2722,
-                2720,
-                2718,
-                2716,
-                2714,
-                2712,
-                2708,
-                2706,
-                2704,
-                2702,
-                2700,
-                2698,
-                2696,
-                2694,
-                2692,
-                2690,
-                2686,
-                2684,
-                2682,
-                2680,
-                2678,
-                2676,
-                2674,
-                2670,
-                2668,
-                2666,
-                2664,
-                2662,
-                2658,
-                2656,
-                2654,
-                2652,
-                2650,
-                2646,
-                2644,
-                2642,
-                2640,
-                2636,
-                2634,
-                2632,
-                2628,
-                2626,
-                2624,
-                2622,
-                2618,
-                2616,
-                2614,
-                2610,
-                2608,
-                2606,
-                2602,
-                2600,
-                2598,
-                2594,
-                2592,
-                2590,
-                2586,
-                2584,
-                2580,
-                2578,
-                2576,
-                2572,
-                2570,
-                2566,
-                2564,
-                2560,
-                2558,
-                2556,
-                2552,
-                2550,
-                2546,
-                2544,
-                2540,
-                2538,
-                2534,
-                2532,
-                2528,
-                2526,
-                2522,
-                2520,
-                2516,
-                2514,
-                2510,
-                2508,
-                2504,
-                2500,
-                2498,
-                2494,
-                2492,
-                2488,
-                2486,
-                2482,
-                2478,
-                2476,
-                2472,
-                2470,
-                2466,
-                2462,
-                2460,
-                2456,
-                2452,
-                2450,
-                2446,
-                2442,
-                2440,
-                2436,
-                2432,
-                2430,
-                2426,
-                2422,
-                2420,
-                2416,
-                2412,
-                2410,
-                2406,
-                2402,
-                2398,
-                2396,
-                2392,
-                2388,
-                2384,
-                2382,
-                2378,
-                2374,
-                2370,
-                2366,
-                2364,
-                2360,
-                2356,
-                2352,
-                2348,
-                2346,
-                2342,
-                2338,
-                2334,
-                2330,
-                2326,
-                2324,
-                2320,
-                2316,
-                2312,
-                2308,
-                2304,
-                2300,
-                2296,
-                2292,
-                2290,
-                2286,
-                2282,
-                2278,
-                2274,
-                2270,
-                2266,
-                2262,
-                2258,
-                2254,
-                2250,
-                2246,
-                2242,
-                2238,
-                2234,
-                2230,
-                2226,
-                2222,
-                2218,
-                2214,
-                2210,
-                2206,
-                2202,
-                2198,
-                2194,
-                2190,
-                2186,
-                2182,
-                2178,
-                2174,
-                2170,
-                2166,
-                2162,
-                2158,
-                2154,
-                2150,
-                2144,
-                2140,
-                2136,
-                2132,
-                2128,
-                2124,
-                2120,
-                2116,
-                2112,
-                2106,
-                2102,
-                2098,
-                2094,
-                2090,
-                2086,
-                2080,
-                2076,
-                2072,
-                2068,
-                2064,
-                2060,
-                2054,
-                2050,
-                2046,
-                2042,
-                2036,
-                2032,
-                2028,
-                2024,
-                2020,
-                2014,
-                2010,
-                2006,
-                2002,
-                1996,
-                1992,
-                1988,
-                1982,
-                1978,
-                1974,
-                1970,
-                1964,
-                1960,
-                1956,
-                1950,
-                1946,
-                1942,
-                1936,
-                1932,
-                1928,
-                1922,
-                1918,
-                1914,
-                1908,
-                1904,
-                1900,
-                1894,
-                1890,
-                1886,
-                1880,
-                1876,
-                1870,
-                1866,
-                1862,
-                1856,
-                1852,
-                1846,
-                1842,
-                1838,
-                1832,
-                1828,
-                1822,
-                1818,
-                1812,
-                1808,
-                1804,
-                1798,
-                1794,
-                1788,
-                1784,
-                1778,
-                1774,
-                1768,
-                1764,
-                1758,
-                1754,
-                1748,
-                1744,
-                1738,
-                1734,
-                1728,
-                1724,
-                1718,
-                1714,
-                1708,
-                1704,
-                1698,
-                1694,
-                1688,
-                1684,
-                1678,
-                1672,
-                1668,
-                1662,
-                1658,
-                1652,
-                1648,
-                1642,
-                1636,
-                1632,
-                1626,
-                1622,
-                1616,
-                1610,
-                1606,
-                1600,
-                1596,
-                1590,
-                1584,
-                1580,
-                1574,
-                1570,
-                1564,
-                1558,
-                1554,
-                1548,
-                1542,
-                1538,
-                1532,
-                1526,
-                1522,
-                1516,
-                1510,
-                1506,
-                1500,
-                1494,
-                1490,
-                1484,
-                1478,
-                1474,
-                1468,
-                1462,
-                1456,
-                1452,
-                1446,
-                1440,
-                1436,
-                1430,
-                1424,
-                1418,
-                1414,
-                1408,
-                1402,
-                1396,
-                1392,
-                1386,
-                1380,
-                1374,
-                1370,
-                1364,
-                1358,
-                1352,
-                1348,
-                1342,
-                1336,
-                1330,
-                1324,
-                1320,
-                1314,
-                1308,
-                1302,
-                1296,
-                1292,
-                1286,
-                1280,
-                1274,
-                1268,
-                1264,
-                1258,
-                1252,
-                1246,
-                1240,
-                1234,
-                1230,
-                1224,
-                1218,
-                1212,
-                1206,
-                1200,
-                1194,
-                1190,
-                1184,
-                1178,
-                1172,
-                1166,
-                1160,
-                1154,
-                1148,
-                1144,
-                1138,
-                1132,
-                1126,
-                1120,
-                1114,
-                1108,
-                1102,
-                1096,
-                1092,
-                1086,
-                1080,
-                1074,
-                1068,
-                1062,
-                1056,
-                1050,
-                1044,
-                1038,
-                1032,
-                1026,
-                1020,
-                1014,
-                1010,
-                1004,
-                998,
-                992,
-                986,
-                980,
-                974,
-                968,
-                962,
-                956,
-                950,
-                944,
-                938,
-                932,
-                926,
-                920,
-                914,
-                908,
-                902,
-                896,
-                890,
-                884,
-                878,
-                872,
-                866,
-                860,
-                854,
-                848,
-                842,
-                836,
-                830,
-                824,
-                818,
-                812,
-                806,
-                800,
-                794,
-                788,
-                782,
-                776,
-                770,
-                764,
-                758,
-                752,
-                746,
-                740,
-                734,
-                728,
-                722,
-                716,
-                710,
-                704,
-                698,
-                692,
-                686,
-                678,
-                672,
-                666,
-                660,
-                654,
-                648,
-                642,
-                636,
-                630,
-                624,
-                618,
-                612,
-                606,
-                600,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-                0,
-            ]
-
-    def second_axis_vals(self, first_val):
-        first_idx = self._first_axis_vals.index(first_val)
-        Ny = self.lon_spacing()[first_idx]
-        second_spacing = 360 / Ny
-        return [i * second_spacing for i in range(Ny)]
-
-    def map_second_axis(self, first_val, lower, upper):
-        axis_lines = self.second_axis_vals(first_val)
-        return_vals = [val for val in axis_lines if lower <= val <= upper]
-        return return_vals
-
-    def axes_idx_to_reduced_ll_idx(self, first_idx, second_idx):
-        Ny_array = self.lon_spacing()
-        idx = 0
-        for i in range(self._resolution):
-            if i != first_idx:
-                idx += Ny_array[i]
-            else:
-                idx += second_idx
-                return idx
-
-    def find_second_idx(self, first_val, second_val):
-        tol = 1e-10
-        second_axis_vals = self.second_axis_vals(first_val)
-        second_idx = bisect.bisect_left(second_axis_vals, second_val - tol)
-        return second_idx
-
-    def unmap(self, first_val, second_val):
-        tol = 1e-8
-        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
-        first_idx = self._first_axis_vals.index(first_val)
-        second_val = [i for i in self.second_axis_vals(first_val) if second_val - tol <= i <= second_val + tol][0]
-        second_idx = self.second_axis_vals(first_val).index(second_val)
-        reduced_ll_index = self.axes_idx_to_reduced_ll_idx(first_idx, second_idx)
-        return reduced_ll_index
-
-
-class HealpixGridMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
-        self._mapped_axes = mapped_axes
-        self._base_axis = base_axis
-        self._resolution = resolution
-        self._axis_reversed = {mapped_axes[0]: True, mapped_axes[1]: False}
-        self._first_axis_vals = self.first_axis_vals()
-
-    def first_axis_vals(self):
-        rad2deg = 180 / math.pi
-        vals = [0] * (4 * self._resolution - 1)
-
-        # Polar caps
-        for i in range(1, self._resolution):
-            val = 90 - (rad2deg * math.acos(1 - (i * i / (3 * self._resolution * self._resolution))))
-            vals[i - 1] = val
-            vals[4 * self._resolution - 1 - i] = -val
-        # Equatorial belts
-        for i in range(self._resolution, 2 * self._resolution):
-            val = 90 - (rad2deg * math.acos((4 * self._resolution - 2 * i) / (3 * self._resolution)))
-            vals[i - 1] = val
-            vals[4 * self._resolution - 1 - i] = -val
-        # Equator
-        vals[2 * self._resolution - 1] = 0
-        return vals
-
-    def map_first_axis(self, lower, upper):
-        axis_lines = self._first_axis_vals
-        return_vals = [val for val in axis_lines if lower <= val <= upper]
-        return return_vals
-
-    def second_axis_vals(self, first_val):
-        tol = 1e-8
-        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
-        idx = self._first_axis_vals.index(first_val)
-
-        # Polar caps
-        if idx < self._resolution - 1 or 3 * self._resolution - 1 < idx <= 4 * self._resolution - 2:
-            start = 45 / (idx + 1)
-            vals = [start + i * (360 / (4 * (idx + 1))) for i in range(4 * (idx + 1))]
-            return vals
-        # Equatorial belts
-        start = 45 / self._resolution
-        if self._resolution - 1 <= idx < 2 * self._resolution - 1 or 2 * self._resolution <= idx < 3 * self._resolution:
-            r_start = start * (2 - (((idx + 1) - self._resolution + 1) % 2))
-            vals = [r_start + i * (360 / (4 * self._resolution)) for i in range(4 * self._resolution)]
-            if vals[-1] == 360:
-                vals[-1] = 0
-            return vals
-        # Equator
-        temp_val = 1 if self._resolution % 2 else 0
-        r_start = start * (1 - temp_val)
-        if idx == 2 * self._resolution - 1:
-            vals = [r_start + i * (360 / (4 * self._resolution)) for i in range(4 * self._resolution)]
-            return vals
-
-    def map_second_axis(self, first_val, lower, upper):
-        axis_lines = self.second_axis_vals(first_val)
-        return_vals = [val for val in axis_lines if lower <= val <= upper]
-        return return_vals
-
-    def axes_idx_to_healpix_idx(self, first_idx, second_idx):
-        idx = 0
-        for i in range(self._resolution - 1):
-            if i != first_idx:
-                idx += 4 * (i + 1)
-            else:
-                idx += second_idx
-                return idx
-        for i in range(self._resolution - 1, 3 * self._resolution):
-            if i != first_idx:
-                idx += 4 * self._resolution
-            else:
-                idx += second_idx
-                return idx
-        for i in range(3 * self._resolution, 4 * self._resolution - 1):
-            if i != first_idx:
-                idx += 4 * (4 * self._resolution - 1 - i + 1)
-            else:
-                idx += second_idx
-                return idx
-
-    def find_second_idx(self, first_val, second_val):
-        tol = 1e-10
-        second_axis_vals = self.second_axis_vals(first_val)
-        second_idx = bisect.bisect_left(second_axis_vals, second_val - tol)
-        return second_idx
-
-    def unmap_first_val_to_start_line_idx(self, first_val):
-        tol = 1e-8
-        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
-        first_idx = self._first_axis_vals.index(first_val)
-        idx = 0
-        for i in range(self._resolution - 1):
-            if i != first_idx:
-                idx += 4 * (i + 1)
-            else:
-                return idx
-        for i in range(self._resolution - 1, 3 * self._resolution):
-            if i != first_idx:
-                idx += 4 * self._resolution
-            else:
-                return idx
-        for i in range(3 * self._resolution, 4 * self._resolution - 1):
-            if i != first_idx:
-                idx += 4 * (4 * self._resolution - 1 - i + 1)
-            else:
-                return idx
-
-    def unmap(self, first_val, second_val):
-        tol = 1e-8
-        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
-        first_idx = self._first_axis_vals.index(first_val)
-        second_val = [i for i in self.second_axis_vals(first_val) if second_val - tol <= i <= second_val + tol][0]
-        second_idx = self.second_axis_vals(first_val).index(second_val)
-        healpix_index = self.axes_idx_to_healpix_idx(first_idx, second_idx)
-        return healpix_index
-
-
-class OctahedralGridMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
-        self._mapped_axes = mapped_axes
-        self._base_axis = base_axis
-        self._resolution = resolution
-        self._first_axis_vals = self.first_axis_vals()
-        self._first_idx_map = self.create_first_idx_map()
-        self._second_axis_spacing = {}
-        self._axis_reversed = {mapped_axes[0]: True, mapped_axes[1]: False}
-
-    def gauss_first_guess(self):
-        i = 0
-        gvals = [
-            2.4048255577e0,
-            5.5200781103e0,
-            8.6537279129e0,
-            11.7915344391e0,
-            14.9309177086e0,
-            18.0710639679e0,
-            21.2116366299e0,
-            24.3524715308e0,
-            27.4934791320e0,
-            30.6346064684e0,
-            33.7758202136e0,
-            36.9170983537e0,
-            40.0584257646e0,
-            43.1997917132e0,
-            46.3411883717e0,
-            49.4826098974e0,
-            52.6240518411e0,
-            55.7655107550e0,
-            58.9069839261e0,
-            62.0484691902e0,
-            65.1899648002e0,
-            68.3314693299e0,
-            71.4729816036e0,
-            74.6145006437e0,
-            77.7560256304e0,
-            80.8975558711e0,
-            84.0390907769e0,
-            87.1806298436e0,
-            90.3221726372e0,
-            93.4637187819e0,
-            96.6052679510e0,
-            99.7468198587e0,
-            102.8883742542e0,
-            106.0299309165e0,
-            109.1714896498e0,
-            112.3130502805e0,
-            115.4546126537e0,
-            118.5961766309e0,
-            121.7377420880e0,
-            124.8793089132e0,
-            128.0208770059e0,
-            131.1624462752e0,
-            134.3040166383e0,
-            137.4455880203e0,
-            140.5871603528e0,
-            143.7287335737e0,
-            146.8703076258e0,
-            150.0118824570e0,
-            153.1534580192e0,
-            156.2950342685e0,
-        ]
-
-        numVals = len(gvals)
-        vals = []
-        for i in range(self._resolution):
-            if i < numVals:
-                vals.append(gvals[i])
-            else:
-                vals.append(vals[i - 1] + math.pi)
-        return vals
-
-    def get_precomputed_values_N1280(self):
-        lats = [0] * 2560
-        # lats = SortedList()
-        # lats = {}
-        lats[0] = 89.946187715665616
-        lats[1] = 89.876478353332288
-        lats[2] = 89.806357319542244
-        lats[3] = 89.736143271609578
-        lats[4] = 89.6658939412157
-        lats[5] = 89.595627537554492
-        lats[6] = 89.525351592371393
-        lats[7] = 89.45506977912261
-        lats[8] = 89.3847841013921
-        lats[9] = 89.314495744374256
-        lats[10] = 89.24420545380525
-        lats[11] = 89.173913722284126
-        lats[12] = 89.103620888238879
-        lats[13] = 89.033327191845927
-        lats[14] = 88.96303280826325
-        lats[15] = 88.892737868230952
-        lats[16] = 88.822442471310097
-        lats[17] = 88.752146694650691
-        lats[18] = 88.681850598961759
-        lats[19] = 88.611554232668382
-        lats[20] = 88.541257634868515
-        lats[21] = 88.470960837474877
-        lats[22] = 88.40066386679355
-        lats[23] = 88.330366744702559
-        lats[24] = 88.26006948954614
-        lats[25] = 88.189772116820762
-        lats[26] = 88.119474639706425
-        lats[27] = 88.049177069484486
-        lats[28] = 87.978879415867283
-        lats[29] = 87.908581687261687
-        lats[30] = 87.838283890981543
-        lats[31] = 87.767986033419561
-        lats[32] = 87.697688120188062
-        lats[33] = 87.627390156234085
-        lats[34] = 87.557092145935584
-        lats[35] = 87.486794093180748
-        lats[36] = 87.416496001434894
-        lats[37] = 87.346197873795816
-        lats[38] = 87.275899713041966
-        lats[39] = 87.205601521672108
-        lats[40] = 87.135303301939786
-        lats[41] = 87.065005055882821
-        lats[42] = 86.994706785348129
-        lats[43] = 86.924408492014166
-        lats[44] = 86.854110177408927
-        lats[45] = 86.783811842927179
-        lats[46] = 86.713513489844246
-        lats[47] = 86.643215119328573
-        lats[48] = 86.572916732453024
-        lats[49] = 86.502618330203831
-        lats[50] = 86.432319913489792
-        lats[51] = 86.362021483149363
-        lats[52] = 86.291723039957418
-        lats[53] = 86.221424584631109
-        lats[54] = 86.151126117835304
-        lats[55] = 86.080827640187209
-        lats[56] = 86.010529152260403
-        lats[57] = 85.940230654588888
-        lats[58] = 85.869932147670127
-        lats[59] = 85.799633631968391
-        lats[60] = 85.729335107917464
-        lats[61] = 85.659036575922883
-        lats[62] = 85.588738036364362
-        lats[63] = 85.518439489597966
-        lats[64] = 85.448140935957483
-        lats[65] = 85.377842375756586
-        lats[66] = 85.307543809290152
-        lats[67] = 85.237245236835548
-        lats[68] = 85.16694665865414
-        lats[69] = 85.09664807499216
-        lats[70] = 85.026349486081983
-        lats[71] = 84.95605089214304
-        lats[72] = 84.885752293382765
-        lats[73] = 84.81545368999717
-        lats[74] = 84.745155082171991
-        lats[75] = 84.674856470082915
-        lats[76] = 84.604557853896708
-        lats[77] = 84.534259233771479
-        lats[78] = 84.463960609857125
-        lats[79] = 84.393661982296322
-        lats[80] = 84.323363351224444
-        lats[81] = 84.253064716770425
-        lats[82] = 84.18276607905679
-        lats[83] = 84.112467438200326
-        lats[84] = 84.042168794312317
-        lats[85] = 83.971870147498763
-        lats[86] = 83.901571497860914
-        lats[87] = 83.831272845495249
-        lats[88] = 83.760974190494011
-        lats[89] = 83.690675532945292
-        lats[90] = 83.620376872933264
-        lats[91] = 83.550078210538487
-        lats[92] = 83.479779545838113
-        lats[93] = 83.409480878905782
-        lats[94] = 83.339182209812321
-        lats[95] = 83.268883538625232
-        lats[96] = 83.198584865409657
-        lats[97] = 83.128286190227698
-        lats[98] = 83.057987513139125
-        lats[99] = 82.987688834201322
-        lats[100] = 82.917390153469313
-        lats[101] = 82.84709147099602
-        lats[102] = 82.77679278683226
-        lats[103] = 82.706494101026948
-        lats[104] = 82.63619541362705
-        lats[105] = 82.56589672467787
-        lats[106] = 82.495598034222837
-        lats[107] = 82.425299342304029
-        lats[108] = 82.355000648961692
-        lats[109] = 82.284701954234833
-        lats[110] = 82.214403258160871
-        lats[111] = 82.144104560776
-        lats[112] = 82.073805862115165
-        lats[113] = 82.003507162211946
-        lats[114] = 81.933208461098829
-        lats[115] = 81.862909758807191
-        lats[116] = 81.792611055367345
-        lats[117] = 81.722312350808508
-        lats[118] = 81.652013645158945
-        lats[119] = 81.581714938445955
-        lats[120] = 81.511416230696042
-        lats[121] = 81.441117521934686
-        lats[122] = 81.370818812186627
-        lats[123] = 81.300520101475826
-        lats[124] = 81.230221389825374
-        lats[125] = 81.159922677257711
-        lats[126] = 81.089623963794551
-        lats[127] = 81.019325249456955
-        lats[128] = 80.949026534265244
-        lats[129] = 80.878727818239184
-        lats[130] = 80.808429101397948
-        lats[131] = 80.73813038376008
-        lats[132] = 80.667831665343556
-        lats[133] = 80.59753294616587
-        lats[134] = 80.527234226243991
-        lats[135] = 80.456935505594302
-        lats[136] = 80.386636784232863
-        lats[137] = 80.316338062175078
-        lats[138] = 80.246039339436052
-        lats[139] = 80.175740616030438
-        lats[140] = 80.105441891972376
-        lats[141] = 80.035143167275749
-        lats[142] = 79.9648444419539
-        lats[143] = 79.894545716019948
-        lats[144] = 79.824246989486554
-        lats[145] = 79.753948262366038
-        lats[146] = 79.683649534670437
-        lats[147] = 79.61335080641139
-        lats[148] = 79.543052077600308
-        lats[149] = 79.472753348248219
-        lats[150] = 79.402454618365894
-        lats[151] = 79.332155887963822
-        lats[152] = 79.261857157052191
-        lats[153] = 79.191558425640977
-        lats[154] = 79.121259693739859
-        lats[155] = 79.050960961358285
-        lats[156] = 78.980662228505423
-        lats[157] = 78.910363495190211
-        lats[158] = 78.840064761421445
-        lats[159] = 78.769766027207638
-        lats[160] = 78.699467292557102
-        lats[161] = 78.629168557477882
-        lats[162] = 78.558869821977908
-        lats[163] = 78.488571086064923
-        lats[164] = 78.418272349746417
-        lats[165] = 78.347973613029708
-        lats[166] = 78.277674875922045
-        lats[167] = 78.207376138430348
-        lats[168] = 78.137077400561424
-        lats[169] = 78.066778662322022
-        lats[170] = 77.996479923718596
-        lats[171] = 77.926181184757539
-        lats[172] = 77.855882445445019
-        lats[173] = 77.785583705787161
-        lats[174] = 77.71528496578982
-        lats[175] = 77.644986225458879
-        lats[176] = 77.574687484799924
-        lats[177] = 77.504388743818524
-        lats[178] = 77.434090002520122
-        lats[179] = 77.363791260909963
-        lats[180] = 77.293492518993247
-        lats[181] = 77.22319377677502
-        lats[182] = 77.15289503426024
-        lats[183] = 77.082596291453768
-        lats[184] = 77.012297548360323
-        lats[185] = 76.941998804984564
-        lats[186] = 76.871700061330955
-        lats[187] = 76.801401317404
-        lats[188] = 76.731102573208048
-        lats[189] = 76.660803828747362
-        lats[190] = 76.59050508402602
-        lats[191] = 76.520206339048215
-        lats[192] = 76.449907593817869
-        lats[193] = 76.379608848338933
-        lats[194] = 76.3093101026152
-        lats[195] = 76.239011356650423
-        lats[196] = 76.16871261044831
-        lats[197] = 76.098413864012443
-        lats[198] = 76.028115117346374
-        lats[199] = 75.957816370453543
-        lats[200] = 75.887517623337317
-        lats[201] = 75.81721887600105
-        lats[202] = 75.746920128447996
-        lats[203] = 75.67662138068134
-        lats[204] = 75.60632263270422
-        lats[205] = 75.536023884519707
-        lats[206] = 75.465725136130786
-        lats[207] = 75.395426387540439
-        lats[208] = 75.325127638751567
-        lats[209] = 75.254828889766983
-        lats[210] = 75.184530140589501
-        lats[211] = 75.114231391221821
-        lats[212] = 75.043932641666672
-        lats[213] = 74.973633891926625
-        lats[214] = 74.903335142004323
-        lats[215] = 74.833036391902269
-        lats[216] = 74.762737641622991
-        lats[217] = 74.692438891168877
-        lats[218] = 74.622140140542356
-        lats[219] = 74.551841389745761
-        lats[220] = 74.481542638781434
-        lats[221] = 74.411243887651622
-        lats[222] = 74.340945136358584
-        lats[223] = 74.270646384904481
-        lats[224] = 74.200347633291472
-        lats[225] = 74.13004888152166
-        lats[226] = 74.059750129597163
-        lats[227] = 73.98945137751997
-        lats[228] = 73.919152625292114
-        lats[229] = 73.848853872915541
-        lats[230] = 73.778555120392184
-        lats[231] = 73.70825636772399
-        lats[232] = 73.637957614912779
-        lats[233] = 73.567658861960396
-        lats[234] = 73.497360108868662
-        lats[235] = 73.427061355639339
-        lats[236] = 73.356762602274188
-        lats[237] = 73.2864638487749
-        lats[238] = 73.216165095143182
-        lats[239] = 73.145866341380668
-        lats[240] = 73.075567587489019
-        lats[241] = 73.005268833469799
-        lats[242] = 72.934970079324657
-        lats[243] = 72.864671325055056
-        lats[244] = 72.794372570662574
-        lats[245] = 72.724073816148703
-        lats[246] = 72.653775061514935
-        lats[247] = 72.583476306762691
-        lats[248] = 72.513177551893421
-        lats[249] = 72.442878796908545
-        lats[250] = 72.3725800418094
-        lats[251] = 72.302281286597392
-        lats[252] = 72.231982531273843
-        lats[253] = 72.161683775840089
-        lats[254] = 72.091385020297409
-        lats[255] = 72.02108626464711
-        lats[256] = 71.950787508890414
-        lats[257] = 71.880488753028587
-        lats[258] = 71.810189997062835
-        lats[259] = 71.739891240994368
-        lats[260] = 71.669592484824364
-        lats[261] = 71.599293728553988
-        lats[262] = 71.528994972184378
-        lats[263] = 71.458696215716685
-        lats[264] = 71.388397459152031
-        lats[265] = 71.318098702491469
-        lats[266] = 71.247799945736105
-        lats[267] = 71.177501188887007
-        lats[268] = 71.107202431945211
-        lats[269] = 71.036903674911756
-        lats[270] = 70.966604917787635
-        lats[271] = 70.896306160573886
-        lats[272] = 70.826007403271475
-        lats[273] = 70.755708645881384
-        lats[274] = 70.685409888404578
-        lats[275] = 70.615111130841967
-        lats[276] = 70.544812373194532
-        lats[277] = 70.474513615463138
-        lats[278] = 70.404214857648739
-        lats[279] = 70.333916099752187
-        lats[280] = 70.263617341774406
-        lats[281] = 70.193318583716191
-        lats[282] = 70.123019825578467
-        lats[283] = 70.052721067362043
-        lats[284] = 69.982422309067744
-        lats[285] = 69.912123550696421
-        lats[286] = 69.841824792248843
-        lats[287] = 69.771526033725834
-        lats[288] = 69.701227275128161
-        lats[289] = 69.630928516456592
-        lats[290] = 69.560629757711908
-        lats[291] = 69.490330998894862
-        lats[292] = 69.420032240006194
-        lats[293] = 69.349733481046613
-        lats[294] = 69.279434722016902
-        lats[295] = 69.209135962917699
-        lats[296] = 69.138837203749759
-        lats[297] = 69.068538444513763
-        lats[298] = 68.998239685210365
-        lats[299] = 68.927940925840304
-        lats[300] = 68.85764216640419
-        lats[301] = 68.787343406902693
-        lats[302] = 68.717044647336493
-        lats[303] = 68.646745887706189
-        lats[304] = 68.576447128012447
-        lats[305] = 68.506148368255865
-        lats[306] = 68.435849608437067
-        lats[307] = 68.365550848556666
-        lats[308] = 68.295252088615257
-        lats[309] = 68.224953328613438
-        lats[310] = 68.154654568551791
-        lats[311] = 68.084355808430871
-        lats[312] = 68.014057048251274
-        lats[313] = 67.943758288013555
-        lats[314] = 67.873459527718282
-        lats[315] = 67.803160767365966
-        lats[316] = 67.732862006957205
-        lats[317] = 67.662563246492482
-        lats[318] = 67.592264485972336
-        lats[319] = 67.521965725397308
-        lats[320] = 67.451666964767895
-        lats[321] = 67.381368204084609
-        lats[322] = 67.311069443347961
-        lats[323] = 67.240770682558434
-        lats[324] = 67.170471921716526
-        lats[325] = 67.100173160822706
-        lats[326] = 67.029874399877471
-        lats[327] = 66.95957563888129
-        lats[328] = 66.889276877834618
-        lats[329] = 66.818978116737924
-        lats[330] = 66.748679355591662
-        lats[331] = 66.678380594396273
-        lats[332] = 66.608081833152212
-        lats[333] = 66.537783071859891
-        lats[334] = 66.467484310519808
-        lats[335] = 66.397185549132331
-        lats[336] = 66.326886787697887
-        lats[337] = 66.256588026216932
-        lats[338] = 66.186289264689833
-        lats[339] = 66.115990503117033
-        lats[340] = 66.045691741498899
-        lats[341] = 65.975392979835888
-        lats[342] = 65.905094218128355
-        lats[343] = 65.834795456376696
-        lats[344] = 65.764496694581283
-        lats[345] = 65.694197932742526
-        lats[346] = 65.623899170860767
-        lats[347] = 65.553600408936404
-        lats[348] = 65.483301646969792
-        lats[349] = 65.413002884961315
-        lats[350] = 65.342704122911286
-        lats[351] = 65.272405360820116
-        lats[352] = 65.202106598688133
-        lats[353] = 65.131807836515677
-        lats[354] = 65.061509074303089
-        lats[355] = 64.991210312050711
-        lats[356] = 64.920911549758912
-        lats[357] = 64.850612787427963
-        lats[358] = 64.780314025058246
-        lats[359] = 64.710015262650074
-        lats[360] = 64.639716500203733
-        lats[361] = 64.569417737719576
-        lats[362] = 64.499118975197902
-        lats[363] = 64.428820212639039
-        lats[364] = 64.358521450043284
-        lats[365] = 64.288222687410922
-        lats[366] = 64.21792392474228
-        lats[367] = 64.147625162037642
-        lats[368] = 64.07732639929732
-        lats[369] = 64.00702763652157
-        lats[370] = 63.93672887371072
-        lats[371] = 63.866430110865004
-        lats[372] = 63.796131347984762
-        lats[373] = 63.725832585070251
-        lats[374] = 63.655533822121711
-        lats[375] = 63.585235059139464
-        lats[376] = 63.514936296123757
-        lats[377] = 63.444637533074854
-        lats[378] = 63.374338769993031
-        lats[379] = 63.304040006878537
-        lats[380] = 63.23374124373165
-        lats[381] = 63.163442480552604
-        lats[382] = 63.093143717341647
-        lats[383] = 63.022844954099064
-        lats[384] = 62.952546190825068
-        lats[385] = 62.882247427519928
-        lats[386] = 62.811948664183866
-        lats[387] = 62.741649900817137
-        lats[388] = 62.67135113741999
-        lats[389] = 62.60105237399263
-        lats[390] = 62.530753610535321
-        lats[391] = 62.460454847048261
-        lats[392] = 62.3901560835317
-        lats[393] = 62.319857319985871
-        lats[394] = 62.249558556410982
-        lats[395] = 62.179259792807258
-        lats[396] = 62.108961029174914
-        lats[397] = 62.038662265514176
-        lats[398] = 61.968363501825259
-        lats[399] = 61.898064738108381
-        lats[400] = 61.827765974363729
-        lats[401] = 61.757467210591535
-        lats[402] = 61.687168446791986
-        lats[403] = 61.616869682965287
-        lats[404] = 61.546570919111666
-        lats[405] = 61.476272155231321
-        lats[406] = 61.405973391324409
-        lats[407] = 61.335674627391185
-        lats[408] = 61.265375863431785
-        lats[409] = 61.195077099446451
-        lats[410] = 61.124778335435344
-        lats[411] = 61.054479571398652
-        lats[412] = 60.984180807336578
-        lats[413] = 60.913882043249295
-        lats[414] = 60.843583279137007
-        lats[415] = 60.773284514999872
-        lats[416] = 60.702985750838074
-        lats[417] = 60.632686986651805
-        lats[418] = 60.562388222441243
-        lats[419] = 60.492089458206543
-        lats[420] = 60.421790693947884
-        lats[421] = 60.35149192966545
-        lats[422] = 60.28119316535939
-        lats[423] = 60.21089440102989
-        lats[424] = 60.140595636677112
-        lats[425] = 60.070296872301235
-        lats[426] = 59.999998107902378
-        lats[427] = 59.929699343480763
-        lats[428] = 59.859400579036503
-        lats[429] = 59.78910181456979
-        lats[430] = 59.718803050080759
-        lats[431] = 59.64850428556958
-        lats[432] = 59.578205521036402
-        lats[433] = 59.507906756481383
-        lats[434] = 59.43760799190467
-        lats[435] = 59.3673092273064
-        lats[436] = 59.29701046268675
-        lats[437] = 59.226711698045854
-        lats[438] = 59.156412933383855
-        lats[439] = 59.086114168700909
-        lats[440] = 59.015815403997145
-        lats[441] = 58.945516639272725
-        lats[442] = 58.875217874527763
-        lats[443] = 58.804919109762423
-        lats[444] = 58.73462034497684
-        lats[445] = 58.664321580171141
-        lats[446] = 58.594022815345468
-        lats[447] = 58.523724050499972
-        lats[448] = 58.453425285634758
-        lats[449] = 58.383126520749968
-        lats[450] = 58.312827755845746
-        lats[451] = 58.242528990922203
-        lats[452] = 58.172230225979497
-        lats[453] = 58.101931461017728
-        lats[454] = 58.031632696037022
-        lats[455] = 57.961333931037537
-        lats[456] = 57.891035166019364
-        lats[457] = 57.820736400982646
-        lats[458] = 57.75043763592749
-        lats[459] = 57.680138870854037
-        lats[460] = 57.60984010576238
-        lats[461] = 57.539541340652676
-        lats[462] = 57.469242575525016
-        lats[463] = 57.398943810379521
-        lats[464] = 57.328645045216312
-        lats[465] = 57.258346280035504
-        lats[466] = 57.188047514837208
-        lats[467] = 57.117748749621541
-        lats[468] = 57.047449984388614
-        lats[469] = 56.977151219138541
-        lats[470] = 56.90685245387143
-        lats[471] = 56.836553688587379
-        lats[472] = 56.766254923286517
-        lats[473] = 56.695956157968951
-        lats[474] = 56.625657392634771
-        lats[475] = 56.555358627284086
-        lats[476] = 56.485059861917016
-        lats[477] = 56.41476109653366
-        lats[478] = 56.34446233113411
-        lats[479] = 56.274163565718467
-        lats[480] = 56.203864800286865
-        lats[481] = 56.133566034839362
-        lats[482] = 56.063267269376091
-        lats[483] = 55.992968503897131
-        lats[484] = 55.922669738402583
-        lats[485] = 55.852370972892551
-        lats[486] = 55.782072207367136
-        lats[487] = 55.711773441826416
-        lats[488] = 55.641474676270505
-        lats[489] = 55.571175910699488
-        lats[490] = 55.500877145113449
-        lats[491] = 55.430578379512511
-        lats[492] = 55.360279613896743
-        lats[493] = 55.289980848266232
-        lats[494] = 55.219682082621084
-        lats[495] = 55.149383316961377
-        lats[496] = 55.07908455128721
-        lats[497] = 55.008785785598668
-        lats[498] = 54.938487019895831
-        lats[499] = 54.868188254178797
-        lats[500] = 54.797889488447652
-        lats[501] = 54.727590722702473
-        lats[502] = 54.657291956943347
-        lats[503] = 54.586993191170357
-        lats[504] = 54.516694425383605
-        lats[505] = 54.446395659583146
-        lats[506] = 54.376096893769081
-        lats[507] = 54.305798127941479
-        lats[508] = 54.235499362100448
-        lats[509] = 54.165200596246031
-        lats[510] = 54.094901830378333
-        lats[511] = 54.024603064497434
-        lats[512] = 53.954304298603383
-        lats[513] = 53.884005532696307
-        lats[514] = 53.813706766776235
-        lats[515] = 53.743408000843282
-        lats[516] = 53.673109234897495
-        lats[517] = 53.602810468938962
-        lats[518] = 53.53251170296776
-        lats[519] = 53.462212936983953
-        lats[520] = 53.391914170987633
-        lats[521] = 53.321615404978871
-        lats[522] = 53.251316638957725
-        lats[523] = 53.181017872924265
-        lats[524] = 53.110719106878584
-        lats[525] = 53.040420340820731
-        lats[526] = 52.970121574750792
-        lats[527] = 52.899822808668837
-        lats[528] = 52.829524042574917
-        lats[529] = 52.759225276469131
-        lats[530] = 52.688926510351514
-        lats[531] = 52.618627744222159
-        lats[532] = 52.548328978081123
-        lats[533] = 52.478030211928477
-        lats[534] = 52.407731445764284
-        lats[535] = 52.337432679588609
-        lats[536] = 52.26713391340153
-        lats[537] = 52.196835147203096
-        lats[538] = 52.126536380993372
-        lats[539] = 52.056237614772435
-        lats[540] = 51.985938848540336
-        lats[541] = 51.915640082297152
-        lats[542] = 51.845341316042933
-        lats[543] = 51.775042549777737
-        lats[544] = 51.704743783501634
-        lats[545] = 51.634445017214695
-        lats[546] = 51.56414625091697
-        lats[547] = 51.493847484608516
-        lats[548] = 51.423548718289396
-        lats[549] = 51.353249951959683
-        lats[550] = 51.282951185619417
-        lats[551] = 51.21265241926865
-        lats[552] = 51.14235365290746
-        lats[553] = 51.072054886535909
-        lats[554] = 51.001756120154049
-        lats[555] = 50.931457353761914
-        lats[556] = 50.86115858735959
-        lats[557] = 50.790859820947119
-        lats[558] = 50.720561054524559
-        lats[559] = 50.650262288091959
-        lats[560] = 50.579963521649397
-        lats[561] = 50.509664755196901
-        lats[562] = 50.439365988734544
-        lats[563] = 50.369067222262359
-        lats[564] = 50.298768455780426
-        lats[565] = 50.228469689288779
-        lats[566] = 50.158170922787484
-        lats[567] = 50.087872156276575
-        lats[568] = 50.017573389756123
-        lats[569] = 49.947274623226157
-        lats[570] = 49.876975856686762
-        lats[571] = 49.80667709013796
-        lats[572] = 49.736378323579807
-        lats[573] = 49.66607955701236
-        lats[574] = 49.595780790435676
-        lats[575] = 49.525482023849783
-        lats[576] = 49.455183257254745
-        lats[577] = 49.384884490650613
-        lats[578] = 49.314585724037435
-        lats[579] = 49.244286957415234
-        lats[580] = 49.173988190784094
-        lats[581] = 49.103689424144044
-        lats[582] = 49.03339065749514
-        lats[583] = 48.963091890837418
-        lats[584] = 48.892793124170929
-        lats[585] = 48.822494357495721
-        lats[586] = 48.752195590811837
-        lats[587] = 48.681896824119335
-        lats[588] = 48.611598057418242
-        lats[589] = 48.541299290708608
-        lats[590] = 48.47100052399049
-        lats[591] = 48.400701757263917
-        lats[592] = 48.330402990528938
-        lats[593] = 48.260104223785596
-        lats[594] = 48.189805457033941
-        lats[595] = 48.119506690274015
-        lats[596] = 48.049207923505868
-        lats[597] = 47.978909156729507
-        lats[598] = 47.908610389945018
-        lats[599] = 47.838311623152421
-        lats[600] = 47.76801285635176
-        lats[601] = 47.697714089543084
-        lats[602] = 47.627415322726435
-        lats[603] = 47.557116555901828
-        lats[604] = 47.486817789069342
-        lats[605] = 47.416519022228997
-        lats[606] = 47.346220255380835
-        lats[607] = 47.275921488524894
-        lats[608] = 47.205622721661214
-        lats[609] = 47.13532395478984
-        lats[610] = 47.065025187910805
-        lats[611] = 46.994726421024154
-        lats[612] = 46.924427654129929
-        lats[613] = 46.85412888722815
-        lats[614] = 46.783830120318882
-        lats[615] = 46.713531353402139
-        lats[616] = 46.643232586477971
-        lats[617] = 46.572933819546414
-        lats[618] = 46.502635052607502
-        lats[619] = 46.432336285661272
-        lats[620] = 46.362037518707766
-        lats[621] = 46.291738751747012
-        lats[622] = 46.221439984779053
-        lats[623] = 46.151141217803925
-        lats[624] = 46.080842450821663
-        lats[625] = 46.01054368383231
-        lats[626] = 45.94024491683588
-        lats[627] = 45.869946149832437
-        lats[628] = 45.799647382821995
-        lats[629] = 45.729348615804589
-        lats[630] = 45.659049848780263
-        lats[631] = 45.588751081749038
-        lats[632] = 45.51845231471097
-        lats[633] = 45.448153547666081
-        lats[634] = 45.377854780614399
-        lats[635] = 45.30755601355596
-        lats[636] = 45.237257246490813
-        lats[637] = 45.166958479418959
-        lats[638] = 45.096659712340461
-        lats[639] = 45.026360945255341
-        lats[640] = 44.956062178163634
-        lats[641] = 44.885763411065362
-        lats[642] = 44.81546464396056
-        lats[643] = 44.745165876849271
-        lats[644] = 44.674867109731515
-        lats[645] = 44.604568342607337
-        lats[646] = 44.534269575476756
-        lats[647] = 44.463970808339802
-        lats[648] = 44.39367204119651
-        lats[649] = 44.323373274046915
-        lats[650] = 44.253074506891046
-        lats[651] = 44.182775739728925
-        lats[652] = 44.112476972560586
-        lats[653] = 44.042178205386072
-        lats[654] = 43.971879438205391
-        lats[655] = 43.9015806710186
-        lats[656] = 43.831281903825705
-        lats[657] = 43.760983136626741
-        lats[658] = 43.690684369421732
-        lats[659] = 43.620385602210717
-        lats[660] = 43.550086834993728
-        lats[661] = 43.479788067770777
-        lats[662] = 43.409489300541907
-        lats[663] = 43.339190533307139
-        lats[664] = 43.26889176606651
-        lats[665] = 43.19859299882004
-        lats[666] = 43.128294231567757
-        lats[667] = 43.057995464309691
-        lats[668] = 42.987696697045862
-        lats[669] = 42.917397929776307
-        lats[670] = 42.847099162501053
-        lats[671] = 42.776800395220121
-        lats[672] = 42.706501627933541
-        lats[673] = 42.63620286064134
-        lats[674] = 42.565904093343548
-        lats[675] = 42.495605326040177
-        lats[676] = 42.425306558731272
-        lats[677] = 42.355007791416853
-        lats[678] = 42.284709024096927
-        lats[679] = 42.214410256771551
-        lats[680] = 42.144111489440725
-        lats[681] = 42.073812722104492
-        lats[682] = 42.003513954762873
-        lats[683] = 41.933215187415882
-        lats[684] = 41.862916420063563
-        lats[685] = 41.792617652705921
-        lats[686] = 41.722318885343
-        lats[687] = 41.6520201179748
-        lats[688] = 41.581721350601363
-        lats[689] = 41.511422583222718
-        lats[690] = 41.441123815838885
-        lats[691] = 41.370825048449873
-        lats[692] = 41.300526281055724
-        lats[693] = 41.230227513656445
-        lats[694] = 41.159928746252085
-        lats[695] = 41.089629978842645
-        lats[696] = 41.01933121142816
-        lats[697] = 40.949032444008644
-        lats[698] = 40.878733676584126
-        lats[699] = 40.808434909154634
-        lats[700] = 40.738136141720176
-        lats[701] = 40.667837374280786
-        lats[702] = 40.597538606836487
-        lats[703] = 40.527239839387299
-        lats[704] = 40.456941071933244
-        lats[705] = 40.386642304474343
-        lats[706] = 40.316343537010617
-        lats[707] = 40.246044769542102
-        lats[708] = 40.175746002068806
-        lats[709] = 40.105447234590748
-        lats[710] = 40.035148467107952
-        lats[711] = 39.964849699620437
-        lats[712] = 39.894550932128247
-        lats[713] = 39.824252164631375
-        lats[714] = 39.753953397129855
-        lats[715] = 39.683654629623703
-        lats[716] = 39.613355862112947
-        lats[717] = 39.543057094597607
-        lats[718] = 39.472758327077692
-        lats[719] = 39.402459559553229
-        lats[720] = 39.332160792024254
-        lats[721] = 39.261862024490775
-        lats[722] = 39.191563256952804
-        lats[723] = 39.121264489410365
-        lats[724] = 39.050965721863491
-        lats[725] = 38.980666954312184
-        lats[726] = 38.910368186756479
-        lats[727] = 38.840069419196389
-        lats[728] = 38.769770651631937
-        lats[729] = 38.699471884063136
-        lats[730] = 38.629173116490001
-        lats[731] = 38.558874348912568
-        lats[732] = 38.488575581330842
-        lats[733] = 38.418276813744846
-        lats[734] = 38.347978046154608
-        lats[735] = 38.277679278560143
-        lats[736] = 38.20738051096145
-        lats[737] = 38.137081743358586
-        lats[738] = 38.066782975751536
-        lats[739] = 37.99648420814033
-        lats[740] = 37.926185440524989
-        lats[741] = 37.855886672905527
-        lats[742] = 37.785587905281965
-        lats[743] = 37.715289137654317
-        lats[744] = 37.644990370022605
-        lats[745] = 37.574691602386856
-        lats[746] = 37.504392834747065
-        lats[747] = 37.434094067103274
-        lats[748] = 37.363795299455489
-        lats[749] = 37.293496531803719
-        lats[750] = 37.223197764147997
-        lats[751] = 37.152898996488332
-        lats[752] = 37.082600228824752
-        lats[753] = 37.012301461157264
-        lats[754] = 36.942002693485883
-        lats[755] = 36.871703925810628
-        lats[756] = 36.801405158131523
-        lats[757] = 36.731106390448581
-        lats[758] = 36.660807622761808
-        lats[759] = 36.590508855071242
-        lats[760] = 36.520210087376888
-        lats[761] = 36.449911319678755
-        lats[762] = 36.379612551976876
-        lats[763] = 36.309313784271254
-        lats[764] = 36.239015016561908
-        lats[765] = 36.16871624884886
-        lats[766] = 36.098417481132117
-        lats[767] = 36.028118713411708
-        lats[768] = 35.957819945687639
-        lats[769] = 35.887521177959933
-        lats[770] = 35.817222410228595
-        lats[771] = 35.746923642493655
-        lats[772] = 35.676624874755113
-        lats[773] = 35.606326107012997
-        lats[774] = 35.536027339267314
-        lats[775] = 35.465728571518085
-        lats[776] = 35.395429803765317
-        lats[777] = 35.325131036009047
-        lats[778] = 35.254832268249267
-        lats[779] = 35.184533500486005
-        lats[780] = 35.114234732719261
-        lats[781] = 35.043935964949064
-        lats[782] = 34.973637197175435
-        lats[783] = 34.903338429398374
-        lats[784] = 34.833039661617903
-        lats[785] = 34.762740893834028
-        lats[786] = 34.692442126046771
-        lats[787] = 34.622143358256153
-        lats[788] = 34.551844590462188
-        lats[789] = 34.481545822664863
-        lats[790] = 34.411247054864234
-        lats[791] = 34.340948287060286
-        lats[792] = 34.270649519253041
-        lats[793] = 34.200350751442521
-        lats[794] = 34.130051983628725
-        lats[795] = 34.059753215811682
-        lats[796] = 33.989454447991392
-        lats[797] = 33.919155680167876
-        lats[798] = 33.848856912341155
-        lats[799] = 33.778558144511237
-        lats[800] = 33.708259376678136
-        lats[801] = 33.637960608841851
-        lats[802] = 33.567661841002426
-        lats[803] = 33.497363073159853
-        lats[804] = 33.42706430531414
-        lats[805] = 33.356765537465314
-        lats[806] = 33.286466769613391
-        lats[807] = 33.216168001758369
-        lats[808] = 33.145869233900278
-        lats[809] = 33.075570466039117
-        lats[810] = 33.005271698174909
-        lats[811] = 32.934972930307666
-        lats[812] = 32.864674162437396
-        lats[813] = 32.794375394564113
-        lats[814] = 32.724076626687825
-        lats[815] = 32.653777858808567
-        lats[816] = 32.583479090926325
-        lats[817] = 32.513180323041112
-        lats[818] = 32.442881555152965
-        lats[819] = 32.372582787261891
-        lats[820] = 32.302284019367875
-        lats[821] = 32.231985251470959
-        lats[822] = 32.161686483571145
-        lats[823] = 32.091387715668439
-        lats[824] = 32.021088947762863
-        lats[825] = 31.950790179854422
-        lats[826] = 31.880491411943137
-        lats[827] = 31.810192644029012
-        lats[828] = 31.739893876112063
-        lats[829] = 31.669595108192297
-        lats[830] = 31.599296340269738
-        lats[831] = 31.528997572344384
-        lats[832] = 31.458698804416255
-        lats[833] = 31.388400036485361
-        lats[834] = 31.318101268551715
-        lats[835] = 31.247802500615318
-        lats[836] = 31.177503732676204
-        lats[837] = 31.107204964734358
-        lats[838] = 31.036906196789811
-        lats[839] = 30.966607428842572
-        lats[840] = 30.896308660892647
-        lats[841] = 30.826009892940046
-        lats[842] = 30.755711124984781
-        lats[843] = 30.685412357026873
-        lats[844] = 30.615113589066322
-        lats[845] = 30.544814821103138
-        lats[846] = 30.47451605313735
-        lats[847] = 30.404217285168947
-        lats[848] = 30.333918517197947
-        lats[849] = 30.263619749224372
-        lats[850] = 30.19332098124822
-        lats[851] = 30.123022213269511
-        lats[852] = 30.052723445288244
-        lats[853] = 29.98242467730444
-        lats[854] = 29.91212590931811
-        lats[855] = 29.841827141329258
-        lats[856] = 29.771528373337894
-        lats[857] = 29.701229605344039
-        lats[858] = 29.630930837347698
-        lats[859] = 29.560632069348884
-        lats[860] = 29.490333301347597
-        lats[861] = 29.420034533343859
-        lats[862] = 29.349735765337677
-        lats[863] = 29.279436997329057
-        lats[864] = 29.209138229318015
-        lats[865] = 29.138839461304556
-        lats[866] = 29.068540693288696
-        lats[867] = 28.998241925270449
-        lats[868] = 28.927943157249814
-        lats[869] = 28.857644389226806
-        lats[870] = 28.787345621201432
-        lats[871] = 28.717046853173709
-        lats[872] = 28.646748085143642
-        lats[873] = 28.576449317111244
-        lats[874] = 28.506150549076519
-        lats[875] = 28.435851781039485
-        lats[876] = 28.365553013000145
-        lats[877] = 28.29525424495851
-        lats[878] = 28.224955476914594
-        lats[879] = 28.154656708868405
-        lats[880] = 28.084357940819952
-        lats[881] = 28.014059172769244
-        lats[882] = 27.94376040471629
-        lats[883] = 27.873461636661098
-        lats[884] = 27.803162868603682
-        lats[885] = 27.732864100544052
-        lats[886] = 27.662565332482213
-        lats[887] = 27.592266564418171
-        lats[888] = 27.521967796351948
-        lats[889] = 27.451669028283543
-        lats[890] = 27.381370260212968
-        lats[891] = 27.311071492140236
-        lats[892] = 27.240772724065348
-        lats[893] = 27.170473955988321
-        lats[894] = 27.100175187909159
-        lats[895] = 27.029876419827872
-        lats[896] = 26.959577651744471
-        lats[897] = 26.889278883658971
-        lats[898] = 26.818980115571364
-        lats[899] = 26.748681347481678
-        lats[900] = 26.678382579389908
-        lats[901] = 26.608083811296069
-        lats[902] = 26.53778504320017
-        lats[903] = 26.467486275102218
-        lats[904] = 26.397187507002222
-        lats[905] = 26.326888738900195
-        lats[906] = 26.256589970796135
-        lats[907] = 26.186291202690064
-        lats[908] = 26.115992434581983
-        lats[909] = 26.045693666471902
-        lats[910] = 25.975394898359827
-        lats[911] = 25.90509613024577
-        lats[912] = 25.834797362129745
-        lats[913] = 25.764498594011751
-        lats[914] = 25.694199825891793
-        lats[915] = 25.623901057769892
-        lats[916] = 25.553602289646051
-        lats[917] = 25.483303521520277
-        lats[918] = 25.413004753392578
-        lats[919] = 25.342705985262967
-        lats[920] = 25.272407217131445
-        lats[921] = 25.202108448998025
-        lats[922] = 25.13180968086272
-        lats[923] = 25.061510912725527
-        lats[924] = 24.991212144586456
-        lats[925] = 24.920913376445526
-        lats[926] = 24.850614608302738
-        lats[927] = 24.780315840158096
-        lats[928] = 24.710017072011613
-        lats[929] = 24.639718303863294
-        lats[930] = 24.569419535713152
-        lats[931] = 24.499120767561195
-        lats[932] = 24.428821999407425
-        lats[933] = 24.358523231251851
-        lats[934] = 24.288224463094483
-        lats[935] = 24.217925694935328
-        lats[936] = 24.1476269267744
-        lats[937] = 24.077328158611696
-        lats[938] = 24.007029390447226
-        lats[939] = 23.936730622281004
-        lats[940] = 23.866431854113038
-        lats[941] = 23.796133085943328
-        lats[942] = 23.725834317771888
-        lats[943] = 23.655535549598721
-        lats[944] = 23.585236781423838
-        lats[945] = 23.514938013247242
-        lats[946] = 23.444639245068949
-        lats[947] = 23.374340476888957
-        lats[948] = 23.304041708707278
-        lats[949] = 23.233742940523921
-        lats[950] = 23.163444172338895
-        lats[951] = 23.0931454041522
-        lats[952] = 23.022846635963852
-        lats[953] = 22.952547867773848
-        lats[954] = 22.882249099582204
-        lats[955] = 22.811950331388925
-        lats[956] = 22.741651563194019
-        lats[957] = 22.671352794997489
-        lats[958] = 22.60105402679935
-        lats[959] = 22.530755258599601
-        lats[960] = 22.460456490398254
-        lats[961] = 22.390157722195315
-        lats[962] = 22.319858953990789
-        lats[963] = 22.249560185784691
-        lats[964] = 22.179261417577013
-        lats[965] = 22.108962649367779
-        lats[966] = 22.038663881156989
-        lats[967] = 21.968365112944642
-        lats[968] = 21.898066344730758
-        lats[969] = 21.827767576515338
-        lats[970] = 21.757468808298391
-        lats[971] = 21.687170040079913
-        lats[972] = 21.616871271859928
-        lats[973] = 21.546572503638437
-        lats[974] = 21.47627373541544
-        lats[975] = 21.40597496719095
-        lats[976] = 21.335676198964972
-        lats[977] = 21.265377430737512
-        lats[978] = 21.195078662508585
-        lats[979] = 21.124779894278181
-        lats[980] = 21.054481126046323
-        lats[981] = 20.984182357813012
-        lats[982] = 20.913883589578251
-        lats[983] = 20.843584821342048
-        lats[984] = 20.773286053104417
-        lats[985] = 20.702987284865355
-        lats[986] = 20.632688516624874
-        lats[987] = 20.562389748382977
-        lats[988] = 20.492090980139672
-        lats[989] = 20.421792211894967
-        lats[990] = 20.35149344364887
-        lats[991] = 20.28119467540138
-        lats[992] = 20.210895907152516
-        lats[993] = 20.140597138902272
-        lats[994] = 20.070298370650661
-        lats[995] = 19.999999602397686
-        lats[996] = 19.929700834143357
-        lats[997] = 19.859402065887682
-        lats[998] = 19.789103297630657
-        lats[999] = 19.718804529372303
-        lats[1000] = 19.648505761112613
-        lats[1001] = 19.578206992851602
-        lats[1002] = 19.507908224589269
-        lats[1003] = 19.437609456325632
-        lats[1004] = 19.367310688060684
-        lats[1005] = 19.297011919794439
-        lats[1006] = 19.226713151526898
-        lats[1007] = 19.15641438325807
-        lats[1008] = 19.086115614987968
-        lats[1009] = 19.015816846716586
-        lats[1010] = 18.945518078443939
-        lats[1011] = 18.875219310170031
-        lats[1012] = 18.804920541894862
-        lats[1013] = 18.734621773618446
-        lats[1014] = 18.664323005340787
-        lats[1015] = 18.594024237061891
-        lats[1016] = 18.523725468781763
-        lats[1017] = 18.453426700500408
-        lats[1018] = 18.383127932217832
-        lats[1019] = 18.312829163934047
-        lats[1020] = 18.242530395649048
-        lats[1021] = 18.172231627362851
-        lats[1022] = 18.101932859075458
-        lats[1023] = 18.031634090786874
-        lats[1024] = 17.96133532249711
-        lats[1025] = 17.89103655420616
-        lats[1026] = 17.820737785914044
-        lats[1027] = 17.75043901762076
-        lats[1028] = 17.680140249326314
-        lats[1029] = 17.60984148103071
-        lats[1030] = 17.539542712733962
-        lats[1031] = 17.469243944436066
-        lats[1032] = 17.39894517613704
-        lats[1033] = 17.328646407836878
-        lats[1034] = 17.258347639535586
-        lats[1035] = 17.188048871233182
-        lats[1036] = 17.117750102929655
-        lats[1037] = 17.04745133462502
-        lats[1038] = 16.977152566319283
-        lats[1039] = 16.906853798012452
-        lats[1040] = 16.836555029704527
-        lats[1041] = 16.766256261395515
-        lats[1042] = 16.69595749308542
-        lats[1043] = 16.625658724774254
-        lats[1044] = 16.555359956462013
-        lats[1045] = 16.485061188148713
-        lats[1046] = 16.41476241983435
-        lats[1047] = 16.344463651518936
-        lats[1048] = 16.274164883202477
-        lats[1049] = 16.203866114884974
-        lats[1050] = 16.133567346566434
-        lats[1051] = 16.063268578246863
-        lats[1052] = 15.992969809926265
-        lats[1053] = 15.922671041604652
-        lats[1054] = 15.852372273282016
-        lats[1055] = 15.78207350495838
-        lats[1056] = 15.711774736633735
-        lats[1057] = 15.641475968308091
-        lats[1058] = 15.571177199981456
-        lats[1059] = 15.500878431653829
-        lats[1060] = 15.430579663325226
-        lats[1061] = 15.360280894995643
-        lats[1062] = 15.289982126665089
-        lats[1063] = 15.219683358333569
-        lats[1064] = 15.149384590001089
-        lats[1065] = 15.07908582166765
-        lats[1066] = 15.008787053333259
-        lats[1067] = 14.938488284997929
-        lats[1068] = 14.868189516661655
-        lats[1069] = 14.797890748324447
-        lats[1070] = 14.727591979986309
-        lats[1071] = 14.657293211647247
-        lats[1072] = 14.586994443307265
-        lats[1073] = 14.516695674966371
-        lats[1074] = 14.446396906624567
-        lats[1075] = 14.376098138281863
-        lats[1076] = 14.305799369938256
-        lats[1077] = 14.23550060159376
-        lats[1078] = 14.165201833248371
-        lats[1079] = 14.0949030649021
-        lats[1080] = 14.024604296554955
-        lats[1081] = 13.954305528206934
-        lats[1082] = 13.884006759858046
-        lats[1083] = 13.813707991508297
-        lats[1084] = 13.743409223157688
-        lats[1085] = 13.673110454806226
-        lats[1086] = 13.602811686453919
-        lats[1087] = 13.532512918100766
-        lats[1088] = 13.46221414974678
-        lats[1089] = 13.391915381391959
-        lats[1090] = 13.32161661303631
-        lats[1091] = 13.251317844679837
-        lats[1092] = 13.181019076322551
-        lats[1093] = 13.110720307964451
-        lats[1094] = 13.040421539605545
-        lats[1095] = 12.970122771245832
-        lats[1096] = 12.899824002885323
-        lats[1097] = 12.829525234524022
-        lats[1098] = 12.759226466161934
-        lats[1099] = 12.688927697799061
-        lats[1100] = 12.618628929435411
-        lats[1101] = 12.548330161070988
-        lats[1102] = 12.478031392705796
-        lats[1103] = 12.407732624339841
-        lats[1104] = 12.337433855973126
-        lats[1105] = 12.267135087605659
-        lats[1106] = 12.196836319237443
-        lats[1107] = 12.126537550868482
-        lats[1108] = 12.056238782498781
-        lats[1109] = 11.985940014128348
-        lats[1110] = 11.915641245757183
-        lats[1111] = 11.845342477385294
-        lats[1112] = 11.775043709012685
-        lats[1113] = 11.704744940639358
-        lats[1114] = 11.634446172265324
-        lats[1115] = 11.564147403890583
-        lats[1116] = 11.493848635515141
-        lats[1117] = 11.423549867139002
-        lats[1118] = 11.35325109876217
-        lats[1119] = 11.282952330384653
-        lats[1120] = 11.212653562006453
-        lats[1121] = 11.142354793627575
-        lats[1122] = 11.072056025248026
-        lats[1123] = 11.001757256867807
-        lats[1124] = 10.931458488486923
-        lats[1125] = 10.861159720105382
-        lats[1126] = 10.790860951723188
-        lats[1127] = 10.720562183340341
-        lats[1128] = 10.65026341495685
-        lats[1129] = 10.579964646572719
-        lats[1130] = 10.509665878187954
-        lats[1131] = 10.439367109802557
-        lats[1132] = 10.369068341416533
-        lats[1133] = 10.298769573029887
-        lats[1134] = 10.228470804642624
-        lats[1135] = 10.158172036254747
-        lats[1136] = 10.087873267866264
-        lats[1137] = 10.017574499477174
-        lats[1138] = 9.9472757310874869
-        lats[1139] = 9.8769769626972046
-        lats[1140] = 9.8066781943063344
-        lats[1141] = 9.7363794259148779
-        lats[1142] = 9.6660806575228388
-        lats[1143] = 9.5957818891302242
-        lats[1144] = 9.5254831207370376
-        lats[1145] = 9.4551843523432826
-        lats[1146] = 9.3848855839489662
-        lats[1147] = 9.3145868155540921
-        lats[1148] = 9.2442880471586619
-        lats[1149] = 9.1739892787626829
-        lats[1150] = 9.1036905103661585
-        lats[1151] = 9.0333917419690941
-        lats[1152] = 8.963092973571495
-        lats[1153] = 8.8927942051733631
-        lats[1154] = 8.8224954367747017
-        lats[1155] = 8.7521966683755217
-        lats[1156] = 8.6818978999758194
-        lats[1157] = 8.6115991315756055
-        lats[1158] = 8.5413003631748801
-        lats[1159] = 8.4710015947736537
-        lats[1160] = 8.4007028263719228
-        lats[1161] = 8.3304040579696963
-        lats[1162] = 8.2601052895669778
-        lats[1163] = 8.1898065211637725
-        lats[1164] = 8.1195077527600841
-        lats[1165] = 8.049208984355916
-        lats[1166] = 7.9789102159512737
-        lats[1167] = 7.9086114475461606
-        lats[1168] = 7.8383126791405831
-        lats[1169] = 7.7680139107345463
-        lats[1170] = 7.6977151423280494
-        lats[1171] = 7.6274163739210996
-        lats[1172] = 7.557117605513703
-        lats[1173] = 7.4868188371058624
-        lats[1174] = 7.4165200686975803
-        lats[1175] = 7.3462213002888648
-        lats[1176] = 7.2759225318797176
-        lats[1177] = 7.2056237634701441
-        lats[1178] = 7.1353249950601469
-        lats[1179] = 7.0650262266497315
-        lats[1180] = 6.994727458238903
-        lats[1181] = 6.924428689827665
-        lats[1182] = 6.8541299214160212
-        lats[1183] = 6.7838311530039768
-        lats[1184] = 6.7135323845915353
-        lats[1185] = 6.6432336161787013
-        lats[1186] = 6.5729348477654792
-        lats[1187] = 6.5026360793518734
-        lats[1188] = 6.4323373109378874
-        lats[1189] = 6.3620385425235257
-        lats[1190] = 6.2917397741087928
-        lats[1191] = 6.2214410056936931
-        lats[1192] = 6.151142237278231
-        lats[1193] = 6.0808434688624091
-        lats[1194] = 6.0105447004462347
-        lats[1195] = 5.9402459320297085
-        lats[1196] = 5.869947163612836
-        lats[1197] = 5.7996483951956233
-        lats[1198] = 5.729349626778073
-        lats[1199] = 5.6590508583601888
-        lats[1200] = 5.5887520899419751
-        lats[1201] = 5.5184533215234373
-        lats[1202] = 5.4481545531045787
-        lats[1203] = 5.3778557846854023
-        lats[1204] = 5.3075570162659149
-        lats[1205] = 5.2372582478461194
-        lats[1206] = 5.1669594794260192
-        lats[1207] = 5.0966607110056197
-        lats[1208] = 5.0263619425849244
-        lats[1209] = 4.9560631741639369
-        lats[1210] = 4.8857644057426626
-        lats[1211] = 4.8154656373211049
-        lats[1212] = 4.7451668688992683
-        lats[1213] = 4.6748681004771564
-        lats[1214] = 4.6045693320547736
-        lats[1215] = 4.5342705636321252
-        lats[1216] = 4.4639717952092139
-        lats[1217] = 4.3936730267860451
-        lats[1218] = 4.3233742583626205
-        lats[1219] = 4.2530754899389471
-        lats[1220] = 4.1827767215150269
-        lats[1221] = 4.1124779530908659
-        lats[1222] = 4.0421791846664661
-        lats[1223] = 3.9718804162418326
-        lats[1224] = 3.90158164781697
-        lats[1225] = 3.8312828793918823
-        lats[1226] = 3.7609841109665734
-        lats[1227] = 3.6906853425410477
-        lats[1228] = 3.6203865741153085
-        lats[1229] = 3.5500878056893601
-        lats[1230] = 3.4797890372632065
-        lats[1231] = 3.4094902688368531
-        lats[1232] = 3.339191500410303
-        lats[1233] = 3.2688927319835597
-        lats[1234] = 3.1985939635566285
-        lats[1235] = 3.1282951951295126
-        lats[1236] = 3.0579964267022164
-        lats[1237] = 2.9876976582747439
-        lats[1238] = 2.9173988898470999
-        lats[1239] = 2.8471001214192873
-        lats[1240] = 2.7768013529913107
-        lats[1241] = 2.7065025845631743
-        lats[1242] = 2.6362038161348824
-        lats[1243] = 2.5659050477064382
-        lats[1244] = 2.4956062792778466
-        lats[1245] = 2.4253075108491116
-        lats[1246] = 2.3550087424202366
-        lats[1247] = 2.2847099739912267
-        lats[1248] = 2.2144112055620848
-        lats[1249] = 2.1441124371328155
-        lats[1250] = 2.0738136687034232
-        lats[1251] = 2.0035149002739114
-        lats[1252] = 1.9332161318442849
-        lats[1253] = 1.8629173634145471
-        lats[1254] = 1.792618594984702
-        lats[1255] = 1.7223198265547539
-        lats[1256] = 1.6520210581247066
-        lats[1257] = 1.5817222896945646
-        lats[1258] = 1.5114235212643317
-        lats[1259] = 1.4411247528340119
-        lats[1260] = 1.3708259844036093
-        lats[1261] = 1.300527215973128
-        lats[1262] = 1.2302284475425722
-        lats[1263] = 1.1599296791119456
-        lats[1264] = 1.0896309106812523
-        lats[1265] = 1.0193321422504964
-        lats[1266] = 0.949033373819682
-        lats[1267] = 0.87873460538881287
-        lats[1268] = 0.80843583695789356
-        lats[1269] = 0.73813706852692773
-        lats[1270] = 0.66783830009591949
-        lats[1271] = 0.59753953166487306
-        lats[1272] = 0.52724076323379232
-        lats[1273] = 0.45694199480268116
-        lats[1274] = 0.3866432263715438
-        lats[1275] = 0.31634445794038429
-        lats[1276] = 0.24604568950920663
-        lats[1277] = 0.17574692107801482
-        lats[1278] = 0.10544815264681295
-        lats[1279] = 0.035149384215604956
-        lats[1280] = -0.035149384215604956
-        lats[1281] = -0.10544815264681295
-        lats[1282] = -0.17574692107801482
-        lats[1283] = -0.24604568950920663
-        lats[1284] = -0.31634445794038429
-        lats[1285] = -0.3866432263715438
-        lats[1286] = -0.45694199480268116
-        lats[1287] = -0.52724076323379232
-        lats[1288] = -0.59753953166487306
-        lats[1289] = -0.66783830009591949
-        lats[1290] = -0.73813706852692773
-        lats[1291] = -0.80843583695789356
-        lats[1292] = -0.87873460538881287
-        lats[1293] = -0.949033373819682
-        lats[1294] = -1.0193321422504964
-        lats[1295] = -1.0896309106812523
-        lats[1296] = -1.1599296791119456
-        lats[1297] = -1.2302284475425722
-        lats[1298] = -1.300527215973128
-        lats[1299] = -1.3708259844036093
-        lats[1300] = -1.4411247528340119
-        lats[1301] = -1.5114235212643317
-        lats[1302] = -1.5817222896945646
-        lats[1303] = -1.6520210581247066
-        lats[1304] = -1.7223198265547539
-        lats[1305] = -1.792618594984702
-        lats[1306] = -1.8629173634145471
-        lats[1307] = -1.9332161318442849
-        lats[1308] = -2.0035149002739114
-        lats[1309] = -2.0738136687034232
-        lats[1310] = -2.1441124371328155
-        lats[1311] = -2.2144112055620848
-        lats[1312] = -2.2847099739912267
-        lats[1313] = -2.3550087424202366
-        lats[1314] = -2.4253075108491116
-        lats[1315] = -2.4956062792778466
-        lats[1316] = -2.5659050477064382
-        lats[1317] = -2.6362038161348824
-        lats[1318] = -2.7065025845631743
-        lats[1319] = -2.7768013529913107
-        lats[1320] = -2.8471001214192873
-        lats[1321] = -2.9173988898470999
-        lats[1322] = -2.9876976582747439
-        lats[1323] = -3.0579964267022164
-        lats[1324] = -3.1282951951295126
-        lats[1325] = -3.1985939635566285
-        lats[1326] = -3.2688927319835597
-        lats[1327] = -3.339191500410303
-        lats[1328] = -3.4094902688368531
-        lats[1329] = -3.4797890372632065
-        lats[1330] = -3.5500878056893601
-        lats[1331] = -3.6203865741153085
-        lats[1332] = -3.6906853425410477
-        lats[1333] = -3.7609841109665734
-        lats[1334] = -3.8312828793918823
-        lats[1335] = -3.90158164781697
-        lats[1336] = -3.9718804162418326
-        lats[1337] = -4.0421791846664661
-        lats[1338] = -4.1124779530908659
-        lats[1339] = -4.1827767215150269
-        lats[1340] = -4.2530754899389471
-        lats[1341] = -4.3233742583626205
-        lats[1342] = -4.3936730267860451
-        lats[1343] = -4.4639717952092139
-        lats[1344] = -4.5342705636321252
-        lats[1345] = -4.6045693320547736
-        lats[1346] = -4.6748681004771564
-        lats[1347] = -4.7451668688992683
-        lats[1348] = -4.8154656373211049
-        lats[1349] = -4.8857644057426626
-        lats[1350] = -4.9560631741639369
-        lats[1351] = -5.0263619425849244
-        lats[1352] = -5.0966607110056197
-        lats[1353] = -5.1669594794260192
-        lats[1354] = -5.2372582478461194
-        lats[1355] = -5.3075570162659149
-        lats[1356] = -5.3778557846854023
-        lats[1357] = -5.4481545531045787
-        lats[1358] = -5.5184533215234373
-        lats[1359] = -5.5887520899419751
-        lats[1360] = -5.6590508583601888
-        lats[1361] = -5.729349626778073
-        lats[1362] = -5.7996483951956233
-        lats[1363] = -5.869947163612836
-        lats[1364] = -5.9402459320297085
-        lats[1365] = -6.0105447004462347
-        lats[1366] = -6.0808434688624091
-        lats[1367] = -6.151142237278231
-        lats[1368] = -6.2214410056936931
-        lats[1369] = -6.2917397741087928
-        lats[1370] = -6.3620385425235257
-        lats[1371] = -6.4323373109378874
-        lats[1372] = -6.5026360793518734
-        lats[1373] = -6.5729348477654792
-        lats[1374] = -6.6432336161787013
-        lats[1375] = -6.7135323845915353
-        lats[1376] = -6.7838311530039768
-        lats[1377] = -6.8541299214160212
-        lats[1378] = -6.924428689827665
-        lats[1379] = -6.994727458238903
-        lats[1380] = -7.0650262266497315
-        lats[1381] = -7.1353249950601469
-        lats[1382] = -7.2056237634701441
-        lats[1383] = -7.2759225318797176
-        lats[1384] = -7.3462213002888648
-        lats[1385] = -7.4165200686975803
-        lats[1386] = -7.4868188371058624
-        lats[1387] = -7.557117605513703
-        lats[1388] = -7.6274163739210996
-        lats[1389] = -7.6977151423280494
-        lats[1390] = -7.7680139107345463
-        lats[1391] = -7.8383126791405831
-        lats[1392] = -7.9086114475461606
-        lats[1393] = -7.9789102159512737
-        lats[1394] = -8.049208984355916
-        lats[1395] = -8.1195077527600841
-        lats[1396] = -8.1898065211637725
-        lats[1397] = -8.2601052895669778
-        lats[1398] = -8.3304040579696963
-        lats[1399] = -8.4007028263719228
-        lats[1400] = -8.4710015947736537
-        lats[1401] = -8.5413003631748801
-        lats[1402] = -8.6115991315756055
-        lats[1403] = -8.6818978999758194
-        lats[1404] = -8.7521966683755217
-        lats[1405] = -8.8224954367747017
-        lats[1406] = -8.8927942051733631
-        lats[1407] = -8.963092973571495
-        lats[1408] = -9.0333917419690941
-        lats[1409] = -9.1036905103661585
-        lats[1410] = -9.1739892787626829
-        lats[1411] = -9.2442880471586619
-        lats[1412] = -9.3145868155540921
-        lats[1413] = -9.3848855839489662
-        lats[1414] = -9.4551843523432826
-        lats[1415] = -9.5254831207370376
-        lats[1416] = -9.5957818891302242
-        lats[1417] = -9.6660806575228388
-        lats[1418] = -9.7363794259148779
-        lats[1419] = -9.8066781943063344
-        lats[1420] = -9.8769769626972046
-        lats[1421] = -9.9472757310874869
-        lats[1422] = -10.017574499477174
-        lats[1423] = -10.087873267866264
-        lats[1424] = -10.158172036254747
-        lats[1425] = -10.228470804642624
-        lats[1426] = -10.298769573029887
-        lats[1427] = -10.369068341416533
-        lats[1428] = -10.439367109802557
-        lats[1429] = -10.509665878187954
-        lats[1430] = -10.579964646572719
-        lats[1431] = -10.65026341495685
-        lats[1432] = -10.720562183340341
-        lats[1433] = -10.790860951723188
-        lats[1434] = -10.861159720105382
-        lats[1435] = -10.931458488486923
-        lats[1436] = -11.001757256867807
-        lats[1437] = -11.072056025248026
-        lats[1438] = -11.142354793627575
-        lats[1439] = -11.212653562006453
-        lats[1440] = -11.282952330384653
-        lats[1441] = -11.35325109876217
-        lats[1442] = -11.423549867139002
-        lats[1443] = -11.493848635515141
-        lats[1444] = -11.564147403890583
-        lats[1445] = -11.634446172265324
-        lats[1446] = -11.704744940639358
-        lats[1447] = -11.775043709012685
-        lats[1448] = -11.845342477385294
-        lats[1449] = -11.915641245757183
-        lats[1450] = -11.985940014128348
-        lats[1451] = -12.056238782498781
-        lats[1452] = -12.126537550868482
-        lats[1453] = -12.196836319237443
-        lats[1454] = -12.267135087605659
-        lats[1455] = -12.337433855973126
-        lats[1456] = -12.407732624339841
-        lats[1457] = -12.478031392705796
-        lats[1458] = -12.548330161070988
-        lats[1459] = -12.618628929435411
-        lats[1460] = -12.688927697799061
-        lats[1461] = -12.759226466161934
-        lats[1462] = -12.829525234524022
-        lats[1463] = -12.899824002885323
-        lats[1464] = -12.970122771245832
-        lats[1465] = -13.040421539605545
-        lats[1466] = -13.110720307964451
-        lats[1467] = -13.181019076322551
-        lats[1468] = -13.251317844679837
-        lats[1469] = -13.32161661303631
-        lats[1470] = -13.391915381391959
-        lats[1471] = -13.46221414974678
-        lats[1472] = -13.532512918100766
-        lats[1473] = -13.602811686453919
-        lats[1474] = -13.673110454806226
-        lats[1475] = -13.743409223157688
-        lats[1476] = -13.813707991508297
-        lats[1477] = -13.884006759858046
-        lats[1478] = -13.954305528206934
-        lats[1479] = -14.024604296554955
-        lats[1480] = -14.0949030649021
-        lats[1481] = -14.165201833248371
-        lats[1482] = -14.23550060159376
-        lats[1483] = -14.305799369938256
-        lats[1484] = -14.376098138281863
-        lats[1485] = -14.446396906624567
-        lats[1486] = -14.516695674966371
-        lats[1487] = -14.586994443307265
-        lats[1488] = -14.657293211647247
-        lats[1489] = -14.727591979986309
-        lats[1490] = -14.797890748324447
-        lats[1491] = -14.868189516661655
-        lats[1492] = -14.938488284997929
-        lats[1493] = -15.008787053333259
-        lats[1494] = -15.07908582166765
-        lats[1495] = -15.149384590001089
-        lats[1496] = -15.219683358333569
-        lats[1497] = -15.289982126665089
-        lats[1498] = -15.360280894995643
-        lats[1499] = -15.430579663325226
-        lats[1500] = -15.500878431653829
-        lats[1501] = -15.571177199981456
-        lats[1502] = -15.641475968308091
-        lats[1503] = -15.711774736633735
-        lats[1504] = -15.78207350495838
-        lats[1505] = -15.852372273282016
-        lats[1506] = -15.922671041604652
-        lats[1507] = -15.992969809926265
-        lats[1508] = -16.063268578246863
-        lats[1509] = -16.133567346566434
-        lats[1510] = -16.203866114884974
-        lats[1511] = -16.274164883202477
-        lats[1512] = -16.344463651518936
-        lats[1513] = -16.41476241983435
-        lats[1514] = -16.485061188148713
-        lats[1515] = -16.555359956462013
-        lats[1516] = -16.625658724774254
-        lats[1517] = -16.69595749308542
-        lats[1518] = -16.766256261395515
-        lats[1519] = -16.836555029704527
-        lats[1520] = -16.906853798012452
-        lats[1521] = -16.977152566319283
-        lats[1522] = -17.04745133462502
-        lats[1523] = -17.117750102929655
-        lats[1524] = -17.188048871233182
-        lats[1525] = -17.258347639535586
-        lats[1526] = -17.328646407836878
-        lats[1527] = -17.39894517613704
-        lats[1528] = -17.469243944436066
-        lats[1529] = -17.539542712733962
-        lats[1530] = -17.60984148103071
-        lats[1531] = -17.680140249326314
-        lats[1532] = -17.75043901762076
-        lats[1533] = -17.820737785914044
-        lats[1534] = -17.89103655420616
-        lats[1535] = -17.96133532249711
-        lats[1536] = -18.031634090786874
-        lats[1537] = -18.101932859075458
-        lats[1538] = -18.172231627362851
-        lats[1539] = -18.242530395649048
-        lats[1540] = -18.312829163934047
-        lats[1541] = -18.383127932217832
-        lats[1542] = -18.453426700500408
-        lats[1543] = -18.523725468781763
-        lats[1544] = -18.594024237061891
-        lats[1545] = -18.664323005340787
-        lats[1546] = -18.734621773618446
-        lats[1547] = -18.804920541894862
-        lats[1548] = -18.875219310170031
-        lats[1549] = -18.945518078443939
-        lats[1550] = -19.015816846716586
-        lats[1551] = -19.086115614987968
-        lats[1552] = -19.15641438325807
-        lats[1553] = -19.226713151526898
-        lats[1554] = -19.297011919794439
-        lats[1555] = -19.367310688060684
-        lats[1556] = -19.437609456325632
-        lats[1557] = -19.507908224589269
-        lats[1558] = -19.578206992851602
-        lats[1559] = -19.648505761112613
-        lats[1560] = -19.718804529372303
-        lats[1561] = -19.789103297630657
-        lats[1562] = -19.859402065887682
-        lats[1563] = -19.929700834143357
-        lats[1564] = -19.999999602397686
-        lats[1565] = -20.070298370650661
-        lats[1566] = -20.140597138902272
-        lats[1567] = -20.210895907152516
-        lats[1568] = -20.28119467540138
-        lats[1569] = -20.35149344364887
-        lats[1570] = -20.421792211894967
-        lats[1571] = -20.492090980139672
-        lats[1572] = -20.562389748382977
-        lats[1573] = -20.632688516624874
-        lats[1574] = -20.702987284865355
-        lats[1575] = -20.773286053104417
-        lats[1576] = -20.843584821342048
-        lats[1577] = -20.913883589578251
-        lats[1578] = -20.984182357813012
-        lats[1579] = -21.054481126046323
-        lats[1580] = -21.124779894278181
-        lats[1581] = -21.195078662508585
-        lats[1582] = -21.265377430737512
-        lats[1583] = -21.335676198964972
-        lats[1584] = -21.40597496719095
-        lats[1585] = -21.47627373541544
-        lats[1586] = -21.546572503638437
-        lats[1587] = -21.616871271859928
-        lats[1588] = -21.687170040079913
-        lats[1589] = -21.757468808298391
-        lats[1590] = -21.827767576515338
-        lats[1591] = -21.898066344730758
-        lats[1592] = -21.968365112944642
-        lats[1593] = -22.038663881156989
-        lats[1594] = -22.108962649367779
-        lats[1595] = -22.179261417577013
-        lats[1596] = -22.249560185784691
-        lats[1597] = -22.319858953990789
-        lats[1598] = -22.390157722195315
-        lats[1599] = -22.460456490398254
-        lats[1600] = -22.530755258599601
-        lats[1601] = -22.60105402679935
-        lats[1602] = -22.671352794997489
-        lats[1603] = -22.741651563194019
-        lats[1604] = -22.811950331388925
-        lats[1605] = -22.882249099582204
-        lats[1606] = -22.952547867773848
-        lats[1607] = -23.022846635963852
-        lats[1608] = -23.0931454041522
-        lats[1609] = -23.163444172338895
-        lats[1610] = -23.233742940523921
-        lats[1611] = -23.304041708707278
-        lats[1612] = -23.374340476888957
-        lats[1613] = -23.444639245068949
-        lats[1614] = -23.514938013247242
-        lats[1615] = -23.585236781423838
-        lats[1616] = -23.655535549598721
-        lats[1617] = -23.725834317771888
-        lats[1618] = -23.796133085943328
-        lats[1619] = -23.866431854113038
-        lats[1620] = -23.936730622281004
-        lats[1621] = -24.007029390447226
-        lats[1622] = -24.077328158611696
-        lats[1623] = -24.1476269267744
-        lats[1624] = -24.217925694935328
-        lats[1625] = -24.288224463094483
-        lats[1626] = -24.358523231251851
-        lats[1627] = -24.428821999407425
-        lats[1628] = -24.499120767561195
-        lats[1629] = -24.569419535713152
-        lats[1630] = -24.639718303863294
-        lats[1631] = -24.710017072011613
-        lats[1632] = -24.780315840158096
-        lats[1633] = -24.850614608302738
-        lats[1634] = -24.920913376445526
-        lats[1635] = -24.991212144586456
-        lats[1636] = -25.061510912725527
-        lats[1637] = -25.13180968086272
-        lats[1638] = -25.202108448998025
-        lats[1639] = -25.272407217131445
-        lats[1640] = -25.342705985262967
-        lats[1641] = -25.413004753392578
-        lats[1642] = -25.483303521520277
-        lats[1643] = -25.553602289646051
-        lats[1644] = -25.623901057769892
-        lats[1645] = -25.694199825891793
-        lats[1646] = -25.764498594011751
-        lats[1647] = -25.834797362129745
-        lats[1648] = -25.90509613024577
-        lats[1649] = -25.975394898359827
-        lats[1650] = -26.045693666471902
-        lats[1651] = -26.115992434581983
-        lats[1652] = -26.186291202690064
-        lats[1653] = -26.256589970796135
-        lats[1654] = -26.326888738900195
-        lats[1655] = -26.397187507002222
-        lats[1656] = -26.467486275102218
-        lats[1657] = -26.53778504320017
-        lats[1658] = -26.608083811296069
-        lats[1659] = -26.678382579389908
-        lats[1660] = -26.748681347481678
-        lats[1661] = -26.818980115571364
-        lats[1662] = -26.889278883658971
-        lats[1663] = -26.959577651744471
-        lats[1664] = -27.029876419827872
-        lats[1665] = -27.100175187909159
-        lats[1666] = -27.170473955988321
-        lats[1667] = -27.240772724065348
-        lats[1668] = -27.311071492140236
-        lats[1669] = -27.381370260212968
-        lats[1670] = -27.451669028283543
-        lats[1671] = -27.521967796351948
-        lats[1672] = -27.592266564418171
-        lats[1673] = -27.662565332482213
-        lats[1674] = -27.732864100544052
-        lats[1675] = -27.803162868603682
-        lats[1676] = -27.873461636661098
-        lats[1677] = -27.94376040471629
-        lats[1678] = -28.014059172769244
-        lats[1679] = -28.084357940819952
-        lats[1680] = -28.154656708868405
-        lats[1681] = -28.224955476914594
-        lats[1682] = -28.29525424495851
-        lats[1683] = -28.365553013000145
-        lats[1684] = -28.435851781039485
-        lats[1685] = -28.506150549076519
-        lats[1686] = -28.576449317111244
-        lats[1687] = -28.646748085143642
-        lats[1688] = -28.717046853173709
-        lats[1689] = -28.787345621201432
-        lats[1690] = -28.857644389226806
-        lats[1691] = -28.927943157249814
-        lats[1692] = -28.998241925270449
-        lats[1693] = -29.068540693288696
-        lats[1694] = -29.138839461304556
-        lats[1695] = -29.209138229318015
-        lats[1696] = -29.279436997329057
-        lats[1697] = -29.349735765337677
-        lats[1698] = -29.420034533343859
-        lats[1699] = -29.490333301347597
-        lats[1700] = -29.560632069348884
-        lats[1701] = -29.630930837347698
-        lats[1702] = -29.701229605344039
-        lats[1703] = -29.771528373337894
-        lats[1704] = -29.841827141329258
-        lats[1705] = -29.91212590931811
-        lats[1706] = -29.98242467730444
-        lats[1707] = -30.052723445288244
-        lats[1708] = -30.123022213269511
-        lats[1709] = -30.19332098124822
-        lats[1710] = -30.263619749224372
-        lats[1711] = -30.333918517197947
-        lats[1712] = -30.404217285168947
-        lats[1713] = -30.47451605313735
-        lats[1714] = -30.544814821103138
-        lats[1715] = -30.615113589066322
-        lats[1716] = -30.685412357026873
-        lats[1717] = -30.755711124984781
-        lats[1718] = -30.826009892940046
-        lats[1719] = -30.896308660892647
-        lats[1720] = -30.966607428842572
-        lats[1721] = -31.036906196789811
-        lats[1722] = -31.107204964734358
-        lats[1723] = -31.177503732676204
-        lats[1724] = -31.247802500615318
-        lats[1725] = -31.318101268551715
-        lats[1726] = -31.388400036485361
-        lats[1727] = -31.458698804416255
-        lats[1728] = -31.528997572344384
-        lats[1729] = -31.599296340269738
-        lats[1730] = -31.669595108192297
-        lats[1731] = -31.739893876112063
-        lats[1732] = -31.810192644029012
-        lats[1733] = -31.880491411943137
-        lats[1734] = -31.950790179854422
-        lats[1735] = -32.021088947762863
-        lats[1736] = -32.091387715668439
-        lats[1737] = -32.161686483571145
-        lats[1738] = -32.231985251470959
-        lats[1739] = -32.302284019367875
-        lats[1740] = -32.372582787261891
-        lats[1741] = -32.442881555152965
-        lats[1742] = -32.513180323041112
-        lats[1743] = -32.583479090926325
-        lats[1744] = -32.653777858808567
-        lats[1745] = -32.724076626687825
-        lats[1746] = -32.794375394564113
-        lats[1747] = -32.864674162437396
-        lats[1748] = -32.934972930307666
-        lats[1749] = -33.005271698174909
-        lats[1750] = -33.075570466039117
-        lats[1751] = -33.145869233900278
-        lats[1752] = -33.216168001758369
-        lats[1753] = -33.286466769613391
-        lats[1754] = -33.356765537465314
-        lats[1755] = -33.42706430531414
-        lats[1756] = -33.497363073159853
-        lats[1757] = -33.567661841002426
-        lats[1758] = -33.637960608841851
-        lats[1759] = -33.708259376678136
-        lats[1760] = -33.778558144511237
-        lats[1761] = -33.848856912341155
-        lats[1762] = -33.919155680167876
-        lats[1763] = -33.989454447991392
-        lats[1764] = -34.059753215811682
-        lats[1765] = -34.130051983628725
-        lats[1766] = -34.200350751442521
-        lats[1767] = -34.270649519253041
-        lats[1768] = -34.340948287060286
-        lats[1769] = -34.411247054864234
-        lats[1770] = -34.481545822664863
-        lats[1771] = -34.551844590462188
-        lats[1772] = -34.622143358256153
-        lats[1773] = -34.692442126046771
-        lats[1774] = -34.762740893834028
-        lats[1775] = -34.833039661617903
-        lats[1776] = -34.903338429398374
-        lats[1777] = -34.973637197175435
-        lats[1778] = -35.043935964949064
-        lats[1779] = -35.114234732719261
-        lats[1780] = -35.184533500486005
-        lats[1781] = -35.254832268249267
-        lats[1782] = -35.325131036009047
-        lats[1783] = -35.395429803765317
-        lats[1784] = -35.465728571518085
-        lats[1785] = -35.536027339267314
-        lats[1786] = -35.606326107012997
-        lats[1787] = -35.676624874755113
-        lats[1788] = -35.746923642493655
-        lats[1789] = -35.817222410228595
-        lats[1790] = -35.887521177959933
-        lats[1791] = -35.957819945687639
-        lats[1792] = -36.028118713411708
-        lats[1793] = -36.098417481132117
-        lats[1794] = -36.16871624884886
-        lats[1795] = -36.239015016561908
-        lats[1796] = -36.309313784271254
-        lats[1797] = -36.379612551976876
-        lats[1798] = -36.449911319678755
-        lats[1799] = -36.520210087376888
-        lats[1800] = -36.590508855071242
-        lats[1801] = -36.660807622761808
-        lats[1802] = -36.731106390448581
-        lats[1803] = -36.801405158131523
-        lats[1804] = -36.871703925810628
-        lats[1805] = -36.942002693485883
-        lats[1806] = -37.012301461157264
-        lats[1807] = -37.082600228824752
-        lats[1808] = -37.152898996488332
-        lats[1809] = -37.223197764147997
-        lats[1810] = -37.293496531803719
-        lats[1811] = -37.363795299455489
-        lats[1812] = -37.434094067103274
-        lats[1813] = -37.504392834747065
-        lats[1814] = -37.574691602386856
-        lats[1815] = -37.644990370022605
-        lats[1816] = -37.715289137654317
-        lats[1817] = -37.785587905281965
-        lats[1818] = -37.855886672905527
-        lats[1819] = -37.926185440524989
-        lats[1820] = -37.99648420814033
-        lats[1821] = -38.066782975751536
-        lats[1822] = -38.137081743358586
-        lats[1823] = -38.20738051096145
-        lats[1824] = -38.277679278560143
-        lats[1825] = -38.347978046154608
-        lats[1826] = -38.418276813744846
-        lats[1827] = -38.488575581330842
-        lats[1828] = -38.558874348912568
-        lats[1829] = -38.629173116490001
-        lats[1830] = -38.699471884063136
-        lats[1831] = -38.769770651631937
-        lats[1832] = -38.840069419196389
-        lats[1833] = -38.910368186756479
-        lats[1834] = -38.980666954312184
-        lats[1835] = -39.050965721863491
-        lats[1836] = -39.121264489410365
-        lats[1837] = -39.191563256952804
-        lats[1838] = -39.261862024490775
-        lats[1839] = -39.332160792024254
-        lats[1840] = -39.402459559553229
-        lats[1841] = -39.472758327077692
-        lats[1842] = -39.543057094597607
-        lats[1843] = -39.613355862112947
-        lats[1844] = -39.683654629623703
-        lats[1845] = -39.753953397129855
-        lats[1846] = -39.824252164631375
-        lats[1847] = -39.894550932128247
-        lats[1848] = -39.964849699620437
-        lats[1849] = -40.035148467107952
-        lats[1850] = -40.105447234590748
-        lats[1851] = -40.175746002068806
-        lats[1852] = -40.246044769542102
-        lats[1853] = -40.316343537010617
-        lats[1854] = -40.386642304474343
-        lats[1855] = -40.456941071933244
-        lats[1856] = -40.527239839387299
-        lats[1857] = -40.597538606836487
-        lats[1858] = -40.667837374280786
-        lats[1859] = -40.738136141720176
-        lats[1860] = -40.808434909154634
-        lats[1861] = -40.878733676584126
-        lats[1862] = -40.949032444008644
-        lats[1863] = -41.01933121142816
-        lats[1864] = -41.089629978842645
-        lats[1865] = -41.159928746252085
-        lats[1866] = -41.230227513656445
-        lats[1867] = -41.300526281055724
-        lats[1868] = -41.370825048449873
-        lats[1869] = -41.441123815838885
-        lats[1870] = -41.511422583222718
-        lats[1871] = -41.581721350601363
-        lats[1872] = -41.6520201179748
-        lats[1873] = -41.722318885343
-        lats[1874] = -41.792617652705921
-        lats[1875] = -41.862916420063563
-        lats[1876] = -41.933215187415882
-        lats[1877] = -42.003513954762873
-        lats[1878] = -42.073812722104492
-        lats[1879] = -42.144111489440725
-        lats[1880] = -42.214410256771551
-        lats[1881] = -42.284709024096927
-        lats[1882] = -42.355007791416853
-        lats[1883] = -42.425306558731272
-        lats[1884] = -42.495605326040177
-        lats[1885] = -42.565904093343548
-        lats[1886] = -42.63620286064134
-        lats[1887] = -42.706501627933541
-        lats[1888] = -42.776800395220121
-        lats[1889] = -42.847099162501053
-        lats[1890] = -42.917397929776307
-        lats[1891] = -42.987696697045862
-        lats[1892] = -43.057995464309691
-        lats[1893] = -43.128294231567757
-        lats[1894] = -43.19859299882004
-        lats[1895] = -43.26889176606651
-        lats[1896] = -43.339190533307139
-        lats[1897] = -43.409489300541907
-        lats[1898] = -43.479788067770777
-        lats[1899] = -43.550086834993728
-        lats[1900] = -43.620385602210717
-        lats[1901] = -43.690684369421732
-        lats[1902] = -43.760983136626741
-        lats[1903] = -43.831281903825705
-        lats[1904] = -43.9015806710186
-        lats[1905] = -43.971879438205391
-        lats[1906] = -44.042178205386072
-        lats[1907] = -44.112476972560586
-        lats[1908] = -44.182775739728925
-        lats[1909] = -44.253074506891046
-        lats[1910] = -44.323373274046915
-        lats[1911] = -44.39367204119651
-        lats[1912] = -44.463970808339802
-        lats[1913] = -44.534269575476756
-        lats[1914] = -44.604568342607337
-        lats[1915] = -44.674867109731515
-        lats[1916] = -44.745165876849271
-        lats[1917] = -44.81546464396056
-        lats[1918] = -44.885763411065362
-        lats[1919] = -44.956062178163634
-        lats[1920] = -45.026360945255341
-        lats[1921] = -45.096659712340461
-        lats[1922] = -45.166958479418959
-        lats[1923] = -45.237257246490813
-        lats[1924] = -45.30755601355596
-        lats[1925] = -45.377854780614399
-        lats[1926] = -45.448153547666081
-        lats[1927] = -45.51845231471097
-        lats[1928] = -45.588751081749038
-        lats[1929] = -45.659049848780263
-        lats[1930] = -45.729348615804589
-        lats[1931] = -45.799647382821995
-        lats[1932] = -45.869946149832437
-        lats[1933] = -45.94024491683588
-        lats[1934] = -46.01054368383231
-        lats[1935] = -46.080842450821663
-        lats[1936] = -46.151141217803925
-        lats[1937] = -46.221439984779053
-        lats[1938] = -46.291738751747012
-        lats[1939] = -46.362037518707766
-        lats[1940] = -46.432336285661272
-        lats[1941] = -46.502635052607502
-        lats[1942] = -46.572933819546414
-        lats[1943] = -46.643232586477971
-        lats[1944] = -46.713531353402139
-        lats[1945] = -46.783830120318882
-        lats[1946] = -46.85412888722815
-        lats[1947] = -46.924427654129929
-        lats[1948] = -46.994726421024154
-        lats[1949] = -47.065025187910805
-        lats[1950] = -47.13532395478984
-        lats[1951] = -47.205622721661214
-        lats[1952] = -47.275921488524894
-        lats[1953] = -47.346220255380835
-        lats[1954] = -47.416519022228997
-        lats[1955] = -47.486817789069342
-        lats[1956] = -47.557116555901828
-        lats[1957] = -47.627415322726435
-        lats[1958] = -47.697714089543084
-        lats[1959] = -47.76801285635176
-        lats[1960] = -47.838311623152421
-        lats[1961] = -47.908610389945018
-        lats[1962] = -47.978909156729507
-        lats[1963] = -48.049207923505868
-        lats[1964] = -48.119506690274015
-        lats[1965] = -48.189805457033941
-        lats[1966] = -48.260104223785596
-        lats[1967] = -48.330402990528938
-        lats[1968] = -48.400701757263917
-        lats[1969] = -48.47100052399049
-        lats[1970] = -48.541299290708608
-        lats[1971] = -48.611598057418242
-        lats[1972] = -48.681896824119335
-        lats[1973] = -48.752195590811837
-        lats[1974] = -48.822494357495721
-        lats[1975] = -48.892793124170929
-        lats[1976] = -48.963091890837418
-        lats[1977] = -49.03339065749514
-        lats[1978] = -49.103689424144044
-        lats[1979] = -49.173988190784094
-        lats[1980] = -49.244286957415234
-        lats[1981] = -49.314585724037435
-        lats[1982] = -49.384884490650613
-        lats[1983] = -49.455183257254745
-        lats[1984] = -49.525482023849783
-        lats[1985] = -49.595780790435676
-        lats[1986] = -49.66607955701236
-        lats[1987] = -49.736378323579807
-        lats[1988] = -49.80667709013796
-        lats[1989] = -49.876975856686762
-        lats[1990] = -49.947274623226157
-        lats[1991] = -50.017573389756123
-        lats[1992] = -50.087872156276575
-        lats[1993] = -50.158170922787484
-        lats[1994] = -50.228469689288779
-        lats[1995] = -50.298768455780426
-        lats[1996] = -50.369067222262359
-        lats[1997] = -50.439365988734544
-        lats[1998] = -50.509664755196901
-        lats[1999] = -50.579963521649397
-        lats[2000] = -50.650262288091959
-        lats[2001] = -50.720561054524559
-        lats[2002] = -50.790859820947119
-        lats[2003] = -50.86115858735959
-        lats[2004] = -50.931457353761914
-        lats[2005] = -51.001756120154049
-        lats[2006] = -51.072054886535909
-        lats[2007] = -51.14235365290746
-        lats[2008] = -51.21265241926865
-        lats[2009] = -51.282951185619417
-        lats[2010] = -51.353249951959683
-        lats[2011] = -51.423548718289396
-        lats[2012] = -51.493847484608516
-        lats[2013] = -51.56414625091697
-        lats[2014] = -51.634445017214695
-        lats[2015] = -51.704743783501634
-        lats[2016] = -51.775042549777737
-        lats[2017] = -51.845341316042933
-        lats[2018] = -51.915640082297152
-        lats[2019] = -51.985938848540336
-        lats[2020] = -52.056237614772435
-        lats[2021] = -52.126536380993372
-        lats[2022] = -52.196835147203096
-        lats[2023] = -52.26713391340153
-        lats[2024] = -52.337432679588609
-        lats[2025] = -52.407731445764284
-        lats[2026] = -52.478030211928477
-        lats[2027] = -52.548328978081123
-        lats[2028] = -52.618627744222159
-        lats[2029] = -52.688926510351514
-        lats[2030] = -52.759225276469131
-        lats[2031] = -52.829524042574917
-        lats[2032] = -52.899822808668837
-        lats[2033] = -52.970121574750792
-        lats[2034] = -53.040420340820731
-        lats[2035] = -53.110719106878584
-        lats[2036] = -53.181017872924265
-        lats[2037] = -53.251316638957725
-        lats[2038] = -53.321615404978871
-        lats[2039] = -53.391914170987633
-        lats[2040] = -53.462212936983953
-        lats[2041] = -53.53251170296776
-        lats[2042] = -53.602810468938962
-        lats[2043] = -53.673109234897495
-        lats[2044] = -53.743408000843282
-        lats[2045] = -53.813706766776235
-        lats[2046] = -53.884005532696307
-        lats[2047] = -53.954304298603383
-        lats[2048] = -54.024603064497434
-        lats[2049] = -54.094901830378333
-        lats[2050] = -54.165200596246031
-        lats[2051] = -54.235499362100448
-        lats[2052] = -54.305798127941479
-        lats[2053] = -54.376096893769081
-        lats[2054] = -54.446395659583146
-        lats[2055] = -54.516694425383605
-        lats[2056] = -54.586993191170357
-        lats[2057] = -54.657291956943347
-        lats[2058] = -54.727590722702473
-        lats[2059] = -54.797889488447652
-        lats[2060] = -54.868188254178797
-        lats[2061] = -54.938487019895831
-        lats[2062] = -55.008785785598668
-        lats[2063] = -55.07908455128721
-        lats[2064] = -55.149383316961377
-        lats[2065] = -55.219682082621084
-        lats[2066] = -55.289980848266232
-        lats[2067] = -55.360279613896743
-        lats[2068] = -55.430578379512511
-        lats[2069] = -55.500877145113449
-        lats[2070] = -55.571175910699488
-        lats[2071] = -55.641474676270505
-        lats[2072] = -55.711773441826416
-        lats[2073] = -55.782072207367136
-        lats[2074] = -55.852370972892551
-        lats[2075] = -55.922669738402583
-        lats[2076] = -55.992968503897131
-        lats[2077] = -56.063267269376091
-        lats[2078] = -56.133566034839362
-        lats[2079] = -56.203864800286865
-        lats[2080] = -56.274163565718467
-        lats[2081] = -56.34446233113411
-        lats[2082] = -56.41476109653366
-        lats[2083] = -56.485059861917016
-        lats[2084] = -56.555358627284086
-        lats[2085] = -56.625657392634771
-        lats[2086] = -56.695956157968951
-        lats[2087] = -56.766254923286517
-        lats[2088] = -56.836553688587379
-        lats[2089] = -56.90685245387143
-        lats[2090] = -56.977151219138541
-        lats[2091] = -57.047449984388614
-        lats[2092] = -57.117748749621541
-        lats[2093] = -57.188047514837208
-        lats[2094] = -57.258346280035504
-        lats[2095] = -57.328645045216312
-        lats[2096] = -57.398943810379521
-        lats[2097] = -57.469242575525016
-        lats[2098] = -57.539541340652676
-        lats[2099] = -57.60984010576238
-        lats[2100] = -57.680138870854037
-        lats[2101] = -57.75043763592749
-        lats[2102] = -57.820736400982646
-        lats[2103] = -57.891035166019364
-        lats[2104] = -57.961333931037537
-        lats[2105] = -58.031632696037022
-        lats[2106] = -58.101931461017728
-        lats[2107] = -58.172230225979497
-        lats[2108] = -58.242528990922203
-        lats[2109] = -58.312827755845746
-        lats[2110] = -58.383126520749968
-        lats[2111] = -58.453425285634758
-        lats[2112] = -58.523724050499972
-        lats[2113] = -58.594022815345468
-        lats[2114] = -58.664321580171141
-        lats[2115] = -58.73462034497684
-        lats[2116] = -58.804919109762423
-        lats[2117] = -58.875217874527763
-        lats[2118] = -58.945516639272725
-        lats[2119] = -59.015815403997145
-        lats[2120] = -59.086114168700909
-        lats[2121] = -59.156412933383855
-        lats[2122] = -59.226711698045854
-        lats[2123] = -59.29701046268675
-        lats[2124] = -59.3673092273064
-        lats[2125] = -59.43760799190467
-        lats[2126] = -59.507906756481383
-        lats[2127] = -59.578205521036402
-        lats[2128] = -59.64850428556958
-        lats[2129] = -59.718803050080759
-        lats[2130] = -59.78910181456979
-        lats[2131] = -59.859400579036503
-        lats[2132] = -59.929699343480763
-        lats[2133] = -59.999998107902378
-        lats[2134] = -60.070296872301235
-        lats[2135] = -60.140595636677112
-        lats[2136] = -60.21089440102989
-        lats[2137] = -60.28119316535939
-        lats[2138] = -60.35149192966545
-        lats[2139] = -60.421790693947884
-        lats[2140] = -60.492089458206543
-        lats[2141] = -60.562388222441243
-        lats[2142] = -60.632686986651805
-        lats[2143] = -60.702985750838074
-        lats[2144] = -60.773284514999872
-        lats[2145] = -60.843583279137007
-        lats[2146] = -60.913882043249295
-        lats[2147] = -60.984180807336578
-        lats[2148] = -61.054479571398652
-        lats[2149] = -61.124778335435344
-        lats[2150] = -61.195077099446451
-        lats[2151] = -61.265375863431785
-        lats[2152] = -61.335674627391185
-        lats[2153] = -61.405973391324409
-        lats[2154] = -61.476272155231321
-        lats[2155] = -61.546570919111666
-        lats[2156] = -61.616869682965287
-        lats[2157] = -61.687168446791986
-        lats[2158] = -61.757467210591535
-        lats[2159] = -61.827765974363729
-        lats[2160] = -61.898064738108381
-        lats[2161] = -61.968363501825259
-        lats[2162] = -62.038662265514176
-        lats[2163] = -62.108961029174914
-        lats[2164] = -62.179259792807258
-        lats[2165] = -62.249558556410982
-        lats[2166] = -62.319857319985871
-        lats[2167] = -62.3901560835317
-        lats[2168] = -62.460454847048261
-        lats[2169] = -62.530753610535321
-        lats[2170] = -62.60105237399263
-        lats[2171] = -62.67135113741999
-        lats[2172] = -62.741649900817137
-        lats[2173] = -62.811948664183866
-        lats[2174] = -62.882247427519928
-        lats[2175] = -62.952546190825068
-        lats[2176] = -63.022844954099064
-        lats[2177] = -63.093143717341647
-        lats[2178] = -63.163442480552604
-        lats[2179] = -63.23374124373165
-        lats[2180] = -63.304040006878537
-        lats[2181] = -63.374338769993031
-        lats[2182] = -63.444637533074854
-        lats[2183] = -63.514936296123757
-        lats[2184] = -63.585235059139464
-        lats[2185] = -63.655533822121711
-        lats[2186] = -63.725832585070251
-        lats[2187] = -63.796131347984762
-        lats[2188] = -63.866430110865004
-        lats[2189] = -63.93672887371072
-        lats[2190] = -64.00702763652157
-        lats[2191] = -64.07732639929732
-        lats[2192] = -64.147625162037642
-        lats[2193] = -64.21792392474228
-        lats[2194] = -64.288222687410922
-        lats[2195] = -64.358521450043284
-        lats[2196] = -64.428820212639039
-        lats[2197] = -64.499118975197902
-        lats[2198] = -64.569417737719576
-        lats[2199] = -64.639716500203733
-        lats[2200] = -64.710015262650074
-        lats[2201] = -64.780314025058246
-        lats[2202] = -64.850612787427963
-        lats[2203] = -64.920911549758912
-        lats[2204] = -64.991210312050711
-        lats[2205] = -65.061509074303089
-        lats[2206] = -65.131807836515677
-        lats[2207] = -65.202106598688133
-        lats[2208] = -65.272405360820116
-        lats[2209] = -65.342704122911286
-        lats[2210] = -65.413002884961315
-        lats[2211] = -65.483301646969792
-        lats[2212] = -65.553600408936404
-        lats[2213] = -65.623899170860767
-        lats[2214] = -65.694197932742526
-        lats[2215] = -65.764496694581283
-        lats[2216] = -65.834795456376696
-        lats[2217] = -65.905094218128355
-        lats[2218] = -65.975392979835888
-        lats[2219] = -66.045691741498899
-        lats[2220] = -66.115990503117033
-        lats[2221] = -66.186289264689833
-        lats[2222] = -66.256588026216932
-        lats[2223] = -66.326886787697887
-        lats[2224] = -66.397185549132331
-        lats[2225] = -66.467484310519808
-        lats[2226] = -66.537783071859891
-        lats[2227] = -66.608081833152212
-        lats[2228] = -66.678380594396273
-        lats[2229] = -66.748679355591662
-        lats[2230] = -66.818978116737924
-        lats[2231] = -66.889276877834618
-        lats[2232] = -66.95957563888129
-        lats[2233] = -67.029874399877471
-        lats[2234] = -67.100173160822706
-        lats[2235] = -67.170471921716526
-        lats[2236] = -67.240770682558434
-        lats[2237] = -67.311069443347961
-        lats[2238] = -67.381368204084609
-        lats[2239] = -67.451666964767895
-        lats[2240] = -67.521965725397308
-        lats[2241] = -67.592264485972336
-        lats[2242] = -67.662563246492482
-        lats[2243] = -67.732862006957205
-        lats[2244] = -67.803160767365966
-        lats[2245] = -67.873459527718282
-        lats[2246] = -67.943758288013555
-        lats[2247] = -68.014057048251274
-        lats[2248] = -68.084355808430871
-        lats[2249] = -68.154654568551791
-        lats[2250] = -68.224953328613438
-        lats[2251] = -68.295252088615257
-        lats[2252] = -68.365550848556666
-        lats[2253] = -68.435849608437067
-        lats[2254] = -68.506148368255865
-        lats[2255] = -68.576447128012447
-        lats[2256] = -68.646745887706189
-        lats[2257] = -68.717044647336493
-        lats[2258] = -68.787343406902693
-        lats[2259] = -68.85764216640419
-        lats[2260] = -68.927940925840304
-        lats[2261] = -68.998239685210365
-        lats[2262] = -69.068538444513763
-        lats[2263] = -69.138837203749759
-        lats[2264] = -69.209135962917699
-        lats[2265] = -69.279434722016902
-        lats[2266] = -69.349733481046613
-        lats[2267] = -69.420032240006194
-        lats[2268] = -69.490330998894862
-        lats[2269] = -69.560629757711908
-        lats[2270] = -69.630928516456592
-        lats[2271] = -69.701227275128161
-        lats[2272] = -69.771526033725834
-        lats[2273] = -69.841824792248843
-        lats[2274] = -69.912123550696421
-        lats[2275] = -69.982422309067744
-        lats[2276] = -70.052721067362043
-        lats[2277] = -70.123019825578467
-        lats[2278] = -70.193318583716191
-        lats[2279] = -70.263617341774406
-        lats[2280] = -70.333916099752187
-        lats[2281] = -70.404214857648739
-        lats[2282] = -70.474513615463138
-        lats[2283] = -70.544812373194532
-        lats[2284] = -70.615111130841967
-        lats[2285] = -70.685409888404578
-        lats[2286] = -70.755708645881384
-        lats[2287] = -70.826007403271475
-        lats[2288] = -70.896306160573886
-        lats[2289] = -70.966604917787635
-        lats[2290] = -71.036903674911756
-        lats[2291] = -71.107202431945211
-        lats[2292] = -71.177501188887007
-        lats[2293] = -71.247799945736105
-        lats[2294] = -71.318098702491469
-        lats[2295] = -71.388397459152031
-        lats[2296] = -71.458696215716685
-        lats[2297] = -71.528994972184378
-        lats[2298] = -71.599293728553988
-        lats[2299] = -71.669592484824364
-        lats[2300] = -71.739891240994368
-        lats[2301] = -71.810189997062835
-        lats[2302] = -71.880488753028587
-        lats[2303] = -71.950787508890414
-        lats[2304] = -72.02108626464711
-        lats[2305] = -72.091385020297409
-        lats[2306] = -72.161683775840089
-        lats[2307] = -72.231982531273843
-        lats[2308] = -72.302281286597392
-        lats[2309] = -72.3725800418094
-        lats[2310] = -72.442878796908545
-        lats[2311] = -72.513177551893421
-        lats[2312] = -72.583476306762691
-        lats[2313] = -72.653775061514935
-        lats[2314] = -72.724073816148703
-        lats[2315] = -72.794372570662574
-        lats[2316] = -72.864671325055056
-        lats[2317] = -72.934970079324657
-        lats[2318] = -73.005268833469799
-        lats[2319] = -73.075567587489019
-        lats[2320] = -73.145866341380668
-        lats[2321] = -73.216165095143182
-        lats[2322] = -73.2864638487749
-        lats[2323] = -73.356762602274188
-        lats[2324] = -73.427061355639339
-        lats[2325] = -73.497360108868662
-        lats[2326] = -73.567658861960396
-        lats[2327] = -73.637957614912779
-        lats[2328] = -73.70825636772399
-        lats[2329] = -73.778555120392184
-        lats[2330] = -73.848853872915541
-        lats[2331] = -73.919152625292114
-        lats[2332] = -73.98945137751997
-        lats[2333] = -74.059750129597163
-        lats[2334] = -74.13004888152166
-        lats[2335] = -74.200347633291472
-        lats[2336] = -74.270646384904481
-        lats[2337] = -74.340945136358584
-        lats[2338] = -74.411243887651622
-        lats[2339] = -74.481542638781434
-        lats[2340] = -74.551841389745761
-        lats[2341] = -74.622140140542356
-        lats[2342] = -74.692438891168877
-        lats[2343] = -74.762737641622991
-        lats[2344] = -74.833036391902269
-        lats[2345] = -74.903335142004323
-        lats[2346] = -74.973633891926625
-        lats[2347] = -75.043932641666672
-        lats[2348] = -75.114231391221821
-        lats[2349] = -75.184530140589501
-        lats[2350] = -75.254828889766983
-        lats[2351] = -75.325127638751567
-        lats[2352] = -75.395426387540439
-        lats[2353] = -75.465725136130786
-        lats[2354] = -75.536023884519707
-        lats[2355] = -75.60632263270422
-        lats[2356] = -75.67662138068134
-        lats[2357] = -75.746920128447996
-        lats[2358] = -75.81721887600105
-        lats[2359] = -75.887517623337317
-        lats[2360] = -75.957816370453543
-        lats[2361] = -76.028115117346374
-        lats[2362] = -76.098413864012443
-        lats[2363] = -76.16871261044831
-        lats[2364] = -76.239011356650423
-        lats[2365] = -76.3093101026152
-        lats[2366] = -76.379608848338933
-        lats[2367] = -76.449907593817869
-        lats[2368] = -76.520206339048215
-        lats[2369] = -76.59050508402602
-        lats[2370] = -76.660803828747362
-        lats[2371] = -76.731102573208048
-        lats[2372] = -76.801401317404
-        lats[2373] = -76.871700061330955
-        lats[2374] = -76.941998804984564
-        lats[2375] = -77.012297548360323
-        lats[2376] = -77.082596291453768
-        lats[2377] = -77.15289503426024
-        lats[2378] = -77.22319377677502
-        lats[2379] = -77.293492518993247
-        lats[2380] = -77.363791260909963
-        lats[2381] = -77.434090002520122
-        lats[2382] = -77.504388743818524
-        lats[2383] = -77.574687484799924
-        lats[2384] = -77.644986225458879
-        lats[2385] = -77.71528496578982
-        lats[2386] = -77.785583705787161
-        lats[2387] = -77.855882445445019
-        lats[2388] = -77.926181184757539
-        lats[2389] = -77.996479923718596
-        lats[2390] = -78.066778662322022
-        lats[2391] = -78.137077400561424
-        lats[2392] = -78.207376138430348
-        lats[2393] = -78.277674875922045
-        lats[2394] = -78.347973613029708
-        lats[2395] = -78.418272349746417
-        lats[2396] = -78.488571086064923
-        lats[2397] = -78.558869821977908
-        lats[2398] = -78.629168557477882
-        lats[2399] = -78.699467292557102
-        lats[2400] = -78.769766027207638
-        lats[2401] = -78.840064761421445
-        lats[2402] = -78.910363495190211
-        lats[2403] = -78.980662228505423
-        lats[2404] = -79.050960961358285
-        lats[2405] = -79.121259693739859
-        lats[2406] = -79.191558425640977
-        lats[2407] = -79.261857157052191
-        lats[2408] = -79.332155887963822
-        lats[2409] = -79.402454618365894
-        lats[2410] = -79.472753348248219
-        lats[2411] = -79.543052077600308
-        lats[2412] = -79.61335080641139
-        lats[2413] = -79.683649534670437
-        lats[2414] = -79.753948262366038
-        lats[2415] = -79.824246989486554
-        lats[2416] = -79.894545716019948
-        lats[2417] = -79.9648444419539
-        lats[2418] = -80.035143167275749
-        lats[2419] = -80.105441891972376
-        lats[2420] = -80.175740616030438
-        lats[2421] = -80.246039339436052
-        lats[2422] = -80.316338062175078
-        lats[2423] = -80.386636784232863
-        lats[2424] = -80.456935505594302
-        lats[2425] = -80.527234226243991
-        lats[2426] = -80.59753294616587
-        lats[2427] = -80.667831665343556
-        lats[2428] = -80.73813038376008
-        lats[2429] = -80.808429101397948
-        lats[2430] = -80.878727818239184
-        lats[2431] = -80.949026534265244
-        lats[2432] = -81.019325249456955
-        lats[2433] = -81.089623963794551
-        lats[2434] = -81.159922677257711
-        lats[2435] = -81.230221389825374
-        lats[2436] = -81.300520101475826
-        lats[2437] = -81.370818812186627
-        lats[2438] = -81.441117521934686
-        lats[2439] = -81.511416230696042
-        lats[2440] = -81.581714938445955
-        lats[2441] = -81.652013645158945
-        lats[2442] = -81.722312350808508
-        lats[2443] = -81.792611055367345
-        lats[2444] = -81.862909758807191
-        lats[2445] = -81.933208461098829
-        lats[2446] = -82.003507162211946
-        lats[2447] = -82.073805862115165
-        lats[2448] = -82.144104560776
-        lats[2449] = -82.214403258160871
-        lats[2450] = -82.284701954234833
-        lats[2451] = -82.355000648961692
-        lats[2452] = -82.425299342304029
-        lats[2453] = -82.495598034222837
-        lats[2454] = -82.56589672467787
-        lats[2455] = -82.63619541362705
-        lats[2456] = -82.706494101026948
-        lats[2457] = -82.77679278683226
-        lats[2458] = -82.84709147099602
-        lats[2459] = -82.917390153469313
-        lats[2460] = -82.987688834201322
-        lats[2461] = -83.057987513139125
-        lats[2462] = -83.128286190227698
-        lats[2463] = -83.198584865409657
-        lats[2464] = -83.268883538625232
-        lats[2465] = -83.339182209812321
-        lats[2466] = -83.409480878905782
-        lats[2467] = -83.479779545838113
-        lats[2468] = -83.550078210538487
-        lats[2469] = -83.620376872933264
-        lats[2470] = -83.690675532945292
-        lats[2471] = -83.760974190494011
-        lats[2472] = -83.831272845495249
-        lats[2473] = -83.901571497860914
-        lats[2474] = -83.971870147498763
-        lats[2475] = -84.042168794312317
-        lats[2476] = -84.112467438200326
-        lats[2477] = -84.18276607905679
-        lats[2478] = -84.253064716770425
-        lats[2479] = -84.323363351224444
-        lats[2480] = -84.393661982296322
-        lats[2481] = -84.463960609857125
-        lats[2482] = -84.534259233771479
-        lats[2483] = -84.604557853896708
-        lats[2484] = -84.674856470082915
-        lats[2485] = -84.745155082171991
-        lats[2486] = -84.81545368999717
-        lats[2487] = -84.885752293382765
-        lats[2488] = -84.95605089214304
-        lats[2489] = -85.026349486081983
-        lats[2490] = -85.09664807499216
-        lats[2491] = -85.16694665865414
-        lats[2492] = -85.237245236835548
-        lats[2493] = -85.307543809290152
-        lats[2494] = -85.377842375756586
-        lats[2495] = -85.448140935957483
-        lats[2496] = -85.518439489597966
-        lats[2497] = -85.588738036364362
-        lats[2498] = -85.659036575922883
-        lats[2499] = -85.729335107917464
-        lats[2500] = -85.799633631968391
-        lats[2501] = -85.869932147670127
-        lats[2502] = -85.940230654588888
-        lats[2503] = -86.010529152260403
-        lats[2504] = -86.080827640187209
-        lats[2505] = -86.151126117835304
-        lats[2506] = -86.221424584631109
-        lats[2507] = -86.291723039957418
-        lats[2508] = -86.362021483149363
-        lats[2509] = -86.432319913489792
-        lats[2510] = -86.502618330203831
-        lats[2511] = -86.572916732453024
-        lats[2512] = -86.643215119328573
-        lats[2513] = -86.713513489844246
-        lats[2514] = -86.783811842927179
-        lats[2515] = -86.854110177408927
-        lats[2516] = -86.924408492014166
-        lats[2517] = -86.994706785348129
-        lats[2518] = -87.065005055882821
-        lats[2519] = -87.135303301939786
-        lats[2520] = -87.205601521672108
-        lats[2521] = -87.275899713041966
-        lats[2522] = -87.346197873795816
-        lats[2523] = -87.416496001434894
-        lats[2524] = -87.486794093180748
-        lats[2525] = -87.557092145935584
-        lats[2526] = -87.627390156234085
-        lats[2527] = -87.697688120188062
-        lats[2528] = -87.767986033419561
-        lats[2529] = -87.838283890981543
-        lats[2530] = -87.908581687261687
-        lats[2531] = -87.978879415867283
-        lats[2532] = -88.049177069484486
-        lats[2533] = -88.119474639706425
-        lats[2534] = -88.189772116820762
-        lats[2535] = -88.26006948954614
-        lats[2536] = -88.330366744702559
-        lats[2537] = -88.40066386679355
-        lats[2538] = -88.470960837474877
-        lats[2539] = -88.541257634868515
-        lats[2540] = -88.611554232668382
-        lats[2541] = -88.681850598961759
-        lats[2542] = -88.752146694650691
-        lats[2543] = -88.822442471310097
-        lats[2544] = -88.892737868230952
-        lats[2545] = -88.96303280826325
-        lats[2546] = -89.033327191845927
-        lats[2547] = -89.103620888238879
-        lats[2548] = -89.173913722284126
-        lats[2549] = -89.24420545380525
-        lats[2550] = -89.314495744374256
-        lats[2551] = -89.3847841013921
-        lats[2552] = -89.45506977912261
-        lats[2553] = -89.525351592371393
-        lats[2554] = -89.595627537554492
-        lats[2555] = -89.6658939412157
-        lats[2556] = -89.736143271609578
-        lats[2557] = -89.806357319542244
-        lats[2558] = -89.876478353332288
-        lats[2559] = -89.946187715665616
-        return lats
-
-    def first_axis_vals(self):
-        if self._resolution == 1280:
-            return self.get_precomputed_values_N1280()
-        else:
-            precision = 1.0e-14
-            nval = self._resolution * 2
-            rad2deg = 180 / math.pi
-            convval = 1 - ((2 / math.pi) * (2 / math.pi)) * 0.25
-            vals = self.gauss_first_guess()
-            new_vals = [0] * nval
-            denom = math.sqrt(((nval + 0.5) * (nval + 0.5)) + convval)
-            for jval in range(self._resolution):
-                root = math.cos(vals[jval] / denom)
-                conv = 1
-                while abs(conv) >= precision:
-                    mem2 = 1
-                    mem1 = root
-                    for legi in range(nval):
-                        legfonc = ((2.0 * (legi + 1) - 1.0) * root * mem1 - legi * mem2) / (legi + 1)
-                        mem2 = mem1
-                        mem1 = legfonc
-                    conv = legfonc / ((nval * (mem2 - root * legfonc)) / (1.0 - (root * root)))
-                    root = root - conv
-                    # add maybe a max iter here to make sure we converge at some point
-                new_vals[jval] = math.asin(root) * rad2deg
-                new_vals[nval - 1 - jval] = -new_vals[jval]
-            return new_vals
-
-    def map_first_axis(self, lower, upper):
-        axis_lines = self._first_axis_vals
-        end_idx = bisect_left_cmp(axis_lines, lower, cmp=lambda x, y: x > y) + 1
-        start_idx = bisect_right_cmp(axis_lines, upper, cmp=lambda x, y: x > y)
-        return_vals = axis_lines[start_idx:end_idx]
-        return return_vals
-
-    def second_axis_vals(self, first_val):
-        first_axis_vals = self._first_axis_vals
-        tol = 1e-10
-        first_idx = bisect_left_cmp(first_axis_vals, first_val - tol, cmp=lambda x, y: x > y)
-        if first_idx >= self._resolution:
-            first_idx = (2 * self._resolution) - 1 - first_idx
-        first_idx = first_idx + 1
-        npoints = 4 * first_idx + 16
-        second_axis_spacing = 360 / npoints
-        second_axis_vals = [i * second_axis_spacing for i in range(npoints)]
-        return second_axis_vals
-
-    def second_axis_spacing(self, first_val):
-        first_axis_vals = self._first_axis_vals
-        tol = 1e-10
-        _first_idx = bisect_left_cmp(first_axis_vals, first_val - tol, cmp=lambda x, y: x > y)
-        first_idx = _first_idx
-        if first_idx >= self._resolution:
-            first_idx = (2 * self._resolution) - 1 - first_idx
-        first_idx = first_idx + 1
-        npoints = 4 * first_idx + 16
-        second_axis_spacing = 360 / npoints
-        return (second_axis_spacing, _first_idx + 1)
-
-    def map_second_axis(self, first_val, lower, upper):
-        second_axis_spacing, first_idx = self.second_axis_spacing(first_val)
-        start_idx = int(lower / second_axis_spacing)
-        end_idx = int(upper / second_axis_spacing) + 1
-        return_vals = [i * second_axis_spacing for i in range(start_idx, end_idx)]
-        return return_vals
-
-    def axes_idx_to_octahedral_idx(self, first_idx, second_idx):
-        # NOTE: for now this takes ~2e-4s per point, so taking significant time -> for 20k points, takes 4s
-        # Would it be better to store a dictionary of first_idx with cumulative number of points on that idx?
-        # Because this is what we are doing here, but we are calculating for each point...
-        # But then this would only work for special grid resolutions, so need to do like a O1280 version of this
-
-        # NOTE: OR somehow cache this for a given first_idx and then only modify the axis idx for second_idx when the
-        # first_idx changes
-        octa_idx = self._first_idx_map[first_idx - 1] + second_idx
-        return octa_idx
-
-    def create_first_idx_map(self):
-        first_idx_list = {}
-        idx = 0
-        for i in range(2 * self._resolution):
-            first_idx_list[i] = idx
-            if i <= self._resolution - 1:
-                idx += 20 + 4 * i
-            else:
-                i = i - self._resolution + 1
-                if i == 1:
-                    idx += 16 + 4 * self._resolution
-                else:
-                    i = i - 1
-                    idx += 16 + 4 * (self._resolution - i)
-        return first_idx_list
-
-    def find_second_axis_idx(self, first_val, second_val):
-        (second_axis_spacing, first_idx) = self.second_axis_spacing(first_val)
-        tol = 1e-8
-        if second_val / second_axis_spacing > int(second_val / second_axis_spacing) + 1 - tol:
-            second_idx = int(second_val / second_axis_spacing) + 1
-        else:
-            second_idx = int(second_val / second_axis_spacing)
-        return (first_idx, second_idx)
-
-    def unmap(self, first_val, second_val):
-        (first_idx, second_idx) = self.find_second_axis_idx(first_val, second_val)
-        octahedral_index = self.axes_idx_to_octahedral_idx(first_idx, second_idx)
-        return octahedral_index
-
-
 _type_to_datacube_mapper_lookup = {
     "octahedral": "OctahedralGridMapper",
     "healpix": "HealpixGridMapper",
diff --git a/polytope/datacube/transformations/mappers/healpix.py b/polytope/datacube/transformations/mappers/healpix.py
new file mode 100644
index 00000000..627a1be9
--- /dev/null
+++ b/polytope/datacube/transformations/mappers/healpix.py
@@ -0,0 +1,123 @@
+import bisect
+import math
+
+from ..datacube_mappers import DatacubeMapper
+
+
+class HealpixGridMapper(DatacubeMapper):
+    def __init__(self, base_axis, mapped_axes, resolution):
+        self._mapped_axes = mapped_axes
+        self._base_axis = base_axis
+        self._resolution = resolution
+        self._axis_reversed = {mapped_axes[0]: True, mapped_axes[1]: False}
+        self._first_axis_vals = self.first_axis_vals()
+
+    def first_axis_vals(self):
+        rad2deg = 180 / math.pi
+        vals = [0] * (4 * self._resolution - 1)
+
+        # Polar caps
+        for i in range(1, self._resolution):
+            val = 90 - (rad2deg * math.acos(1 - (i * i / (3 * self._resolution * self._resolution))))
+            vals[i - 1] = val
+            vals[4 * self._resolution - 1 - i] = -val
+        # Equatorial belts
+        for i in range(self._resolution, 2 * self._resolution):
+            val = 90 - (rad2deg * math.acos((4 * self._resolution - 2 * i) / (3 * self._resolution)))
+            vals[i - 1] = val
+            vals[4 * self._resolution - 1 - i] = -val
+        # Equator
+        vals[2 * self._resolution - 1] = 0
+        return vals
+
+    def map_first_axis(self, lower, upper):
+        axis_lines = self._first_axis_vals
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def second_axis_vals(self, first_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        idx = self._first_axis_vals.index(first_val)
+
+        # Polar caps
+        if idx < self._resolution - 1 or 3 * self._resolution - 1 < idx <= 4 * self._resolution - 2:
+            start = 45 / (idx + 1)
+            vals = [start + i * (360 / (4 * (idx + 1))) for i in range(4 * (idx + 1))]
+            return vals
+        # Equatorial belts
+        start = 45 / self._resolution
+        if self._resolution - 1 <= idx < 2 * self._resolution - 1 or 2 * self._resolution <= idx < 3 * self._resolution:
+            r_start = start * (2 - (((idx + 1) - self._resolution + 1) % 2))
+            vals = [r_start + i * (360 / (4 * self._resolution)) for i in range(4 * self._resolution)]
+            if vals[-1] == 360:
+                vals[-1] = 0
+            return vals
+        # Equator
+        temp_val = 1 if self._resolution % 2 else 0
+        r_start = start * (1 - temp_val)
+        if idx == 2 * self._resolution - 1:
+            vals = [r_start + i * (360 / (4 * self._resolution)) for i in range(4 * self._resolution)]
+            return vals
+
+    def map_second_axis(self, first_val, lower, upper):
+        axis_lines = self.second_axis_vals(first_val)
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def axes_idx_to_healpix_idx(self, first_idx, second_idx):
+        idx = 0
+        for i in range(self._resolution - 1):
+            if i != first_idx:
+                idx += 4 * (i + 1)
+            else:
+                idx += second_idx
+                return idx
+        for i in range(self._resolution - 1, 3 * self._resolution):
+            if i != first_idx:
+                idx += 4 * self._resolution
+            else:
+                idx += second_idx
+                return idx
+        for i in range(3 * self._resolution, 4 * self._resolution - 1):
+            if i != first_idx:
+                idx += 4 * (4 * self._resolution - 1 - i + 1)
+            else:
+                idx += second_idx
+                return idx
+
+    def find_second_idx(self, first_val, second_val):
+        tol = 1e-10
+        second_axis_vals = self.second_axis_vals(first_val)
+        second_idx = bisect.bisect_left(second_axis_vals, second_val - tol)
+        return second_idx
+
+    def unmap_first_val_to_start_line_idx(self, first_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        first_idx = self._first_axis_vals.index(first_val)
+        idx = 0
+        for i in range(self._resolution - 1):
+            if i != first_idx:
+                idx += 4 * (i + 1)
+            else:
+                return idx
+        for i in range(self._resolution - 1, 3 * self._resolution):
+            if i != first_idx:
+                idx += 4 * self._resolution
+            else:
+                return idx
+        for i in range(3 * self._resolution, 4 * self._resolution - 1):
+            if i != first_idx:
+                idx += 4 * (4 * self._resolution - 1 - i + 1)
+            else:
+                return idx
+
+    def unmap(self, first_val, second_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        first_idx = self._first_axis_vals.index(first_val)
+        second_val = [i for i in self.second_axis_vals(first_val) if second_val - tol <= i <= second_val + tol][0]
+        second_idx = self.second_axis_vals(first_val).index(second_val)
+        healpix_index = self.axes_idx_to_healpix_idx(first_idx, second_idx)
+        return healpix_index
diff --git a/polytope/datacube/transformations/mappers/octahedral.py b/polytope/datacube/transformations/mappers/octahedral.py
new file mode 100644
index 00000000..1c24703d
--- /dev/null
+++ b/polytope/datacube/transformations/mappers/octahedral.py
@@ -0,0 +1,2752 @@
+import math
+
+from ....utility.list_tools import bisect_left_cmp, bisect_right_cmp
+from ..datacube_mappers import DatacubeMapper
+
+
+class OctahedralGridMapper(DatacubeMapper):
+    def __init__(self, base_axis, mapped_axes, resolution):
+        self._mapped_axes = mapped_axes
+        self._base_axis = base_axis
+        self._resolution = resolution
+        self._first_axis_vals = self.first_axis_vals()
+        self._first_idx_map = self.create_first_idx_map()
+        self._second_axis_spacing = {}
+        self._axis_reversed = {mapped_axes[0]: True, mapped_axes[1]: False}
+
+    def gauss_first_guess(self):
+        i = 0
+        gvals = [
+            2.4048255577e0,
+            5.5200781103e0,
+            8.6537279129e0,
+            11.7915344391e0,
+            14.9309177086e0,
+            18.0710639679e0,
+            21.2116366299e0,
+            24.3524715308e0,
+            27.4934791320e0,
+            30.6346064684e0,
+            33.7758202136e0,
+            36.9170983537e0,
+            40.0584257646e0,
+            43.1997917132e0,
+            46.3411883717e0,
+            49.4826098974e0,
+            52.6240518411e0,
+            55.7655107550e0,
+            58.9069839261e0,
+            62.0484691902e0,
+            65.1899648002e0,
+            68.3314693299e0,
+            71.4729816036e0,
+            74.6145006437e0,
+            77.7560256304e0,
+            80.8975558711e0,
+            84.0390907769e0,
+            87.1806298436e0,
+            90.3221726372e0,
+            93.4637187819e0,
+            96.6052679510e0,
+            99.7468198587e0,
+            102.8883742542e0,
+            106.0299309165e0,
+            109.1714896498e0,
+            112.3130502805e0,
+            115.4546126537e0,
+            118.5961766309e0,
+            121.7377420880e0,
+            124.8793089132e0,
+            128.0208770059e0,
+            131.1624462752e0,
+            134.3040166383e0,
+            137.4455880203e0,
+            140.5871603528e0,
+            143.7287335737e0,
+            146.8703076258e0,
+            150.0118824570e0,
+            153.1534580192e0,
+            156.2950342685e0,
+        ]
+
+        numVals = len(gvals)
+        vals = []
+        for i in range(self._resolution):
+            if i < numVals:
+                vals.append(gvals[i])
+            else:
+                vals.append(vals[i - 1] + math.pi)
+        return vals
+
+    def get_precomputed_values_N1280(self):
+        lats = [0] * 2560
+        # lats = SortedList()
+        # lats = {}
+        lats[0] = 89.946187715665616
+        lats[1] = 89.876478353332288
+        lats[2] = 89.806357319542244
+        lats[3] = 89.736143271609578
+        lats[4] = 89.6658939412157
+        lats[5] = 89.595627537554492
+        lats[6] = 89.525351592371393
+        lats[7] = 89.45506977912261
+        lats[8] = 89.3847841013921
+        lats[9] = 89.314495744374256
+        lats[10] = 89.24420545380525
+        lats[11] = 89.173913722284126
+        lats[12] = 89.103620888238879
+        lats[13] = 89.033327191845927
+        lats[14] = 88.96303280826325
+        lats[15] = 88.892737868230952
+        lats[16] = 88.822442471310097
+        lats[17] = 88.752146694650691
+        lats[18] = 88.681850598961759
+        lats[19] = 88.611554232668382
+        lats[20] = 88.541257634868515
+        lats[21] = 88.470960837474877
+        lats[22] = 88.40066386679355
+        lats[23] = 88.330366744702559
+        lats[24] = 88.26006948954614
+        lats[25] = 88.189772116820762
+        lats[26] = 88.119474639706425
+        lats[27] = 88.049177069484486
+        lats[28] = 87.978879415867283
+        lats[29] = 87.908581687261687
+        lats[30] = 87.838283890981543
+        lats[31] = 87.767986033419561
+        lats[32] = 87.697688120188062
+        lats[33] = 87.627390156234085
+        lats[34] = 87.557092145935584
+        lats[35] = 87.486794093180748
+        lats[36] = 87.416496001434894
+        lats[37] = 87.346197873795816
+        lats[38] = 87.275899713041966
+        lats[39] = 87.205601521672108
+        lats[40] = 87.135303301939786
+        lats[41] = 87.065005055882821
+        lats[42] = 86.994706785348129
+        lats[43] = 86.924408492014166
+        lats[44] = 86.854110177408927
+        lats[45] = 86.783811842927179
+        lats[46] = 86.713513489844246
+        lats[47] = 86.643215119328573
+        lats[48] = 86.572916732453024
+        lats[49] = 86.502618330203831
+        lats[50] = 86.432319913489792
+        lats[51] = 86.362021483149363
+        lats[52] = 86.291723039957418
+        lats[53] = 86.221424584631109
+        lats[54] = 86.151126117835304
+        lats[55] = 86.080827640187209
+        lats[56] = 86.010529152260403
+        lats[57] = 85.940230654588888
+        lats[58] = 85.869932147670127
+        lats[59] = 85.799633631968391
+        lats[60] = 85.729335107917464
+        lats[61] = 85.659036575922883
+        lats[62] = 85.588738036364362
+        lats[63] = 85.518439489597966
+        lats[64] = 85.448140935957483
+        lats[65] = 85.377842375756586
+        lats[66] = 85.307543809290152
+        lats[67] = 85.237245236835548
+        lats[68] = 85.16694665865414
+        lats[69] = 85.09664807499216
+        lats[70] = 85.026349486081983
+        lats[71] = 84.95605089214304
+        lats[72] = 84.885752293382765
+        lats[73] = 84.81545368999717
+        lats[74] = 84.745155082171991
+        lats[75] = 84.674856470082915
+        lats[76] = 84.604557853896708
+        lats[77] = 84.534259233771479
+        lats[78] = 84.463960609857125
+        lats[79] = 84.393661982296322
+        lats[80] = 84.323363351224444
+        lats[81] = 84.253064716770425
+        lats[82] = 84.18276607905679
+        lats[83] = 84.112467438200326
+        lats[84] = 84.042168794312317
+        lats[85] = 83.971870147498763
+        lats[86] = 83.901571497860914
+        lats[87] = 83.831272845495249
+        lats[88] = 83.760974190494011
+        lats[89] = 83.690675532945292
+        lats[90] = 83.620376872933264
+        lats[91] = 83.550078210538487
+        lats[92] = 83.479779545838113
+        lats[93] = 83.409480878905782
+        lats[94] = 83.339182209812321
+        lats[95] = 83.268883538625232
+        lats[96] = 83.198584865409657
+        lats[97] = 83.128286190227698
+        lats[98] = 83.057987513139125
+        lats[99] = 82.987688834201322
+        lats[100] = 82.917390153469313
+        lats[101] = 82.84709147099602
+        lats[102] = 82.77679278683226
+        lats[103] = 82.706494101026948
+        lats[104] = 82.63619541362705
+        lats[105] = 82.56589672467787
+        lats[106] = 82.495598034222837
+        lats[107] = 82.425299342304029
+        lats[108] = 82.355000648961692
+        lats[109] = 82.284701954234833
+        lats[110] = 82.214403258160871
+        lats[111] = 82.144104560776
+        lats[112] = 82.073805862115165
+        lats[113] = 82.003507162211946
+        lats[114] = 81.933208461098829
+        lats[115] = 81.862909758807191
+        lats[116] = 81.792611055367345
+        lats[117] = 81.722312350808508
+        lats[118] = 81.652013645158945
+        lats[119] = 81.581714938445955
+        lats[120] = 81.511416230696042
+        lats[121] = 81.441117521934686
+        lats[122] = 81.370818812186627
+        lats[123] = 81.300520101475826
+        lats[124] = 81.230221389825374
+        lats[125] = 81.159922677257711
+        lats[126] = 81.089623963794551
+        lats[127] = 81.019325249456955
+        lats[128] = 80.949026534265244
+        lats[129] = 80.878727818239184
+        lats[130] = 80.808429101397948
+        lats[131] = 80.73813038376008
+        lats[132] = 80.667831665343556
+        lats[133] = 80.59753294616587
+        lats[134] = 80.527234226243991
+        lats[135] = 80.456935505594302
+        lats[136] = 80.386636784232863
+        lats[137] = 80.316338062175078
+        lats[138] = 80.246039339436052
+        lats[139] = 80.175740616030438
+        lats[140] = 80.105441891972376
+        lats[141] = 80.035143167275749
+        lats[142] = 79.9648444419539
+        lats[143] = 79.894545716019948
+        lats[144] = 79.824246989486554
+        lats[145] = 79.753948262366038
+        lats[146] = 79.683649534670437
+        lats[147] = 79.61335080641139
+        lats[148] = 79.543052077600308
+        lats[149] = 79.472753348248219
+        lats[150] = 79.402454618365894
+        lats[151] = 79.332155887963822
+        lats[152] = 79.261857157052191
+        lats[153] = 79.191558425640977
+        lats[154] = 79.121259693739859
+        lats[155] = 79.050960961358285
+        lats[156] = 78.980662228505423
+        lats[157] = 78.910363495190211
+        lats[158] = 78.840064761421445
+        lats[159] = 78.769766027207638
+        lats[160] = 78.699467292557102
+        lats[161] = 78.629168557477882
+        lats[162] = 78.558869821977908
+        lats[163] = 78.488571086064923
+        lats[164] = 78.418272349746417
+        lats[165] = 78.347973613029708
+        lats[166] = 78.277674875922045
+        lats[167] = 78.207376138430348
+        lats[168] = 78.137077400561424
+        lats[169] = 78.066778662322022
+        lats[170] = 77.996479923718596
+        lats[171] = 77.926181184757539
+        lats[172] = 77.855882445445019
+        lats[173] = 77.785583705787161
+        lats[174] = 77.71528496578982
+        lats[175] = 77.644986225458879
+        lats[176] = 77.574687484799924
+        lats[177] = 77.504388743818524
+        lats[178] = 77.434090002520122
+        lats[179] = 77.363791260909963
+        lats[180] = 77.293492518993247
+        lats[181] = 77.22319377677502
+        lats[182] = 77.15289503426024
+        lats[183] = 77.082596291453768
+        lats[184] = 77.012297548360323
+        lats[185] = 76.941998804984564
+        lats[186] = 76.871700061330955
+        lats[187] = 76.801401317404
+        lats[188] = 76.731102573208048
+        lats[189] = 76.660803828747362
+        lats[190] = 76.59050508402602
+        lats[191] = 76.520206339048215
+        lats[192] = 76.449907593817869
+        lats[193] = 76.379608848338933
+        lats[194] = 76.3093101026152
+        lats[195] = 76.239011356650423
+        lats[196] = 76.16871261044831
+        lats[197] = 76.098413864012443
+        lats[198] = 76.028115117346374
+        lats[199] = 75.957816370453543
+        lats[200] = 75.887517623337317
+        lats[201] = 75.81721887600105
+        lats[202] = 75.746920128447996
+        lats[203] = 75.67662138068134
+        lats[204] = 75.60632263270422
+        lats[205] = 75.536023884519707
+        lats[206] = 75.465725136130786
+        lats[207] = 75.395426387540439
+        lats[208] = 75.325127638751567
+        lats[209] = 75.254828889766983
+        lats[210] = 75.184530140589501
+        lats[211] = 75.114231391221821
+        lats[212] = 75.043932641666672
+        lats[213] = 74.973633891926625
+        lats[214] = 74.903335142004323
+        lats[215] = 74.833036391902269
+        lats[216] = 74.762737641622991
+        lats[217] = 74.692438891168877
+        lats[218] = 74.622140140542356
+        lats[219] = 74.551841389745761
+        lats[220] = 74.481542638781434
+        lats[221] = 74.411243887651622
+        lats[222] = 74.340945136358584
+        lats[223] = 74.270646384904481
+        lats[224] = 74.200347633291472
+        lats[225] = 74.13004888152166
+        lats[226] = 74.059750129597163
+        lats[227] = 73.98945137751997
+        lats[228] = 73.919152625292114
+        lats[229] = 73.848853872915541
+        lats[230] = 73.778555120392184
+        lats[231] = 73.70825636772399
+        lats[232] = 73.637957614912779
+        lats[233] = 73.567658861960396
+        lats[234] = 73.497360108868662
+        lats[235] = 73.427061355639339
+        lats[236] = 73.356762602274188
+        lats[237] = 73.2864638487749
+        lats[238] = 73.216165095143182
+        lats[239] = 73.145866341380668
+        lats[240] = 73.075567587489019
+        lats[241] = 73.005268833469799
+        lats[242] = 72.934970079324657
+        lats[243] = 72.864671325055056
+        lats[244] = 72.794372570662574
+        lats[245] = 72.724073816148703
+        lats[246] = 72.653775061514935
+        lats[247] = 72.583476306762691
+        lats[248] = 72.513177551893421
+        lats[249] = 72.442878796908545
+        lats[250] = 72.3725800418094
+        lats[251] = 72.302281286597392
+        lats[252] = 72.231982531273843
+        lats[253] = 72.161683775840089
+        lats[254] = 72.091385020297409
+        lats[255] = 72.02108626464711
+        lats[256] = 71.950787508890414
+        lats[257] = 71.880488753028587
+        lats[258] = 71.810189997062835
+        lats[259] = 71.739891240994368
+        lats[260] = 71.669592484824364
+        lats[261] = 71.599293728553988
+        lats[262] = 71.528994972184378
+        lats[263] = 71.458696215716685
+        lats[264] = 71.388397459152031
+        lats[265] = 71.318098702491469
+        lats[266] = 71.247799945736105
+        lats[267] = 71.177501188887007
+        lats[268] = 71.107202431945211
+        lats[269] = 71.036903674911756
+        lats[270] = 70.966604917787635
+        lats[271] = 70.896306160573886
+        lats[272] = 70.826007403271475
+        lats[273] = 70.755708645881384
+        lats[274] = 70.685409888404578
+        lats[275] = 70.615111130841967
+        lats[276] = 70.544812373194532
+        lats[277] = 70.474513615463138
+        lats[278] = 70.404214857648739
+        lats[279] = 70.333916099752187
+        lats[280] = 70.263617341774406
+        lats[281] = 70.193318583716191
+        lats[282] = 70.123019825578467
+        lats[283] = 70.052721067362043
+        lats[284] = 69.982422309067744
+        lats[285] = 69.912123550696421
+        lats[286] = 69.841824792248843
+        lats[287] = 69.771526033725834
+        lats[288] = 69.701227275128161
+        lats[289] = 69.630928516456592
+        lats[290] = 69.560629757711908
+        lats[291] = 69.490330998894862
+        lats[292] = 69.420032240006194
+        lats[293] = 69.349733481046613
+        lats[294] = 69.279434722016902
+        lats[295] = 69.209135962917699
+        lats[296] = 69.138837203749759
+        lats[297] = 69.068538444513763
+        lats[298] = 68.998239685210365
+        lats[299] = 68.927940925840304
+        lats[300] = 68.85764216640419
+        lats[301] = 68.787343406902693
+        lats[302] = 68.717044647336493
+        lats[303] = 68.646745887706189
+        lats[304] = 68.576447128012447
+        lats[305] = 68.506148368255865
+        lats[306] = 68.435849608437067
+        lats[307] = 68.365550848556666
+        lats[308] = 68.295252088615257
+        lats[309] = 68.224953328613438
+        lats[310] = 68.154654568551791
+        lats[311] = 68.084355808430871
+        lats[312] = 68.014057048251274
+        lats[313] = 67.943758288013555
+        lats[314] = 67.873459527718282
+        lats[315] = 67.803160767365966
+        lats[316] = 67.732862006957205
+        lats[317] = 67.662563246492482
+        lats[318] = 67.592264485972336
+        lats[319] = 67.521965725397308
+        lats[320] = 67.451666964767895
+        lats[321] = 67.381368204084609
+        lats[322] = 67.311069443347961
+        lats[323] = 67.240770682558434
+        lats[324] = 67.170471921716526
+        lats[325] = 67.100173160822706
+        lats[326] = 67.029874399877471
+        lats[327] = 66.95957563888129
+        lats[328] = 66.889276877834618
+        lats[329] = 66.818978116737924
+        lats[330] = 66.748679355591662
+        lats[331] = 66.678380594396273
+        lats[332] = 66.608081833152212
+        lats[333] = 66.537783071859891
+        lats[334] = 66.467484310519808
+        lats[335] = 66.397185549132331
+        lats[336] = 66.326886787697887
+        lats[337] = 66.256588026216932
+        lats[338] = 66.186289264689833
+        lats[339] = 66.115990503117033
+        lats[340] = 66.045691741498899
+        lats[341] = 65.975392979835888
+        lats[342] = 65.905094218128355
+        lats[343] = 65.834795456376696
+        lats[344] = 65.764496694581283
+        lats[345] = 65.694197932742526
+        lats[346] = 65.623899170860767
+        lats[347] = 65.553600408936404
+        lats[348] = 65.483301646969792
+        lats[349] = 65.413002884961315
+        lats[350] = 65.342704122911286
+        lats[351] = 65.272405360820116
+        lats[352] = 65.202106598688133
+        lats[353] = 65.131807836515677
+        lats[354] = 65.061509074303089
+        lats[355] = 64.991210312050711
+        lats[356] = 64.920911549758912
+        lats[357] = 64.850612787427963
+        lats[358] = 64.780314025058246
+        lats[359] = 64.710015262650074
+        lats[360] = 64.639716500203733
+        lats[361] = 64.569417737719576
+        lats[362] = 64.499118975197902
+        lats[363] = 64.428820212639039
+        lats[364] = 64.358521450043284
+        lats[365] = 64.288222687410922
+        lats[366] = 64.21792392474228
+        lats[367] = 64.147625162037642
+        lats[368] = 64.07732639929732
+        lats[369] = 64.00702763652157
+        lats[370] = 63.93672887371072
+        lats[371] = 63.866430110865004
+        lats[372] = 63.796131347984762
+        lats[373] = 63.725832585070251
+        lats[374] = 63.655533822121711
+        lats[375] = 63.585235059139464
+        lats[376] = 63.514936296123757
+        lats[377] = 63.444637533074854
+        lats[378] = 63.374338769993031
+        lats[379] = 63.304040006878537
+        lats[380] = 63.23374124373165
+        lats[381] = 63.163442480552604
+        lats[382] = 63.093143717341647
+        lats[383] = 63.022844954099064
+        lats[384] = 62.952546190825068
+        lats[385] = 62.882247427519928
+        lats[386] = 62.811948664183866
+        lats[387] = 62.741649900817137
+        lats[388] = 62.67135113741999
+        lats[389] = 62.60105237399263
+        lats[390] = 62.530753610535321
+        lats[391] = 62.460454847048261
+        lats[392] = 62.3901560835317
+        lats[393] = 62.319857319985871
+        lats[394] = 62.249558556410982
+        lats[395] = 62.179259792807258
+        lats[396] = 62.108961029174914
+        lats[397] = 62.038662265514176
+        lats[398] = 61.968363501825259
+        lats[399] = 61.898064738108381
+        lats[400] = 61.827765974363729
+        lats[401] = 61.757467210591535
+        lats[402] = 61.687168446791986
+        lats[403] = 61.616869682965287
+        lats[404] = 61.546570919111666
+        lats[405] = 61.476272155231321
+        lats[406] = 61.405973391324409
+        lats[407] = 61.335674627391185
+        lats[408] = 61.265375863431785
+        lats[409] = 61.195077099446451
+        lats[410] = 61.124778335435344
+        lats[411] = 61.054479571398652
+        lats[412] = 60.984180807336578
+        lats[413] = 60.913882043249295
+        lats[414] = 60.843583279137007
+        lats[415] = 60.773284514999872
+        lats[416] = 60.702985750838074
+        lats[417] = 60.632686986651805
+        lats[418] = 60.562388222441243
+        lats[419] = 60.492089458206543
+        lats[420] = 60.421790693947884
+        lats[421] = 60.35149192966545
+        lats[422] = 60.28119316535939
+        lats[423] = 60.21089440102989
+        lats[424] = 60.140595636677112
+        lats[425] = 60.070296872301235
+        lats[426] = 59.999998107902378
+        lats[427] = 59.929699343480763
+        lats[428] = 59.859400579036503
+        lats[429] = 59.78910181456979
+        lats[430] = 59.718803050080759
+        lats[431] = 59.64850428556958
+        lats[432] = 59.578205521036402
+        lats[433] = 59.507906756481383
+        lats[434] = 59.43760799190467
+        lats[435] = 59.3673092273064
+        lats[436] = 59.29701046268675
+        lats[437] = 59.226711698045854
+        lats[438] = 59.156412933383855
+        lats[439] = 59.086114168700909
+        lats[440] = 59.015815403997145
+        lats[441] = 58.945516639272725
+        lats[442] = 58.875217874527763
+        lats[443] = 58.804919109762423
+        lats[444] = 58.73462034497684
+        lats[445] = 58.664321580171141
+        lats[446] = 58.594022815345468
+        lats[447] = 58.523724050499972
+        lats[448] = 58.453425285634758
+        lats[449] = 58.383126520749968
+        lats[450] = 58.312827755845746
+        lats[451] = 58.242528990922203
+        lats[452] = 58.172230225979497
+        lats[453] = 58.101931461017728
+        lats[454] = 58.031632696037022
+        lats[455] = 57.961333931037537
+        lats[456] = 57.891035166019364
+        lats[457] = 57.820736400982646
+        lats[458] = 57.75043763592749
+        lats[459] = 57.680138870854037
+        lats[460] = 57.60984010576238
+        lats[461] = 57.539541340652676
+        lats[462] = 57.469242575525016
+        lats[463] = 57.398943810379521
+        lats[464] = 57.328645045216312
+        lats[465] = 57.258346280035504
+        lats[466] = 57.188047514837208
+        lats[467] = 57.117748749621541
+        lats[468] = 57.047449984388614
+        lats[469] = 56.977151219138541
+        lats[470] = 56.90685245387143
+        lats[471] = 56.836553688587379
+        lats[472] = 56.766254923286517
+        lats[473] = 56.695956157968951
+        lats[474] = 56.625657392634771
+        lats[475] = 56.555358627284086
+        lats[476] = 56.485059861917016
+        lats[477] = 56.41476109653366
+        lats[478] = 56.34446233113411
+        lats[479] = 56.274163565718467
+        lats[480] = 56.203864800286865
+        lats[481] = 56.133566034839362
+        lats[482] = 56.063267269376091
+        lats[483] = 55.992968503897131
+        lats[484] = 55.922669738402583
+        lats[485] = 55.852370972892551
+        lats[486] = 55.782072207367136
+        lats[487] = 55.711773441826416
+        lats[488] = 55.641474676270505
+        lats[489] = 55.571175910699488
+        lats[490] = 55.500877145113449
+        lats[491] = 55.430578379512511
+        lats[492] = 55.360279613896743
+        lats[493] = 55.289980848266232
+        lats[494] = 55.219682082621084
+        lats[495] = 55.149383316961377
+        lats[496] = 55.07908455128721
+        lats[497] = 55.008785785598668
+        lats[498] = 54.938487019895831
+        lats[499] = 54.868188254178797
+        lats[500] = 54.797889488447652
+        lats[501] = 54.727590722702473
+        lats[502] = 54.657291956943347
+        lats[503] = 54.586993191170357
+        lats[504] = 54.516694425383605
+        lats[505] = 54.446395659583146
+        lats[506] = 54.376096893769081
+        lats[507] = 54.305798127941479
+        lats[508] = 54.235499362100448
+        lats[509] = 54.165200596246031
+        lats[510] = 54.094901830378333
+        lats[511] = 54.024603064497434
+        lats[512] = 53.954304298603383
+        lats[513] = 53.884005532696307
+        lats[514] = 53.813706766776235
+        lats[515] = 53.743408000843282
+        lats[516] = 53.673109234897495
+        lats[517] = 53.602810468938962
+        lats[518] = 53.53251170296776
+        lats[519] = 53.462212936983953
+        lats[520] = 53.391914170987633
+        lats[521] = 53.321615404978871
+        lats[522] = 53.251316638957725
+        lats[523] = 53.181017872924265
+        lats[524] = 53.110719106878584
+        lats[525] = 53.040420340820731
+        lats[526] = 52.970121574750792
+        lats[527] = 52.899822808668837
+        lats[528] = 52.829524042574917
+        lats[529] = 52.759225276469131
+        lats[530] = 52.688926510351514
+        lats[531] = 52.618627744222159
+        lats[532] = 52.548328978081123
+        lats[533] = 52.478030211928477
+        lats[534] = 52.407731445764284
+        lats[535] = 52.337432679588609
+        lats[536] = 52.26713391340153
+        lats[537] = 52.196835147203096
+        lats[538] = 52.126536380993372
+        lats[539] = 52.056237614772435
+        lats[540] = 51.985938848540336
+        lats[541] = 51.915640082297152
+        lats[542] = 51.845341316042933
+        lats[543] = 51.775042549777737
+        lats[544] = 51.704743783501634
+        lats[545] = 51.634445017214695
+        lats[546] = 51.56414625091697
+        lats[547] = 51.493847484608516
+        lats[548] = 51.423548718289396
+        lats[549] = 51.353249951959683
+        lats[550] = 51.282951185619417
+        lats[551] = 51.21265241926865
+        lats[552] = 51.14235365290746
+        lats[553] = 51.072054886535909
+        lats[554] = 51.001756120154049
+        lats[555] = 50.931457353761914
+        lats[556] = 50.86115858735959
+        lats[557] = 50.790859820947119
+        lats[558] = 50.720561054524559
+        lats[559] = 50.650262288091959
+        lats[560] = 50.579963521649397
+        lats[561] = 50.509664755196901
+        lats[562] = 50.439365988734544
+        lats[563] = 50.369067222262359
+        lats[564] = 50.298768455780426
+        lats[565] = 50.228469689288779
+        lats[566] = 50.158170922787484
+        lats[567] = 50.087872156276575
+        lats[568] = 50.017573389756123
+        lats[569] = 49.947274623226157
+        lats[570] = 49.876975856686762
+        lats[571] = 49.80667709013796
+        lats[572] = 49.736378323579807
+        lats[573] = 49.66607955701236
+        lats[574] = 49.595780790435676
+        lats[575] = 49.525482023849783
+        lats[576] = 49.455183257254745
+        lats[577] = 49.384884490650613
+        lats[578] = 49.314585724037435
+        lats[579] = 49.244286957415234
+        lats[580] = 49.173988190784094
+        lats[581] = 49.103689424144044
+        lats[582] = 49.03339065749514
+        lats[583] = 48.963091890837418
+        lats[584] = 48.892793124170929
+        lats[585] = 48.822494357495721
+        lats[586] = 48.752195590811837
+        lats[587] = 48.681896824119335
+        lats[588] = 48.611598057418242
+        lats[589] = 48.541299290708608
+        lats[590] = 48.47100052399049
+        lats[591] = 48.400701757263917
+        lats[592] = 48.330402990528938
+        lats[593] = 48.260104223785596
+        lats[594] = 48.189805457033941
+        lats[595] = 48.119506690274015
+        lats[596] = 48.049207923505868
+        lats[597] = 47.978909156729507
+        lats[598] = 47.908610389945018
+        lats[599] = 47.838311623152421
+        lats[600] = 47.76801285635176
+        lats[601] = 47.697714089543084
+        lats[602] = 47.627415322726435
+        lats[603] = 47.557116555901828
+        lats[604] = 47.486817789069342
+        lats[605] = 47.416519022228997
+        lats[606] = 47.346220255380835
+        lats[607] = 47.275921488524894
+        lats[608] = 47.205622721661214
+        lats[609] = 47.13532395478984
+        lats[610] = 47.065025187910805
+        lats[611] = 46.994726421024154
+        lats[612] = 46.924427654129929
+        lats[613] = 46.85412888722815
+        lats[614] = 46.783830120318882
+        lats[615] = 46.713531353402139
+        lats[616] = 46.643232586477971
+        lats[617] = 46.572933819546414
+        lats[618] = 46.502635052607502
+        lats[619] = 46.432336285661272
+        lats[620] = 46.362037518707766
+        lats[621] = 46.291738751747012
+        lats[622] = 46.221439984779053
+        lats[623] = 46.151141217803925
+        lats[624] = 46.080842450821663
+        lats[625] = 46.01054368383231
+        lats[626] = 45.94024491683588
+        lats[627] = 45.869946149832437
+        lats[628] = 45.799647382821995
+        lats[629] = 45.729348615804589
+        lats[630] = 45.659049848780263
+        lats[631] = 45.588751081749038
+        lats[632] = 45.51845231471097
+        lats[633] = 45.448153547666081
+        lats[634] = 45.377854780614399
+        lats[635] = 45.30755601355596
+        lats[636] = 45.237257246490813
+        lats[637] = 45.166958479418959
+        lats[638] = 45.096659712340461
+        lats[639] = 45.026360945255341
+        lats[640] = 44.956062178163634
+        lats[641] = 44.885763411065362
+        lats[642] = 44.81546464396056
+        lats[643] = 44.745165876849271
+        lats[644] = 44.674867109731515
+        lats[645] = 44.604568342607337
+        lats[646] = 44.534269575476756
+        lats[647] = 44.463970808339802
+        lats[648] = 44.39367204119651
+        lats[649] = 44.323373274046915
+        lats[650] = 44.253074506891046
+        lats[651] = 44.182775739728925
+        lats[652] = 44.112476972560586
+        lats[653] = 44.042178205386072
+        lats[654] = 43.971879438205391
+        lats[655] = 43.9015806710186
+        lats[656] = 43.831281903825705
+        lats[657] = 43.760983136626741
+        lats[658] = 43.690684369421732
+        lats[659] = 43.620385602210717
+        lats[660] = 43.550086834993728
+        lats[661] = 43.479788067770777
+        lats[662] = 43.409489300541907
+        lats[663] = 43.339190533307139
+        lats[664] = 43.26889176606651
+        lats[665] = 43.19859299882004
+        lats[666] = 43.128294231567757
+        lats[667] = 43.057995464309691
+        lats[668] = 42.987696697045862
+        lats[669] = 42.917397929776307
+        lats[670] = 42.847099162501053
+        lats[671] = 42.776800395220121
+        lats[672] = 42.706501627933541
+        lats[673] = 42.63620286064134
+        lats[674] = 42.565904093343548
+        lats[675] = 42.495605326040177
+        lats[676] = 42.425306558731272
+        lats[677] = 42.355007791416853
+        lats[678] = 42.284709024096927
+        lats[679] = 42.214410256771551
+        lats[680] = 42.144111489440725
+        lats[681] = 42.073812722104492
+        lats[682] = 42.003513954762873
+        lats[683] = 41.933215187415882
+        lats[684] = 41.862916420063563
+        lats[685] = 41.792617652705921
+        lats[686] = 41.722318885343
+        lats[687] = 41.6520201179748
+        lats[688] = 41.581721350601363
+        lats[689] = 41.511422583222718
+        lats[690] = 41.441123815838885
+        lats[691] = 41.370825048449873
+        lats[692] = 41.300526281055724
+        lats[693] = 41.230227513656445
+        lats[694] = 41.159928746252085
+        lats[695] = 41.089629978842645
+        lats[696] = 41.01933121142816
+        lats[697] = 40.949032444008644
+        lats[698] = 40.878733676584126
+        lats[699] = 40.808434909154634
+        lats[700] = 40.738136141720176
+        lats[701] = 40.667837374280786
+        lats[702] = 40.597538606836487
+        lats[703] = 40.527239839387299
+        lats[704] = 40.456941071933244
+        lats[705] = 40.386642304474343
+        lats[706] = 40.316343537010617
+        lats[707] = 40.246044769542102
+        lats[708] = 40.175746002068806
+        lats[709] = 40.105447234590748
+        lats[710] = 40.035148467107952
+        lats[711] = 39.964849699620437
+        lats[712] = 39.894550932128247
+        lats[713] = 39.824252164631375
+        lats[714] = 39.753953397129855
+        lats[715] = 39.683654629623703
+        lats[716] = 39.613355862112947
+        lats[717] = 39.543057094597607
+        lats[718] = 39.472758327077692
+        lats[719] = 39.402459559553229
+        lats[720] = 39.332160792024254
+        lats[721] = 39.261862024490775
+        lats[722] = 39.191563256952804
+        lats[723] = 39.121264489410365
+        lats[724] = 39.050965721863491
+        lats[725] = 38.980666954312184
+        lats[726] = 38.910368186756479
+        lats[727] = 38.840069419196389
+        lats[728] = 38.769770651631937
+        lats[729] = 38.699471884063136
+        lats[730] = 38.629173116490001
+        lats[731] = 38.558874348912568
+        lats[732] = 38.488575581330842
+        lats[733] = 38.418276813744846
+        lats[734] = 38.347978046154608
+        lats[735] = 38.277679278560143
+        lats[736] = 38.20738051096145
+        lats[737] = 38.137081743358586
+        lats[738] = 38.066782975751536
+        lats[739] = 37.99648420814033
+        lats[740] = 37.926185440524989
+        lats[741] = 37.855886672905527
+        lats[742] = 37.785587905281965
+        lats[743] = 37.715289137654317
+        lats[744] = 37.644990370022605
+        lats[745] = 37.574691602386856
+        lats[746] = 37.504392834747065
+        lats[747] = 37.434094067103274
+        lats[748] = 37.363795299455489
+        lats[749] = 37.293496531803719
+        lats[750] = 37.223197764147997
+        lats[751] = 37.152898996488332
+        lats[752] = 37.082600228824752
+        lats[753] = 37.012301461157264
+        lats[754] = 36.942002693485883
+        lats[755] = 36.871703925810628
+        lats[756] = 36.801405158131523
+        lats[757] = 36.731106390448581
+        lats[758] = 36.660807622761808
+        lats[759] = 36.590508855071242
+        lats[760] = 36.520210087376888
+        lats[761] = 36.449911319678755
+        lats[762] = 36.379612551976876
+        lats[763] = 36.309313784271254
+        lats[764] = 36.239015016561908
+        lats[765] = 36.16871624884886
+        lats[766] = 36.098417481132117
+        lats[767] = 36.028118713411708
+        lats[768] = 35.957819945687639
+        lats[769] = 35.887521177959933
+        lats[770] = 35.817222410228595
+        lats[771] = 35.746923642493655
+        lats[772] = 35.676624874755113
+        lats[773] = 35.606326107012997
+        lats[774] = 35.536027339267314
+        lats[775] = 35.465728571518085
+        lats[776] = 35.395429803765317
+        lats[777] = 35.325131036009047
+        lats[778] = 35.254832268249267
+        lats[779] = 35.184533500486005
+        lats[780] = 35.114234732719261
+        lats[781] = 35.043935964949064
+        lats[782] = 34.973637197175435
+        lats[783] = 34.903338429398374
+        lats[784] = 34.833039661617903
+        lats[785] = 34.762740893834028
+        lats[786] = 34.692442126046771
+        lats[787] = 34.622143358256153
+        lats[788] = 34.551844590462188
+        lats[789] = 34.481545822664863
+        lats[790] = 34.411247054864234
+        lats[791] = 34.340948287060286
+        lats[792] = 34.270649519253041
+        lats[793] = 34.200350751442521
+        lats[794] = 34.130051983628725
+        lats[795] = 34.059753215811682
+        lats[796] = 33.989454447991392
+        lats[797] = 33.919155680167876
+        lats[798] = 33.848856912341155
+        lats[799] = 33.778558144511237
+        lats[800] = 33.708259376678136
+        lats[801] = 33.637960608841851
+        lats[802] = 33.567661841002426
+        lats[803] = 33.497363073159853
+        lats[804] = 33.42706430531414
+        lats[805] = 33.356765537465314
+        lats[806] = 33.286466769613391
+        lats[807] = 33.216168001758369
+        lats[808] = 33.145869233900278
+        lats[809] = 33.075570466039117
+        lats[810] = 33.005271698174909
+        lats[811] = 32.934972930307666
+        lats[812] = 32.864674162437396
+        lats[813] = 32.794375394564113
+        lats[814] = 32.724076626687825
+        lats[815] = 32.653777858808567
+        lats[816] = 32.583479090926325
+        lats[817] = 32.513180323041112
+        lats[818] = 32.442881555152965
+        lats[819] = 32.372582787261891
+        lats[820] = 32.302284019367875
+        lats[821] = 32.231985251470959
+        lats[822] = 32.161686483571145
+        lats[823] = 32.091387715668439
+        lats[824] = 32.021088947762863
+        lats[825] = 31.950790179854422
+        lats[826] = 31.880491411943137
+        lats[827] = 31.810192644029012
+        lats[828] = 31.739893876112063
+        lats[829] = 31.669595108192297
+        lats[830] = 31.599296340269738
+        lats[831] = 31.528997572344384
+        lats[832] = 31.458698804416255
+        lats[833] = 31.388400036485361
+        lats[834] = 31.318101268551715
+        lats[835] = 31.247802500615318
+        lats[836] = 31.177503732676204
+        lats[837] = 31.107204964734358
+        lats[838] = 31.036906196789811
+        lats[839] = 30.966607428842572
+        lats[840] = 30.896308660892647
+        lats[841] = 30.826009892940046
+        lats[842] = 30.755711124984781
+        lats[843] = 30.685412357026873
+        lats[844] = 30.615113589066322
+        lats[845] = 30.544814821103138
+        lats[846] = 30.47451605313735
+        lats[847] = 30.404217285168947
+        lats[848] = 30.333918517197947
+        lats[849] = 30.263619749224372
+        lats[850] = 30.19332098124822
+        lats[851] = 30.123022213269511
+        lats[852] = 30.052723445288244
+        lats[853] = 29.98242467730444
+        lats[854] = 29.91212590931811
+        lats[855] = 29.841827141329258
+        lats[856] = 29.771528373337894
+        lats[857] = 29.701229605344039
+        lats[858] = 29.630930837347698
+        lats[859] = 29.560632069348884
+        lats[860] = 29.490333301347597
+        lats[861] = 29.420034533343859
+        lats[862] = 29.349735765337677
+        lats[863] = 29.279436997329057
+        lats[864] = 29.209138229318015
+        lats[865] = 29.138839461304556
+        lats[866] = 29.068540693288696
+        lats[867] = 28.998241925270449
+        lats[868] = 28.927943157249814
+        lats[869] = 28.857644389226806
+        lats[870] = 28.787345621201432
+        lats[871] = 28.717046853173709
+        lats[872] = 28.646748085143642
+        lats[873] = 28.576449317111244
+        lats[874] = 28.506150549076519
+        lats[875] = 28.435851781039485
+        lats[876] = 28.365553013000145
+        lats[877] = 28.29525424495851
+        lats[878] = 28.224955476914594
+        lats[879] = 28.154656708868405
+        lats[880] = 28.084357940819952
+        lats[881] = 28.014059172769244
+        lats[882] = 27.94376040471629
+        lats[883] = 27.873461636661098
+        lats[884] = 27.803162868603682
+        lats[885] = 27.732864100544052
+        lats[886] = 27.662565332482213
+        lats[887] = 27.592266564418171
+        lats[888] = 27.521967796351948
+        lats[889] = 27.451669028283543
+        lats[890] = 27.381370260212968
+        lats[891] = 27.311071492140236
+        lats[892] = 27.240772724065348
+        lats[893] = 27.170473955988321
+        lats[894] = 27.100175187909159
+        lats[895] = 27.029876419827872
+        lats[896] = 26.959577651744471
+        lats[897] = 26.889278883658971
+        lats[898] = 26.818980115571364
+        lats[899] = 26.748681347481678
+        lats[900] = 26.678382579389908
+        lats[901] = 26.608083811296069
+        lats[902] = 26.53778504320017
+        lats[903] = 26.467486275102218
+        lats[904] = 26.397187507002222
+        lats[905] = 26.326888738900195
+        lats[906] = 26.256589970796135
+        lats[907] = 26.186291202690064
+        lats[908] = 26.115992434581983
+        lats[909] = 26.045693666471902
+        lats[910] = 25.975394898359827
+        lats[911] = 25.90509613024577
+        lats[912] = 25.834797362129745
+        lats[913] = 25.764498594011751
+        lats[914] = 25.694199825891793
+        lats[915] = 25.623901057769892
+        lats[916] = 25.553602289646051
+        lats[917] = 25.483303521520277
+        lats[918] = 25.413004753392578
+        lats[919] = 25.342705985262967
+        lats[920] = 25.272407217131445
+        lats[921] = 25.202108448998025
+        lats[922] = 25.13180968086272
+        lats[923] = 25.061510912725527
+        lats[924] = 24.991212144586456
+        lats[925] = 24.920913376445526
+        lats[926] = 24.850614608302738
+        lats[927] = 24.780315840158096
+        lats[928] = 24.710017072011613
+        lats[929] = 24.639718303863294
+        lats[930] = 24.569419535713152
+        lats[931] = 24.499120767561195
+        lats[932] = 24.428821999407425
+        lats[933] = 24.358523231251851
+        lats[934] = 24.288224463094483
+        lats[935] = 24.217925694935328
+        lats[936] = 24.1476269267744
+        lats[937] = 24.077328158611696
+        lats[938] = 24.007029390447226
+        lats[939] = 23.936730622281004
+        lats[940] = 23.866431854113038
+        lats[941] = 23.796133085943328
+        lats[942] = 23.725834317771888
+        lats[943] = 23.655535549598721
+        lats[944] = 23.585236781423838
+        lats[945] = 23.514938013247242
+        lats[946] = 23.444639245068949
+        lats[947] = 23.374340476888957
+        lats[948] = 23.304041708707278
+        lats[949] = 23.233742940523921
+        lats[950] = 23.163444172338895
+        lats[951] = 23.0931454041522
+        lats[952] = 23.022846635963852
+        lats[953] = 22.952547867773848
+        lats[954] = 22.882249099582204
+        lats[955] = 22.811950331388925
+        lats[956] = 22.741651563194019
+        lats[957] = 22.671352794997489
+        lats[958] = 22.60105402679935
+        lats[959] = 22.530755258599601
+        lats[960] = 22.460456490398254
+        lats[961] = 22.390157722195315
+        lats[962] = 22.319858953990789
+        lats[963] = 22.249560185784691
+        lats[964] = 22.179261417577013
+        lats[965] = 22.108962649367779
+        lats[966] = 22.038663881156989
+        lats[967] = 21.968365112944642
+        lats[968] = 21.898066344730758
+        lats[969] = 21.827767576515338
+        lats[970] = 21.757468808298391
+        lats[971] = 21.687170040079913
+        lats[972] = 21.616871271859928
+        lats[973] = 21.546572503638437
+        lats[974] = 21.47627373541544
+        lats[975] = 21.40597496719095
+        lats[976] = 21.335676198964972
+        lats[977] = 21.265377430737512
+        lats[978] = 21.195078662508585
+        lats[979] = 21.124779894278181
+        lats[980] = 21.054481126046323
+        lats[981] = 20.984182357813012
+        lats[982] = 20.913883589578251
+        lats[983] = 20.843584821342048
+        lats[984] = 20.773286053104417
+        lats[985] = 20.702987284865355
+        lats[986] = 20.632688516624874
+        lats[987] = 20.562389748382977
+        lats[988] = 20.492090980139672
+        lats[989] = 20.421792211894967
+        lats[990] = 20.35149344364887
+        lats[991] = 20.28119467540138
+        lats[992] = 20.210895907152516
+        lats[993] = 20.140597138902272
+        lats[994] = 20.070298370650661
+        lats[995] = 19.999999602397686
+        lats[996] = 19.929700834143357
+        lats[997] = 19.859402065887682
+        lats[998] = 19.789103297630657
+        lats[999] = 19.718804529372303
+        lats[1000] = 19.648505761112613
+        lats[1001] = 19.578206992851602
+        lats[1002] = 19.507908224589269
+        lats[1003] = 19.437609456325632
+        lats[1004] = 19.367310688060684
+        lats[1005] = 19.297011919794439
+        lats[1006] = 19.226713151526898
+        lats[1007] = 19.15641438325807
+        lats[1008] = 19.086115614987968
+        lats[1009] = 19.015816846716586
+        lats[1010] = 18.945518078443939
+        lats[1011] = 18.875219310170031
+        lats[1012] = 18.804920541894862
+        lats[1013] = 18.734621773618446
+        lats[1014] = 18.664323005340787
+        lats[1015] = 18.594024237061891
+        lats[1016] = 18.523725468781763
+        lats[1017] = 18.453426700500408
+        lats[1018] = 18.383127932217832
+        lats[1019] = 18.312829163934047
+        lats[1020] = 18.242530395649048
+        lats[1021] = 18.172231627362851
+        lats[1022] = 18.101932859075458
+        lats[1023] = 18.031634090786874
+        lats[1024] = 17.96133532249711
+        lats[1025] = 17.89103655420616
+        lats[1026] = 17.820737785914044
+        lats[1027] = 17.75043901762076
+        lats[1028] = 17.680140249326314
+        lats[1029] = 17.60984148103071
+        lats[1030] = 17.539542712733962
+        lats[1031] = 17.469243944436066
+        lats[1032] = 17.39894517613704
+        lats[1033] = 17.328646407836878
+        lats[1034] = 17.258347639535586
+        lats[1035] = 17.188048871233182
+        lats[1036] = 17.117750102929655
+        lats[1037] = 17.04745133462502
+        lats[1038] = 16.977152566319283
+        lats[1039] = 16.906853798012452
+        lats[1040] = 16.836555029704527
+        lats[1041] = 16.766256261395515
+        lats[1042] = 16.69595749308542
+        lats[1043] = 16.625658724774254
+        lats[1044] = 16.555359956462013
+        lats[1045] = 16.485061188148713
+        lats[1046] = 16.41476241983435
+        lats[1047] = 16.344463651518936
+        lats[1048] = 16.274164883202477
+        lats[1049] = 16.203866114884974
+        lats[1050] = 16.133567346566434
+        lats[1051] = 16.063268578246863
+        lats[1052] = 15.992969809926265
+        lats[1053] = 15.922671041604652
+        lats[1054] = 15.852372273282016
+        lats[1055] = 15.78207350495838
+        lats[1056] = 15.711774736633735
+        lats[1057] = 15.641475968308091
+        lats[1058] = 15.571177199981456
+        lats[1059] = 15.500878431653829
+        lats[1060] = 15.430579663325226
+        lats[1061] = 15.360280894995643
+        lats[1062] = 15.289982126665089
+        lats[1063] = 15.219683358333569
+        lats[1064] = 15.149384590001089
+        lats[1065] = 15.07908582166765
+        lats[1066] = 15.008787053333259
+        lats[1067] = 14.938488284997929
+        lats[1068] = 14.868189516661655
+        lats[1069] = 14.797890748324447
+        lats[1070] = 14.727591979986309
+        lats[1071] = 14.657293211647247
+        lats[1072] = 14.586994443307265
+        lats[1073] = 14.516695674966371
+        lats[1074] = 14.446396906624567
+        lats[1075] = 14.376098138281863
+        lats[1076] = 14.305799369938256
+        lats[1077] = 14.23550060159376
+        lats[1078] = 14.165201833248371
+        lats[1079] = 14.0949030649021
+        lats[1080] = 14.024604296554955
+        lats[1081] = 13.954305528206934
+        lats[1082] = 13.884006759858046
+        lats[1083] = 13.813707991508297
+        lats[1084] = 13.743409223157688
+        lats[1085] = 13.673110454806226
+        lats[1086] = 13.602811686453919
+        lats[1087] = 13.532512918100766
+        lats[1088] = 13.46221414974678
+        lats[1089] = 13.391915381391959
+        lats[1090] = 13.32161661303631
+        lats[1091] = 13.251317844679837
+        lats[1092] = 13.181019076322551
+        lats[1093] = 13.110720307964451
+        lats[1094] = 13.040421539605545
+        lats[1095] = 12.970122771245832
+        lats[1096] = 12.899824002885323
+        lats[1097] = 12.829525234524022
+        lats[1098] = 12.759226466161934
+        lats[1099] = 12.688927697799061
+        lats[1100] = 12.618628929435411
+        lats[1101] = 12.548330161070988
+        lats[1102] = 12.478031392705796
+        lats[1103] = 12.407732624339841
+        lats[1104] = 12.337433855973126
+        lats[1105] = 12.267135087605659
+        lats[1106] = 12.196836319237443
+        lats[1107] = 12.126537550868482
+        lats[1108] = 12.056238782498781
+        lats[1109] = 11.985940014128348
+        lats[1110] = 11.915641245757183
+        lats[1111] = 11.845342477385294
+        lats[1112] = 11.775043709012685
+        lats[1113] = 11.704744940639358
+        lats[1114] = 11.634446172265324
+        lats[1115] = 11.564147403890583
+        lats[1116] = 11.493848635515141
+        lats[1117] = 11.423549867139002
+        lats[1118] = 11.35325109876217
+        lats[1119] = 11.282952330384653
+        lats[1120] = 11.212653562006453
+        lats[1121] = 11.142354793627575
+        lats[1122] = 11.072056025248026
+        lats[1123] = 11.001757256867807
+        lats[1124] = 10.931458488486923
+        lats[1125] = 10.861159720105382
+        lats[1126] = 10.790860951723188
+        lats[1127] = 10.720562183340341
+        lats[1128] = 10.65026341495685
+        lats[1129] = 10.579964646572719
+        lats[1130] = 10.509665878187954
+        lats[1131] = 10.439367109802557
+        lats[1132] = 10.369068341416533
+        lats[1133] = 10.298769573029887
+        lats[1134] = 10.228470804642624
+        lats[1135] = 10.158172036254747
+        lats[1136] = 10.087873267866264
+        lats[1137] = 10.017574499477174
+        lats[1138] = 9.9472757310874869
+        lats[1139] = 9.8769769626972046
+        lats[1140] = 9.8066781943063344
+        lats[1141] = 9.7363794259148779
+        lats[1142] = 9.6660806575228388
+        lats[1143] = 9.5957818891302242
+        lats[1144] = 9.5254831207370376
+        lats[1145] = 9.4551843523432826
+        lats[1146] = 9.3848855839489662
+        lats[1147] = 9.3145868155540921
+        lats[1148] = 9.2442880471586619
+        lats[1149] = 9.1739892787626829
+        lats[1150] = 9.1036905103661585
+        lats[1151] = 9.0333917419690941
+        lats[1152] = 8.963092973571495
+        lats[1153] = 8.8927942051733631
+        lats[1154] = 8.8224954367747017
+        lats[1155] = 8.7521966683755217
+        lats[1156] = 8.6818978999758194
+        lats[1157] = 8.6115991315756055
+        lats[1158] = 8.5413003631748801
+        lats[1159] = 8.4710015947736537
+        lats[1160] = 8.4007028263719228
+        lats[1161] = 8.3304040579696963
+        lats[1162] = 8.2601052895669778
+        lats[1163] = 8.1898065211637725
+        lats[1164] = 8.1195077527600841
+        lats[1165] = 8.049208984355916
+        lats[1166] = 7.9789102159512737
+        lats[1167] = 7.9086114475461606
+        lats[1168] = 7.8383126791405831
+        lats[1169] = 7.7680139107345463
+        lats[1170] = 7.6977151423280494
+        lats[1171] = 7.6274163739210996
+        lats[1172] = 7.557117605513703
+        lats[1173] = 7.4868188371058624
+        lats[1174] = 7.4165200686975803
+        lats[1175] = 7.3462213002888648
+        lats[1176] = 7.2759225318797176
+        lats[1177] = 7.2056237634701441
+        lats[1178] = 7.1353249950601469
+        lats[1179] = 7.0650262266497315
+        lats[1180] = 6.994727458238903
+        lats[1181] = 6.924428689827665
+        lats[1182] = 6.8541299214160212
+        lats[1183] = 6.7838311530039768
+        lats[1184] = 6.7135323845915353
+        lats[1185] = 6.6432336161787013
+        lats[1186] = 6.5729348477654792
+        lats[1187] = 6.5026360793518734
+        lats[1188] = 6.4323373109378874
+        lats[1189] = 6.3620385425235257
+        lats[1190] = 6.2917397741087928
+        lats[1191] = 6.2214410056936931
+        lats[1192] = 6.151142237278231
+        lats[1193] = 6.0808434688624091
+        lats[1194] = 6.0105447004462347
+        lats[1195] = 5.9402459320297085
+        lats[1196] = 5.869947163612836
+        lats[1197] = 5.7996483951956233
+        lats[1198] = 5.729349626778073
+        lats[1199] = 5.6590508583601888
+        lats[1200] = 5.5887520899419751
+        lats[1201] = 5.5184533215234373
+        lats[1202] = 5.4481545531045787
+        lats[1203] = 5.3778557846854023
+        lats[1204] = 5.3075570162659149
+        lats[1205] = 5.2372582478461194
+        lats[1206] = 5.1669594794260192
+        lats[1207] = 5.0966607110056197
+        lats[1208] = 5.0263619425849244
+        lats[1209] = 4.9560631741639369
+        lats[1210] = 4.8857644057426626
+        lats[1211] = 4.8154656373211049
+        lats[1212] = 4.7451668688992683
+        lats[1213] = 4.6748681004771564
+        lats[1214] = 4.6045693320547736
+        lats[1215] = 4.5342705636321252
+        lats[1216] = 4.4639717952092139
+        lats[1217] = 4.3936730267860451
+        lats[1218] = 4.3233742583626205
+        lats[1219] = 4.2530754899389471
+        lats[1220] = 4.1827767215150269
+        lats[1221] = 4.1124779530908659
+        lats[1222] = 4.0421791846664661
+        lats[1223] = 3.9718804162418326
+        lats[1224] = 3.90158164781697
+        lats[1225] = 3.8312828793918823
+        lats[1226] = 3.7609841109665734
+        lats[1227] = 3.6906853425410477
+        lats[1228] = 3.6203865741153085
+        lats[1229] = 3.5500878056893601
+        lats[1230] = 3.4797890372632065
+        lats[1231] = 3.4094902688368531
+        lats[1232] = 3.339191500410303
+        lats[1233] = 3.2688927319835597
+        lats[1234] = 3.1985939635566285
+        lats[1235] = 3.1282951951295126
+        lats[1236] = 3.0579964267022164
+        lats[1237] = 2.9876976582747439
+        lats[1238] = 2.9173988898470999
+        lats[1239] = 2.8471001214192873
+        lats[1240] = 2.7768013529913107
+        lats[1241] = 2.7065025845631743
+        lats[1242] = 2.6362038161348824
+        lats[1243] = 2.5659050477064382
+        lats[1244] = 2.4956062792778466
+        lats[1245] = 2.4253075108491116
+        lats[1246] = 2.3550087424202366
+        lats[1247] = 2.2847099739912267
+        lats[1248] = 2.2144112055620848
+        lats[1249] = 2.1441124371328155
+        lats[1250] = 2.0738136687034232
+        lats[1251] = 2.0035149002739114
+        lats[1252] = 1.9332161318442849
+        lats[1253] = 1.8629173634145471
+        lats[1254] = 1.792618594984702
+        lats[1255] = 1.7223198265547539
+        lats[1256] = 1.6520210581247066
+        lats[1257] = 1.5817222896945646
+        lats[1258] = 1.5114235212643317
+        lats[1259] = 1.4411247528340119
+        lats[1260] = 1.3708259844036093
+        lats[1261] = 1.300527215973128
+        lats[1262] = 1.2302284475425722
+        lats[1263] = 1.1599296791119456
+        lats[1264] = 1.0896309106812523
+        lats[1265] = 1.0193321422504964
+        lats[1266] = 0.949033373819682
+        lats[1267] = 0.87873460538881287
+        lats[1268] = 0.80843583695789356
+        lats[1269] = 0.73813706852692773
+        lats[1270] = 0.66783830009591949
+        lats[1271] = 0.59753953166487306
+        lats[1272] = 0.52724076323379232
+        lats[1273] = 0.45694199480268116
+        lats[1274] = 0.3866432263715438
+        lats[1275] = 0.31634445794038429
+        lats[1276] = 0.24604568950920663
+        lats[1277] = 0.17574692107801482
+        lats[1278] = 0.10544815264681295
+        lats[1279] = 0.035149384215604956
+        lats[1280] = -0.035149384215604956
+        lats[1281] = -0.10544815264681295
+        lats[1282] = -0.17574692107801482
+        lats[1283] = -0.24604568950920663
+        lats[1284] = -0.31634445794038429
+        lats[1285] = -0.3866432263715438
+        lats[1286] = -0.45694199480268116
+        lats[1287] = -0.52724076323379232
+        lats[1288] = -0.59753953166487306
+        lats[1289] = -0.66783830009591949
+        lats[1290] = -0.73813706852692773
+        lats[1291] = -0.80843583695789356
+        lats[1292] = -0.87873460538881287
+        lats[1293] = -0.949033373819682
+        lats[1294] = -1.0193321422504964
+        lats[1295] = -1.0896309106812523
+        lats[1296] = -1.1599296791119456
+        lats[1297] = -1.2302284475425722
+        lats[1298] = -1.300527215973128
+        lats[1299] = -1.3708259844036093
+        lats[1300] = -1.4411247528340119
+        lats[1301] = -1.5114235212643317
+        lats[1302] = -1.5817222896945646
+        lats[1303] = -1.6520210581247066
+        lats[1304] = -1.7223198265547539
+        lats[1305] = -1.792618594984702
+        lats[1306] = -1.8629173634145471
+        lats[1307] = -1.9332161318442849
+        lats[1308] = -2.0035149002739114
+        lats[1309] = -2.0738136687034232
+        lats[1310] = -2.1441124371328155
+        lats[1311] = -2.2144112055620848
+        lats[1312] = -2.2847099739912267
+        lats[1313] = -2.3550087424202366
+        lats[1314] = -2.4253075108491116
+        lats[1315] = -2.4956062792778466
+        lats[1316] = -2.5659050477064382
+        lats[1317] = -2.6362038161348824
+        lats[1318] = -2.7065025845631743
+        lats[1319] = -2.7768013529913107
+        lats[1320] = -2.8471001214192873
+        lats[1321] = -2.9173988898470999
+        lats[1322] = -2.9876976582747439
+        lats[1323] = -3.0579964267022164
+        lats[1324] = -3.1282951951295126
+        lats[1325] = -3.1985939635566285
+        lats[1326] = -3.2688927319835597
+        lats[1327] = -3.339191500410303
+        lats[1328] = -3.4094902688368531
+        lats[1329] = -3.4797890372632065
+        lats[1330] = -3.5500878056893601
+        lats[1331] = -3.6203865741153085
+        lats[1332] = -3.6906853425410477
+        lats[1333] = -3.7609841109665734
+        lats[1334] = -3.8312828793918823
+        lats[1335] = -3.90158164781697
+        lats[1336] = -3.9718804162418326
+        lats[1337] = -4.0421791846664661
+        lats[1338] = -4.1124779530908659
+        lats[1339] = -4.1827767215150269
+        lats[1340] = -4.2530754899389471
+        lats[1341] = -4.3233742583626205
+        lats[1342] = -4.3936730267860451
+        lats[1343] = -4.4639717952092139
+        lats[1344] = -4.5342705636321252
+        lats[1345] = -4.6045693320547736
+        lats[1346] = -4.6748681004771564
+        lats[1347] = -4.7451668688992683
+        lats[1348] = -4.8154656373211049
+        lats[1349] = -4.8857644057426626
+        lats[1350] = -4.9560631741639369
+        lats[1351] = -5.0263619425849244
+        lats[1352] = -5.0966607110056197
+        lats[1353] = -5.1669594794260192
+        lats[1354] = -5.2372582478461194
+        lats[1355] = -5.3075570162659149
+        lats[1356] = -5.3778557846854023
+        lats[1357] = -5.4481545531045787
+        lats[1358] = -5.5184533215234373
+        lats[1359] = -5.5887520899419751
+        lats[1360] = -5.6590508583601888
+        lats[1361] = -5.729349626778073
+        lats[1362] = -5.7996483951956233
+        lats[1363] = -5.869947163612836
+        lats[1364] = -5.9402459320297085
+        lats[1365] = -6.0105447004462347
+        lats[1366] = -6.0808434688624091
+        lats[1367] = -6.151142237278231
+        lats[1368] = -6.2214410056936931
+        lats[1369] = -6.2917397741087928
+        lats[1370] = -6.3620385425235257
+        lats[1371] = -6.4323373109378874
+        lats[1372] = -6.5026360793518734
+        lats[1373] = -6.5729348477654792
+        lats[1374] = -6.6432336161787013
+        lats[1375] = -6.7135323845915353
+        lats[1376] = -6.7838311530039768
+        lats[1377] = -6.8541299214160212
+        lats[1378] = -6.924428689827665
+        lats[1379] = -6.994727458238903
+        lats[1380] = -7.0650262266497315
+        lats[1381] = -7.1353249950601469
+        lats[1382] = -7.2056237634701441
+        lats[1383] = -7.2759225318797176
+        lats[1384] = -7.3462213002888648
+        lats[1385] = -7.4165200686975803
+        lats[1386] = -7.4868188371058624
+        lats[1387] = -7.557117605513703
+        lats[1388] = -7.6274163739210996
+        lats[1389] = -7.6977151423280494
+        lats[1390] = -7.7680139107345463
+        lats[1391] = -7.8383126791405831
+        lats[1392] = -7.9086114475461606
+        lats[1393] = -7.9789102159512737
+        lats[1394] = -8.049208984355916
+        lats[1395] = -8.1195077527600841
+        lats[1396] = -8.1898065211637725
+        lats[1397] = -8.2601052895669778
+        lats[1398] = -8.3304040579696963
+        lats[1399] = -8.4007028263719228
+        lats[1400] = -8.4710015947736537
+        lats[1401] = -8.5413003631748801
+        lats[1402] = -8.6115991315756055
+        lats[1403] = -8.6818978999758194
+        lats[1404] = -8.7521966683755217
+        lats[1405] = -8.8224954367747017
+        lats[1406] = -8.8927942051733631
+        lats[1407] = -8.963092973571495
+        lats[1408] = -9.0333917419690941
+        lats[1409] = -9.1036905103661585
+        lats[1410] = -9.1739892787626829
+        lats[1411] = -9.2442880471586619
+        lats[1412] = -9.3145868155540921
+        lats[1413] = -9.3848855839489662
+        lats[1414] = -9.4551843523432826
+        lats[1415] = -9.5254831207370376
+        lats[1416] = -9.5957818891302242
+        lats[1417] = -9.6660806575228388
+        lats[1418] = -9.7363794259148779
+        lats[1419] = -9.8066781943063344
+        lats[1420] = -9.8769769626972046
+        lats[1421] = -9.9472757310874869
+        lats[1422] = -10.017574499477174
+        lats[1423] = -10.087873267866264
+        lats[1424] = -10.158172036254747
+        lats[1425] = -10.228470804642624
+        lats[1426] = -10.298769573029887
+        lats[1427] = -10.369068341416533
+        lats[1428] = -10.439367109802557
+        lats[1429] = -10.509665878187954
+        lats[1430] = -10.579964646572719
+        lats[1431] = -10.65026341495685
+        lats[1432] = -10.720562183340341
+        lats[1433] = -10.790860951723188
+        lats[1434] = -10.861159720105382
+        lats[1435] = -10.931458488486923
+        lats[1436] = -11.001757256867807
+        lats[1437] = -11.072056025248026
+        lats[1438] = -11.142354793627575
+        lats[1439] = -11.212653562006453
+        lats[1440] = -11.282952330384653
+        lats[1441] = -11.35325109876217
+        lats[1442] = -11.423549867139002
+        lats[1443] = -11.493848635515141
+        lats[1444] = -11.564147403890583
+        lats[1445] = -11.634446172265324
+        lats[1446] = -11.704744940639358
+        lats[1447] = -11.775043709012685
+        lats[1448] = -11.845342477385294
+        lats[1449] = -11.915641245757183
+        lats[1450] = -11.985940014128348
+        lats[1451] = -12.056238782498781
+        lats[1452] = -12.126537550868482
+        lats[1453] = -12.196836319237443
+        lats[1454] = -12.267135087605659
+        lats[1455] = -12.337433855973126
+        lats[1456] = -12.407732624339841
+        lats[1457] = -12.478031392705796
+        lats[1458] = -12.548330161070988
+        lats[1459] = -12.618628929435411
+        lats[1460] = -12.688927697799061
+        lats[1461] = -12.759226466161934
+        lats[1462] = -12.829525234524022
+        lats[1463] = -12.899824002885323
+        lats[1464] = -12.970122771245832
+        lats[1465] = -13.040421539605545
+        lats[1466] = -13.110720307964451
+        lats[1467] = -13.181019076322551
+        lats[1468] = -13.251317844679837
+        lats[1469] = -13.32161661303631
+        lats[1470] = -13.391915381391959
+        lats[1471] = -13.46221414974678
+        lats[1472] = -13.532512918100766
+        lats[1473] = -13.602811686453919
+        lats[1474] = -13.673110454806226
+        lats[1475] = -13.743409223157688
+        lats[1476] = -13.813707991508297
+        lats[1477] = -13.884006759858046
+        lats[1478] = -13.954305528206934
+        lats[1479] = -14.024604296554955
+        lats[1480] = -14.0949030649021
+        lats[1481] = -14.165201833248371
+        lats[1482] = -14.23550060159376
+        lats[1483] = -14.305799369938256
+        lats[1484] = -14.376098138281863
+        lats[1485] = -14.446396906624567
+        lats[1486] = -14.516695674966371
+        lats[1487] = -14.586994443307265
+        lats[1488] = -14.657293211647247
+        lats[1489] = -14.727591979986309
+        lats[1490] = -14.797890748324447
+        lats[1491] = -14.868189516661655
+        lats[1492] = -14.938488284997929
+        lats[1493] = -15.008787053333259
+        lats[1494] = -15.07908582166765
+        lats[1495] = -15.149384590001089
+        lats[1496] = -15.219683358333569
+        lats[1497] = -15.289982126665089
+        lats[1498] = -15.360280894995643
+        lats[1499] = -15.430579663325226
+        lats[1500] = -15.500878431653829
+        lats[1501] = -15.571177199981456
+        lats[1502] = -15.641475968308091
+        lats[1503] = -15.711774736633735
+        lats[1504] = -15.78207350495838
+        lats[1505] = -15.852372273282016
+        lats[1506] = -15.922671041604652
+        lats[1507] = -15.992969809926265
+        lats[1508] = -16.063268578246863
+        lats[1509] = -16.133567346566434
+        lats[1510] = -16.203866114884974
+        lats[1511] = -16.274164883202477
+        lats[1512] = -16.344463651518936
+        lats[1513] = -16.41476241983435
+        lats[1514] = -16.485061188148713
+        lats[1515] = -16.555359956462013
+        lats[1516] = -16.625658724774254
+        lats[1517] = -16.69595749308542
+        lats[1518] = -16.766256261395515
+        lats[1519] = -16.836555029704527
+        lats[1520] = -16.906853798012452
+        lats[1521] = -16.977152566319283
+        lats[1522] = -17.04745133462502
+        lats[1523] = -17.117750102929655
+        lats[1524] = -17.188048871233182
+        lats[1525] = -17.258347639535586
+        lats[1526] = -17.328646407836878
+        lats[1527] = -17.39894517613704
+        lats[1528] = -17.469243944436066
+        lats[1529] = -17.539542712733962
+        lats[1530] = -17.60984148103071
+        lats[1531] = -17.680140249326314
+        lats[1532] = -17.75043901762076
+        lats[1533] = -17.820737785914044
+        lats[1534] = -17.89103655420616
+        lats[1535] = -17.96133532249711
+        lats[1536] = -18.031634090786874
+        lats[1537] = -18.101932859075458
+        lats[1538] = -18.172231627362851
+        lats[1539] = -18.242530395649048
+        lats[1540] = -18.312829163934047
+        lats[1541] = -18.383127932217832
+        lats[1542] = -18.453426700500408
+        lats[1543] = -18.523725468781763
+        lats[1544] = -18.594024237061891
+        lats[1545] = -18.664323005340787
+        lats[1546] = -18.734621773618446
+        lats[1547] = -18.804920541894862
+        lats[1548] = -18.875219310170031
+        lats[1549] = -18.945518078443939
+        lats[1550] = -19.015816846716586
+        lats[1551] = -19.086115614987968
+        lats[1552] = -19.15641438325807
+        lats[1553] = -19.226713151526898
+        lats[1554] = -19.297011919794439
+        lats[1555] = -19.367310688060684
+        lats[1556] = -19.437609456325632
+        lats[1557] = -19.507908224589269
+        lats[1558] = -19.578206992851602
+        lats[1559] = -19.648505761112613
+        lats[1560] = -19.718804529372303
+        lats[1561] = -19.789103297630657
+        lats[1562] = -19.859402065887682
+        lats[1563] = -19.929700834143357
+        lats[1564] = -19.999999602397686
+        lats[1565] = -20.070298370650661
+        lats[1566] = -20.140597138902272
+        lats[1567] = -20.210895907152516
+        lats[1568] = -20.28119467540138
+        lats[1569] = -20.35149344364887
+        lats[1570] = -20.421792211894967
+        lats[1571] = -20.492090980139672
+        lats[1572] = -20.562389748382977
+        lats[1573] = -20.632688516624874
+        lats[1574] = -20.702987284865355
+        lats[1575] = -20.773286053104417
+        lats[1576] = -20.843584821342048
+        lats[1577] = -20.913883589578251
+        lats[1578] = -20.984182357813012
+        lats[1579] = -21.054481126046323
+        lats[1580] = -21.124779894278181
+        lats[1581] = -21.195078662508585
+        lats[1582] = -21.265377430737512
+        lats[1583] = -21.335676198964972
+        lats[1584] = -21.40597496719095
+        lats[1585] = -21.47627373541544
+        lats[1586] = -21.546572503638437
+        lats[1587] = -21.616871271859928
+        lats[1588] = -21.687170040079913
+        lats[1589] = -21.757468808298391
+        lats[1590] = -21.827767576515338
+        lats[1591] = -21.898066344730758
+        lats[1592] = -21.968365112944642
+        lats[1593] = -22.038663881156989
+        lats[1594] = -22.108962649367779
+        lats[1595] = -22.179261417577013
+        lats[1596] = -22.249560185784691
+        lats[1597] = -22.319858953990789
+        lats[1598] = -22.390157722195315
+        lats[1599] = -22.460456490398254
+        lats[1600] = -22.530755258599601
+        lats[1601] = -22.60105402679935
+        lats[1602] = -22.671352794997489
+        lats[1603] = -22.741651563194019
+        lats[1604] = -22.811950331388925
+        lats[1605] = -22.882249099582204
+        lats[1606] = -22.952547867773848
+        lats[1607] = -23.022846635963852
+        lats[1608] = -23.0931454041522
+        lats[1609] = -23.163444172338895
+        lats[1610] = -23.233742940523921
+        lats[1611] = -23.304041708707278
+        lats[1612] = -23.374340476888957
+        lats[1613] = -23.444639245068949
+        lats[1614] = -23.514938013247242
+        lats[1615] = -23.585236781423838
+        lats[1616] = -23.655535549598721
+        lats[1617] = -23.725834317771888
+        lats[1618] = -23.796133085943328
+        lats[1619] = -23.866431854113038
+        lats[1620] = -23.936730622281004
+        lats[1621] = -24.007029390447226
+        lats[1622] = -24.077328158611696
+        lats[1623] = -24.1476269267744
+        lats[1624] = -24.217925694935328
+        lats[1625] = -24.288224463094483
+        lats[1626] = -24.358523231251851
+        lats[1627] = -24.428821999407425
+        lats[1628] = -24.499120767561195
+        lats[1629] = -24.569419535713152
+        lats[1630] = -24.639718303863294
+        lats[1631] = -24.710017072011613
+        lats[1632] = -24.780315840158096
+        lats[1633] = -24.850614608302738
+        lats[1634] = -24.920913376445526
+        lats[1635] = -24.991212144586456
+        lats[1636] = -25.061510912725527
+        lats[1637] = -25.13180968086272
+        lats[1638] = -25.202108448998025
+        lats[1639] = -25.272407217131445
+        lats[1640] = -25.342705985262967
+        lats[1641] = -25.413004753392578
+        lats[1642] = -25.483303521520277
+        lats[1643] = -25.553602289646051
+        lats[1644] = -25.623901057769892
+        lats[1645] = -25.694199825891793
+        lats[1646] = -25.764498594011751
+        lats[1647] = -25.834797362129745
+        lats[1648] = -25.90509613024577
+        lats[1649] = -25.975394898359827
+        lats[1650] = -26.045693666471902
+        lats[1651] = -26.115992434581983
+        lats[1652] = -26.186291202690064
+        lats[1653] = -26.256589970796135
+        lats[1654] = -26.326888738900195
+        lats[1655] = -26.397187507002222
+        lats[1656] = -26.467486275102218
+        lats[1657] = -26.53778504320017
+        lats[1658] = -26.608083811296069
+        lats[1659] = -26.678382579389908
+        lats[1660] = -26.748681347481678
+        lats[1661] = -26.818980115571364
+        lats[1662] = -26.889278883658971
+        lats[1663] = -26.959577651744471
+        lats[1664] = -27.029876419827872
+        lats[1665] = -27.100175187909159
+        lats[1666] = -27.170473955988321
+        lats[1667] = -27.240772724065348
+        lats[1668] = -27.311071492140236
+        lats[1669] = -27.381370260212968
+        lats[1670] = -27.451669028283543
+        lats[1671] = -27.521967796351948
+        lats[1672] = -27.592266564418171
+        lats[1673] = -27.662565332482213
+        lats[1674] = -27.732864100544052
+        lats[1675] = -27.803162868603682
+        lats[1676] = -27.873461636661098
+        lats[1677] = -27.94376040471629
+        lats[1678] = -28.014059172769244
+        lats[1679] = -28.084357940819952
+        lats[1680] = -28.154656708868405
+        lats[1681] = -28.224955476914594
+        lats[1682] = -28.29525424495851
+        lats[1683] = -28.365553013000145
+        lats[1684] = -28.435851781039485
+        lats[1685] = -28.506150549076519
+        lats[1686] = -28.576449317111244
+        lats[1687] = -28.646748085143642
+        lats[1688] = -28.717046853173709
+        lats[1689] = -28.787345621201432
+        lats[1690] = -28.857644389226806
+        lats[1691] = -28.927943157249814
+        lats[1692] = -28.998241925270449
+        lats[1693] = -29.068540693288696
+        lats[1694] = -29.138839461304556
+        lats[1695] = -29.209138229318015
+        lats[1696] = -29.279436997329057
+        lats[1697] = -29.349735765337677
+        lats[1698] = -29.420034533343859
+        lats[1699] = -29.490333301347597
+        lats[1700] = -29.560632069348884
+        lats[1701] = -29.630930837347698
+        lats[1702] = -29.701229605344039
+        lats[1703] = -29.771528373337894
+        lats[1704] = -29.841827141329258
+        lats[1705] = -29.91212590931811
+        lats[1706] = -29.98242467730444
+        lats[1707] = -30.052723445288244
+        lats[1708] = -30.123022213269511
+        lats[1709] = -30.19332098124822
+        lats[1710] = -30.263619749224372
+        lats[1711] = -30.333918517197947
+        lats[1712] = -30.404217285168947
+        lats[1713] = -30.47451605313735
+        lats[1714] = -30.544814821103138
+        lats[1715] = -30.615113589066322
+        lats[1716] = -30.685412357026873
+        lats[1717] = -30.755711124984781
+        lats[1718] = -30.826009892940046
+        lats[1719] = -30.896308660892647
+        lats[1720] = -30.966607428842572
+        lats[1721] = -31.036906196789811
+        lats[1722] = -31.107204964734358
+        lats[1723] = -31.177503732676204
+        lats[1724] = -31.247802500615318
+        lats[1725] = -31.318101268551715
+        lats[1726] = -31.388400036485361
+        lats[1727] = -31.458698804416255
+        lats[1728] = -31.528997572344384
+        lats[1729] = -31.599296340269738
+        lats[1730] = -31.669595108192297
+        lats[1731] = -31.739893876112063
+        lats[1732] = -31.810192644029012
+        lats[1733] = -31.880491411943137
+        lats[1734] = -31.950790179854422
+        lats[1735] = -32.021088947762863
+        lats[1736] = -32.091387715668439
+        lats[1737] = -32.161686483571145
+        lats[1738] = -32.231985251470959
+        lats[1739] = -32.302284019367875
+        lats[1740] = -32.372582787261891
+        lats[1741] = -32.442881555152965
+        lats[1742] = -32.513180323041112
+        lats[1743] = -32.583479090926325
+        lats[1744] = -32.653777858808567
+        lats[1745] = -32.724076626687825
+        lats[1746] = -32.794375394564113
+        lats[1747] = -32.864674162437396
+        lats[1748] = -32.934972930307666
+        lats[1749] = -33.005271698174909
+        lats[1750] = -33.075570466039117
+        lats[1751] = -33.145869233900278
+        lats[1752] = -33.216168001758369
+        lats[1753] = -33.286466769613391
+        lats[1754] = -33.356765537465314
+        lats[1755] = -33.42706430531414
+        lats[1756] = -33.497363073159853
+        lats[1757] = -33.567661841002426
+        lats[1758] = -33.637960608841851
+        lats[1759] = -33.708259376678136
+        lats[1760] = -33.778558144511237
+        lats[1761] = -33.848856912341155
+        lats[1762] = -33.919155680167876
+        lats[1763] = -33.989454447991392
+        lats[1764] = -34.059753215811682
+        lats[1765] = -34.130051983628725
+        lats[1766] = -34.200350751442521
+        lats[1767] = -34.270649519253041
+        lats[1768] = -34.340948287060286
+        lats[1769] = -34.411247054864234
+        lats[1770] = -34.481545822664863
+        lats[1771] = -34.551844590462188
+        lats[1772] = -34.622143358256153
+        lats[1773] = -34.692442126046771
+        lats[1774] = -34.762740893834028
+        lats[1775] = -34.833039661617903
+        lats[1776] = -34.903338429398374
+        lats[1777] = -34.973637197175435
+        lats[1778] = -35.043935964949064
+        lats[1779] = -35.114234732719261
+        lats[1780] = -35.184533500486005
+        lats[1781] = -35.254832268249267
+        lats[1782] = -35.325131036009047
+        lats[1783] = -35.395429803765317
+        lats[1784] = -35.465728571518085
+        lats[1785] = -35.536027339267314
+        lats[1786] = -35.606326107012997
+        lats[1787] = -35.676624874755113
+        lats[1788] = -35.746923642493655
+        lats[1789] = -35.817222410228595
+        lats[1790] = -35.887521177959933
+        lats[1791] = -35.957819945687639
+        lats[1792] = -36.028118713411708
+        lats[1793] = -36.098417481132117
+        lats[1794] = -36.16871624884886
+        lats[1795] = -36.239015016561908
+        lats[1796] = -36.309313784271254
+        lats[1797] = -36.379612551976876
+        lats[1798] = -36.449911319678755
+        lats[1799] = -36.520210087376888
+        lats[1800] = -36.590508855071242
+        lats[1801] = -36.660807622761808
+        lats[1802] = -36.731106390448581
+        lats[1803] = -36.801405158131523
+        lats[1804] = -36.871703925810628
+        lats[1805] = -36.942002693485883
+        lats[1806] = -37.012301461157264
+        lats[1807] = -37.082600228824752
+        lats[1808] = -37.152898996488332
+        lats[1809] = -37.223197764147997
+        lats[1810] = -37.293496531803719
+        lats[1811] = -37.363795299455489
+        lats[1812] = -37.434094067103274
+        lats[1813] = -37.504392834747065
+        lats[1814] = -37.574691602386856
+        lats[1815] = -37.644990370022605
+        lats[1816] = -37.715289137654317
+        lats[1817] = -37.785587905281965
+        lats[1818] = -37.855886672905527
+        lats[1819] = -37.926185440524989
+        lats[1820] = -37.99648420814033
+        lats[1821] = -38.066782975751536
+        lats[1822] = -38.137081743358586
+        lats[1823] = -38.20738051096145
+        lats[1824] = -38.277679278560143
+        lats[1825] = -38.347978046154608
+        lats[1826] = -38.418276813744846
+        lats[1827] = -38.488575581330842
+        lats[1828] = -38.558874348912568
+        lats[1829] = -38.629173116490001
+        lats[1830] = -38.699471884063136
+        lats[1831] = -38.769770651631937
+        lats[1832] = -38.840069419196389
+        lats[1833] = -38.910368186756479
+        lats[1834] = -38.980666954312184
+        lats[1835] = -39.050965721863491
+        lats[1836] = -39.121264489410365
+        lats[1837] = -39.191563256952804
+        lats[1838] = -39.261862024490775
+        lats[1839] = -39.332160792024254
+        lats[1840] = -39.402459559553229
+        lats[1841] = -39.472758327077692
+        lats[1842] = -39.543057094597607
+        lats[1843] = -39.613355862112947
+        lats[1844] = -39.683654629623703
+        lats[1845] = -39.753953397129855
+        lats[1846] = -39.824252164631375
+        lats[1847] = -39.894550932128247
+        lats[1848] = -39.964849699620437
+        lats[1849] = -40.035148467107952
+        lats[1850] = -40.105447234590748
+        lats[1851] = -40.175746002068806
+        lats[1852] = -40.246044769542102
+        lats[1853] = -40.316343537010617
+        lats[1854] = -40.386642304474343
+        lats[1855] = -40.456941071933244
+        lats[1856] = -40.527239839387299
+        lats[1857] = -40.597538606836487
+        lats[1858] = -40.667837374280786
+        lats[1859] = -40.738136141720176
+        lats[1860] = -40.808434909154634
+        lats[1861] = -40.878733676584126
+        lats[1862] = -40.949032444008644
+        lats[1863] = -41.01933121142816
+        lats[1864] = -41.089629978842645
+        lats[1865] = -41.159928746252085
+        lats[1866] = -41.230227513656445
+        lats[1867] = -41.300526281055724
+        lats[1868] = -41.370825048449873
+        lats[1869] = -41.441123815838885
+        lats[1870] = -41.511422583222718
+        lats[1871] = -41.581721350601363
+        lats[1872] = -41.6520201179748
+        lats[1873] = -41.722318885343
+        lats[1874] = -41.792617652705921
+        lats[1875] = -41.862916420063563
+        lats[1876] = -41.933215187415882
+        lats[1877] = -42.003513954762873
+        lats[1878] = -42.073812722104492
+        lats[1879] = -42.144111489440725
+        lats[1880] = -42.214410256771551
+        lats[1881] = -42.284709024096927
+        lats[1882] = -42.355007791416853
+        lats[1883] = -42.425306558731272
+        lats[1884] = -42.495605326040177
+        lats[1885] = -42.565904093343548
+        lats[1886] = -42.63620286064134
+        lats[1887] = -42.706501627933541
+        lats[1888] = -42.776800395220121
+        lats[1889] = -42.847099162501053
+        lats[1890] = -42.917397929776307
+        lats[1891] = -42.987696697045862
+        lats[1892] = -43.057995464309691
+        lats[1893] = -43.128294231567757
+        lats[1894] = -43.19859299882004
+        lats[1895] = -43.26889176606651
+        lats[1896] = -43.339190533307139
+        lats[1897] = -43.409489300541907
+        lats[1898] = -43.479788067770777
+        lats[1899] = -43.550086834993728
+        lats[1900] = -43.620385602210717
+        lats[1901] = -43.690684369421732
+        lats[1902] = -43.760983136626741
+        lats[1903] = -43.831281903825705
+        lats[1904] = -43.9015806710186
+        lats[1905] = -43.971879438205391
+        lats[1906] = -44.042178205386072
+        lats[1907] = -44.112476972560586
+        lats[1908] = -44.182775739728925
+        lats[1909] = -44.253074506891046
+        lats[1910] = -44.323373274046915
+        lats[1911] = -44.39367204119651
+        lats[1912] = -44.463970808339802
+        lats[1913] = -44.534269575476756
+        lats[1914] = -44.604568342607337
+        lats[1915] = -44.674867109731515
+        lats[1916] = -44.745165876849271
+        lats[1917] = -44.81546464396056
+        lats[1918] = -44.885763411065362
+        lats[1919] = -44.956062178163634
+        lats[1920] = -45.026360945255341
+        lats[1921] = -45.096659712340461
+        lats[1922] = -45.166958479418959
+        lats[1923] = -45.237257246490813
+        lats[1924] = -45.30755601355596
+        lats[1925] = -45.377854780614399
+        lats[1926] = -45.448153547666081
+        lats[1927] = -45.51845231471097
+        lats[1928] = -45.588751081749038
+        lats[1929] = -45.659049848780263
+        lats[1930] = -45.729348615804589
+        lats[1931] = -45.799647382821995
+        lats[1932] = -45.869946149832437
+        lats[1933] = -45.94024491683588
+        lats[1934] = -46.01054368383231
+        lats[1935] = -46.080842450821663
+        lats[1936] = -46.151141217803925
+        lats[1937] = -46.221439984779053
+        lats[1938] = -46.291738751747012
+        lats[1939] = -46.362037518707766
+        lats[1940] = -46.432336285661272
+        lats[1941] = -46.502635052607502
+        lats[1942] = -46.572933819546414
+        lats[1943] = -46.643232586477971
+        lats[1944] = -46.713531353402139
+        lats[1945] = -46.783830120318882
+        lats[1946] = -46.85412888722815
+        lats[1947] = -46.924427654129929
+        lats[1948] = -46.994726421024154
+        lats[1949] = -47.065025187910805
+        lats[1950] = -47.13532395478984
+        lats[1951] = -47.205622721661214
+        lats[1952] = -47.275921488524894
+        lats[1953] = -47.346220255380835
+        lats[1954] = -47.416519022228997
+        lats[1955] = -47.486817789069342
+        lats[1956] = -47.557116555901828
+        lats[1957] = -47.627415322726435
+        lats[1958] = -47.697714089543084
+        lats[1959] = -47.76801285635176
+        lats[1960] = -47.838311623152421
+        lats[1961] = -47.908610389945018
+        lats[1962] = -47.978909156729507
+        lats[1963] = -48.049207923505868
+        lats[1964] = -48.119506690274015
+        lats[1965] = -48.189805457033941
+        lats[1966] = -48.260104223785596
+        lats[1967] = -48.330402990528938
+        lats[1968] = -48.400701757263917
+        lats[1969] = -48.47100052399049
+        lats[1970] = -48.541299290708608
+        lats[1971] = -48.611598057418242
+        lats[1972] = -48.681896824119335
+        lats[1973] = -48.752195590811837
+        lats[1974] = -48.822494357495721
+        lats[1975] = -48.892793124170929
+        lats[1976] = -48.963091890837418
+        lats[1977] = -49.03339065749514
+        lats[1978] = -49.103689424144044
+        lats[1979] = -49.173988190784094
+        lats[1980] = -49.244286957415234
+        lats[1981] = -49.314585724037435
+        lats[1982] = -49.384884490650613
+        lats[1983] = -49.455183257254745
+        lats[1984] = -49.525482023849783
+        lats[1985] = -49.595780790435676
+        lats[1986] = -49.66607955701236
+        lats[1987] = -49.736378323579807
+        lats[1988] = -49.80667709013796
+        lats[1989] = -49.876975856686762
+        lats[1990] = -49.947274623226157
+        lats[1991] = -50.017573389756123
+        lats[1992] = -50.087872156276575
+        lats[1993] = -50.158170922787484
+        lats[1994] = -50.228469689288779
+        lats[1995] = -50.298768455780426
+        lats[1996] = -50.369067222262359
+        lats[1997] = -50.439365988734544
+        lats[1998] = -50.509664755196901
+        lats[1999] = -50.579963521649397
+        lats[2000] = -50.650262288091959
+        lats[2001] = -50.720561054524559
+        lats[2002] = -50.790859820947119
+        lats[2003] = -50.86115858735959
+        lats[2004] = -50.931457353761914
+        lats[2005] = -51.001756120154049
+        lats[2006] = -51.072054886535909
+        lats[2007] = -51.14235365290746
+        lats[2008] = -51.21265241926865
+        lats[2009] = -51.282951185619417
+        lats[2010] = -51.353249951959683
+        lats[2011] = -51.423548718289396
+        lats[2012] = -51.493847484608516
+        lats[2013] = -51.56414625091697
+        lats[2014] = -51.634445017214695
+        lats[2015] = -51.704743783501634
+        lats[2016] = -51.775042549777737
+        lats[2017] = -51.845341316042933
+        lats[2018] = -51.915640082297152
+        lats[2019] = -51.985938848540336
+        lats[2020] = -52.056237614772435
+        lats[2021] = -52.126536380993372
+        lats[2022] = -52.196835147203096
+        lats[2023] = -52.26713391340153
+        lats[2024] = -52.337432679588609
+        lats[2025] = -52.407731445764284
+        lats[2026] = -52.478030211928477
+        lats[2027] = -52.548328978081123
+        lats[2028] = -52.618627744222159
+        lats[2029] = -52.688926510351514
+        lats[2030] = -52.759225276469131
+        lats[2031] = -52.829524042574917
+        lats[2032] = -52.899822808668837
+        lats[2033] = -52.970121574750792
+        lats[2034] = -53.040420340820731
+        lats[2035] = -53.110719106878584
+        lats[2036] = -53.181017872924265
+        lats[2037] = -53.251316638957725
+        lats[2038] = -53.321615404978871
+        lats[2039] = -53.391914170987633
+        lats[2040] = -53.462212936983953
+        lats[2041] = -53.53251170296776
+        lats[2042] = -53.602810468938962
+        lats[2043] = -53.673109234897495
+        lats[2044] = -53.743408000843282
+        lats[2045] = -53.813706766776235
+        lats[2046] = -53.884005532696307
+        lats[2047] = -53.954304298603383
+        lats[2048] = -54.024603064497434
+        lats[2049] = -54.094901830378333
+        lats[2050] = -54.165200596246031
+        lats[2051] = -54.235499362100448
+        lats[2052] = -54.305798127941479
+        lats[2053] = -54.376096893769081
+        lats[2054] = -54.446395659583146
+        lats[2055] = -54.516694425383605
+        lats[2056] = -54.586993191170357
+        lats[2057] = -54.657291956943347
+        lats[2058] = -54.727590722702473
+        lats[2059] = -54.797889488447652
+        lats[2060] = -54.868188254178797
+        lats[2061] = -54.938487019895831
+        lats[2062] = -55.008785785598668
+        lats[2063] = -55.07908455128721
+        lats[2064] = -55.149383316961377
+        lats[2065] = -55.219682082621084
+        lats[2066] = -55.289980848266232
+        lats[2067] = -55.360279613896743
+        lats[2068] = -55.430578379512511
+        lats[2069] = -55.500877145113449
+        lats[2070] = -55.571175910699488
+        lats[2071] = -55.641474676270505
+        lats[2072] = -55.711773441826416
+        lats[2073] = -55.782072207367136
+        lats[2074] = -55.852370972892551
+        lats[2075] = -55.922669738402583
+        lats[2076] = -55.992968503897131
+        lats[2077] = -56.063267269376091
+        lats[2078] = -56.133566034839362
+        lats[2079] = -56.203864800286865
+        lats[2080] = -56.274163565718467
+        lats[2081] = -56.34446233113411
+        lats[2082] = -56.41476109653366
+        lats[2083] = -56.485059861917016
+        lats[2084] = -56.555358627284086
+        lats[2085] = -56.625657392634771
+        lats[2086] = -56.695956157968951
+        lats[2087] = -56.766254923286517
+        lats[2088] = -56.836553688587379
+        lats[2089] = -56.90685245387143
+        lats[2090] = -56.977151219138541
+        lats[2091] = -57.047449984388614
+        lats[2092] = -57.117748749621541
+        lats[2093] = -57.188047514837208
+        lats[2094] = -57.258346280035504
+        lats[2095] = -57.328645045216312
+        lats[2096] = -57.398943810379521
+        lats[2097] = -57.469242575525016
+        lats[2098] = -57.539541340652676
+        lats[2099] = -57.60984010576238
+        lats[2100] = -57.680138870854037
+        lats[2101] = -57.75043763592749
+        lats[2102] = -57.820736400982646
+        lats[2103] = -57.891035166019364
+        lats[2104] = -57.961333931037537
+        lats[2105] = -58.031632696037022
+        lats[2106] = -58.101931461017728
+        lats[2107] = -58.172230225979497
+        lats[2108] = -58.242528990922203
+        lats[2109] = -58.312827755845746
+        lats[2110] = -58.383126520749968
+        lats[2111] = -58.453425285634758
+        lats[2112] = -58.523724050499972
+        lats[2113] = -58.594022815345468
+        lats[2114] = -58.664321580171141
+        lats[2115] = -58.73462034497684
+        lats[2116] = -58.804919109762423
+        lats[2117] = -58.875217874527763
+        lats[2118] = -58.945516639272725
+        lats[2119] = -59.015815403997145
+        lats[2120] = -59.086114168700909
+        lats[2121] = -59.156412933383855
+        lats[2122] = -59.226711698045854
+        lats[2123] = -59.29701046268675
+        lats[2124] = -59.3673092273064
+        lats[2125] = -59.43760799190467
+        lats[2126] = -59.507906756481383
+        lats[2127] = -59.578205521036402
+        lats[2128] = -59.64850428556958
+        lats[2129] = -59.718803050080759
+        lats[2130] = -59.78910181456979
+        lats[2131] = -59.859400579036503
+        lats[2132] = -59.929699343480763
+        lats[2133] = -59.999998107902378
+        lats[2134] = -60.070296872301235
+        lats[2135] = -60.140595636677112
+        lats[2136] = -60.21089440102989
+        lats[2137] = -60.28119316535939
+        lats[2138] = -60.35149192966545
+        lats[2139] = -60.421790693947884
+        lats[2140] = -60.492089458206543
+        lats[2141] = -60.562388222441243
+        lats[2142] = -60.632686986651805
+        lats[2143] = -60.702985750838074
+        lats[2144] = -60.773284514999872
+        lats[2145] = -60.843583279137007
+        lats[2146] = -60.913882043249295
+        lats[2147] = -60.984180807336578
+        lats[2148] = -61.054479571398652
+        lats[2149] = -61.124778335435344
+        lats[2150] = -61.195077099446451
+        lats[2151] = -61.265375863431785
+        lats[2152] = -61.335674627391185
+        lats[2153] = -61.405973391324409
+        lats[2154] = -61.476272155231321
+        lats[2155] = -61.546570919111666
+        lats[2156] = -61.616869682965287
+        lats[2157] = -61.687168446791986
+        lats[2158] = -61.757467210591535
+        lats[2159] = -61.827765974363729
+        lats[2160] = -61.898064738108381
+        lats[2161] = -61.968363501825259
+        lats[2162] = -62.038662265514176
+        lats[2163] = -62.108961029174914
+        lats[2164] = -62.179259792807258
+        lats[2165] = -62.249558556410982
+        lats[2166] = -62.319857319985871
+        lats[2167] = -62.3901560835317
+        lats[2168] = -62.460454847048261
+        lats[2169] = -62.530753610535321
+        lats[2170] = -62.60105237399263
+        lats[2171] = -62.67135113741999
+        lats[2172] = -62.741649900817137
+        lats[2173] = -62.811948664183866
+        lats[2174] = -62.882247427519928
+        lats[2175] = -62.952546190825068
+        lats[2176] = -63.022844954099064
+        lats[2177] = -63.093143717341647
+        lats[2178] = -63.163442480552604
+        lats[2179] = -63.23374124373165
+        lats[2180] = -63.304040006878537
+        lats[2181] = -63.374338769993031
+        lats[2182] = -63.444637533074854
+        lats[2183] = -63.514936296123757
+        lats[2184] = -63.585235059139464
+        lats[2185] = -63.655533822121711
+        lats[2186] = -63.725832585070251
+        lats[2187] = -63.796131347984762
+        lats[2188] = -63.866430110865004
+        lats[2189] = -63.93672887371072
+        lats[2190] = -64.00702763652157
+        lats[2191] = -64.07732639929732
+        lats[2192] = -64.147625162037642
+        lats[2193] = -64.21792392474228
+        lats[2194] = -64.288222687410922
+        lats[2195] = -64.358521450043284
+        lats[2196] = -64.428820212639039
+        lats[2197] = -64.499118975197902
+        lats[2198] = -64.569417737719576
+        lats[2199] = -64.639716500203733
+        lats[2200] = -64.710015262650074
+        lats[2201] = -64.780314025058246
+        lats[2202] = -64.850612787427963
+        lats[2203] = -64.920911549758912
+        lats[2204] = -64.991210312050711
+        lats[2205] = -65.061509074303089
+        lats[2206] = -65.131807836515677
+        lats[2207] = -65.202106598688133
+        lats[2208] = -65.272405360820116
+        lats[2209] = -65.342704122911286
+        lats[2210] = -65.413002884961315
+        lats[2211] = -65.483301646969792
+        lats[2212] = -65.553600408936404
+        lats[2213] = -65.623899170860767
+        lats[2214] = -65.694197932742526
+        lats[2215] = -65.764496694581283
+        lats[2216] = -65.834795456376696
+        lats[2217] = -65.905094218128355
+        lats[2218] = -65.975392979835888
+        lats[2219] = -66.045691741498899
+        lats[2220] = -66.115990503117033
+        lats[2221] = -66.186289264689833
+        lats[2222] = -66.256588026216932
+        lats[2223] = -66.326886787697887
+        lats[2224] = -66.397185549132331
+        lats[2225] = -66.467484310519808
+        lats[2226] = -66.537783071859891
+        lats[2227] = -66.608081833152212
+        lats[2228] = -66.678380594396273
+        lats[2229] = -66.748679355591662
+        lats[2230] = -66.818978116737924
+        lats[2231] = -66.889276877834618
+        lats[2232] = -66.95957563888129
+        lats[2233] = -67.029874399877471
+        lats[2234] = -67.100173160822706
+        lats[2235] = -67.170471921716526
+        lats[2236] = -67.240770682558434
+        lats[2237] = -67.311069443347961
+        lats[2238] = -67.381368204084609
+        lats[2239] = -67.451666964767895
+        lats[2240] = -67.521965725397308
+        lats[2241] = -67.592264485972336
+        lats[2242] = -67.662563246492482
+        lats[2243] = -67.732862006957205
+        lats[2244] = -67.803160767365966
+        lats[2245] = -67.873459527718282
+        lats[2246] = -67.943758288013555
+        lats[2247] = -68.014057048251274
+        lats[2248] = -68.084355808430871
+        lats[2249] = -68.154654568551791
+        lats[2250] = -68.224953328613438
+        lats[2251] = -68.295252088615257
+        lats[2252] = -68.365550848556666
+        lats[2253] = -68.435849608437067
+        lats[2254] = -68.506148368255865
+        lats[2255] = -68.576447128012447
+        lats[2256] = -68.646745887706189
+        lats[2257] = -68.717044647336493
+        lats[2258] = -68.787343406902693
+        lats[2259] = -68.85764216640419
+        lats[2260] = -68.927940925840304
+        lats[2261] = -68.998239685210365
+        lats[2262] = -69.068538444513763
+        lats[2263] = -69.138837203749759
+        lats[2264] = -69.209135962917699
+        lats[2265] = -69.279434722016902
+        lats[2266] = -69.349733481046613
+        lats[2267] = -69.420032240006194
+        lats[2268] = -69.490330998894862
+        lats[2269] = -69.560629757711908
+        lats[2270] = -69.630928516456592
+        lats[2271] = -69.701227275128161
+        lats[2272] = -69.771526033725834
+        lats[2273] = -69.841824792248843
+        lats[2274] = -69.912123550696421
+        lats[2275] = -69.982422309067744
+        lats[2276] = -70.052721067362043
+        lats[2277] = -70.123019825578467
+        lats[2278] = -70.193318583716191
+        lats[2279] = -70.263617341774406
+        lats[2280] = -70.333916099752187
+        lats[2281] = -70.404214857648739
+        lats[2282] = -70.474513615463138
+        lats[2283] = -70.544812373194532
+        lats[2284] = -70.615111130841967
+        lats[2285] = -70.685409888404578
+        lats[2286] = -70.755708645881384
+        lats[2287] = -70.826007403271475
+        lats[2288] = -70.896306160573886
+        lats[2289] = -70.966604917787635
+        lats[2290] = -71.036903674911756
+        lats[2291] = -71.107202431945211
+        lats[2292] = -71.177501188887007
+        lats[2293] = -71.247799945736105
+        lats[2294] = -71.318098702491469
+        lats[2295] = -71.388397459152031
+        lats[2296] = -71.458696215716685
+        lats[2297] = -71.528994972184378
+        lats[2298] = -71.599293728553988
+        lats[2299] = -71.669592484824364
+        lats[2300] = -71.739891240994368
+        lats[2301] = -71.810189997062835
+        lats[2302] = -71.880488753028587
+        lats[2303] = -71.950787508890414
+        lats[2304] = -72.02108626464711
+        lats[2305] = -72.091385020297409
+        lats[2306] = -72.161683775840089
+        lats[2307] = -72.231982531273843
+        lats[2308] = -72.302281286597392
+        lats[2309] = -72.3725800418094
+        lats[2310] = -72.442878796908545
+        lats[2311] = -72.513177551893421
+        lats[2312] = -72.583476306762691
+        lats[2313] = -72.653775061514935
+        lats[2314] = -72.724073816148703
+        lats[2315] = -72.794372570662574
+        lats[2316] = -72.864671325055056
+        lats[2317] = -72.934970079324657
+        lats[2318] = -73.005268833469799
+        lats[2319] = -73.075567587489019
+        lats[2320] = -73.145866341380668
+        lats[2321] = -73.216165095143182
+        lats[2322] = -73.2864638487749
+        lats[2323] = -73.356762602274188
+        lats[2324] = -73.427061355639339
+        lats[2325] = -73.497360108868662
+        lats[2326] = -73.567658861960396
+        lats[2327] = -73.637957614912779
+        lats[2328] = -73.70825636772399
+        lats[2329] = -73.778555120392184
+        lats[2330] = -73.848853872915541
+        lats[2331] = -73.919152625292114
+        lats[2332] = -73.98945137751997
+        lats[2333] = -74.059750129597163
+        lats[2334] = -74.13004888152166
+        lats[2335] = -74.200347633291472
+        lats[2336] = -74.270646384904481
+        lats[2337] = -74.340945136358584
+        lats[2338] = -74.411243887651622
+        lats[2339] = -74.481542638781434
+        lats[2340] = -74.551841389745761
+        lats[2341] = -74.622140140542356
+        lats[2342] = -74.692438891168877
+        lats[2343] = -74.762737641622991
+        lats[2344] = -74.833036391902269
+        lats[2345] = -74.903335142004323
+        lats[2346] = -74.973633891926625
+        lats[2347] = -75.043932641666672
+        lats[2348] = -75.114231391221821
+        lats[2349] = -75.184530140589501
+        lats[2350] = -75.254828889766983
+        lats[2351] = -75.325127638751567
+        lats[2352] = -75.395426387540439
+        lats[2353] = -75.465725136130786
+        lats[2354] = -75.536023884519707
+        lats[2355] = -75.60632263270422
+        lats[2356] = -75.67662138068134
+        lats[2357] = -75.746920128447996
+        lats[2358] = -75.81721887600105
+        lats[2359] = -75.887517623337317
+        lats[2360] = -75.957816370453543
+        lats[2361] = -76.028115117346374
+        lats[2362] = -76.098413864012443
+        lats[2363] = -76.16871261044831
+        lats[2364] = -76.239011356650423
+        lats[2365] = -76.3093101026152
+        lats[2366] = -76.379608848338933
+        lats[2367] = -76.449907593817869
+        lats[2368] = -76.520206339048215
+        lats[2369] = -76.59050508402602
+        lats[2370] = -76.660803828747362
+        lats[2371] = -76.731102573208048
+        lats[2372] = -76.801401317404
+        lats[2373] = -76.871700061330955
+        lats[2374] = -76.941998804984564
+        lats[2375] = -77.012297548360323
+        lats[2376] = -77.082596291453768
+        lats[2377] = -77.15289503426024
+        lats[2378] = -77.22319377677502
+        lats[2379] = -77.293492518993247
+        lats[2380] = -77.363791260909963
+        lats[2381] = -77.434090002520122
+        lats[2382] = -77.504388743818524
+        lats[2383] = -77.574687484799924
+        lats[2384] = -77.644986225458879
+        lats[2385] = -77.71528496578982
+        lats[2386] = -77.785583705787161
+        lats[2387] = -77.855882445445019
+        lats[2388] = -77.926181184757539
+        lats[2389] = -77.996479923718596
+        lats[2390] = -78.066778662322022
+        lats[2391] = -78.137077400561424
+        lats[2392] = -78.207376138430348
+        lats[2393] = -78.277674875922045
+        lats[2394] = -78.347973613029708
+        lats[2395] = -78.418272349746417
+        lats[2396] = -78.488571086064923
+        lats[2397] = -78.558869821977908
+        lats[2398] = -78.629168557477882
+        lats[2399] = -78.699467292557102
+        lats[2400] = -78.769766027207638
+        lats[2401] = -78.840064761421445
+        lats[2402] = -78.910363495190211
+        lats[2403] = -78.980662228505423
+        lats[2404] = -79.050960961358285
+        lats[2405] = -79.121259693739859
+        lats[2406] = -79.191558425640977
+        lats[2407] = -79.261857157052191
+        lats[2408] = -79.332155887963822
+        lats[2409] = -79.402454618365894
+        lats[2410] = -79.472753348248219
+        lats[2411] = -79.543052077600308
+        lats[2412] = -79.61335080641139
+        lats[2413] = -79.683649534670437
+        lats[2414] = -79.753948262366038
+        lats[2415] = -79.824246989486554
+        lats[2416] = -79.894545716019948
+        lats[2417] = -79.9648444419539
+        lats[2418] = -80.035143167275749
+        lats[2419] = -80.105441891972376
+        lats[2420] = -80.175740616030438
+        lats[2421] = -80.246039339436052
+        lats[2422] = -80.316338062175078
+        lats[2423] = -80.386636784232863
+        lats[2424] = -80.456935505594302
+        lats[2425] = -80.527234226243991
+        lats[2426] = -80.59753294616587
+        lats[2427] = -80.667831665343556
+        lats[2428] = -80.73813038376008
+        lats[2429] = -80.808429101397948
+        lats[2430] = -80.878727818239184
+        lats[2431] = -80.949026534265244
+        lats[2432] = -81.019325249456955
+        lats[2433] = -81.089623963794551
+        lats[2434] = -81.159922677257711
+        lats[2435] = -81.230221389825374
+        lats[2436] = -81.300520101475826
+        lats[2437] = -81.370818812186627
+        lats[2438] = -81.441117521934686
+        lats[2439] = -81.511416230696042
+        lats[2440] = -81.581714938445955
+        lats[2441] = -81.652013645158945
+        lats[2442] = -81.722312350808508
+        lats[2443] = -81.792611055367345
+        lats[2444] = -81.862909758807191
+        lats[2445] = -81.933208461098829
+        lats[2446] = -82.003507162211946
+        lats[2447] = -82.073805862115165
+        lats[2448] = -82.144104560776
+        lats[2449] = -82.214403258160871
+        lats[2450] = -82.284701954234833
+        lats[2451] = -82.355000648961692
+        lats[2452] = -82.425299342304029
+        lats[2453] = -82.495598034222837
+        lats[2454] = -82.56589672467787
+        lats[2455] = -82.63619541362705
+        lats[2456] = -82.706494101026948
+        lats[2457] = -82.77679278683226
+        lats[2458] = -82.84709147099602
+        lats[2459] = -82.917390153469313
+        lats[2460] = -82.987688834201322
+        lats[2461] = -83.057987513139125
+        lats[2462] = -83.128286190227698
+        lats[2463] = -83.198584865409657
+        lats[2464] = -83.268883538625232
+        lats[2465] = -83.339182209812321
+        lats[2466] = -83.409480878905782
+        lats[2467] = -83.479779545838113
+        lats[2468] = -83.550078210538487
+        lats[2469] = -83.620376872933264
+        lats[2470] = -83.690675532945292
+        lats[2471] = -83.760974190494011
+        lats[2472] = -83.831272845495249
+        lats[2473] = -83.901571497860914
+        lats[2474] = -83.971870147498763
+        lats[2475] = -84.042168794312317
+        lats[2476] = -84.112467438200326
+        lats[2477] = -84.18276607905679
+        lats[2478] = -84.253064716770425
+        lats[2479] = -84.323363351224444
+        lats[2480] = -84.393661982296322
+        lats[2481] = -84.463960609857125
+        lats[2482] = -84.534259233771479
+        lats[2483] = -84.604557853896708
+        lats[2484] = -84.674856470082915
+        lats[2485] = -84.745155082171991
+        lats[2486] = -84.81545368999717
+        lats[2487] = -84.885752293382765
+        lats[2488] = -84.95605089214304
+        lats[2489] = -85.026349486081983
+        lats[2490] = -85.09664807499216
+        lats[2491] = -85.16694665865414
+        lats[2492] = -85.237245236835548
+        lats[2493] = -85.307543809290152
+        lats[2494] = -85.377842375756586
+        lats[2495] = -85.448140935957483
+        lats[2496] = -85.518439489597966
+        lats[2497] = -85.588738036364362
+        lats[2498] = -85.659036575922883
+        lats[2499] = -85.729335107917464
+        lats[2500] = -85.799633631968391
+        lats[2501] = -85.869932147670127
+        lats[2502] = -85.940230654588888
+        lats[2503] = -86.010529152260403
+        lats[2504] = -86.080827640187209
+        lats[2505] = -86.151126117835304
+        lats[2506] = -86.221424584631109
+        lats[2507] = -86.291723039957418
+        lats[2508] = -86.362021483149363
+        lats[2509] = -86.432319913489792
+        lats[2510] = -86.502618330203831
+        lats[2511] = -86.572916732453024
+        lats[2512] = -86.643215119328573
+        lats[2513] = -86.713513489844246
+        lats[2514] = -86.783811842927179
+        lats[2515] = -86.854110177408927
+        lats[2516] = -86.924408492014166
+        lats[2517] = -86.994706785348129
+        lats[2518] = -87.065005055882821
+        lats[2519] = -87.135303301939786
+        lats[2520] = -87.205601521672108
+        lats[2521] = -87.275899713041966
+        lats[2522] = -87.346197873795816
+        lats[2523] = -87.416496001434894
+        lats[2524] = -87.486794093180748
+        lats[2525] = -87.557092145935584
+        lats[2526] = -87.627390156234085
+        lats[2527] = -87.697688120188062
+        lats[2528] = -87.767986033419561
+        lats[2529] = -87.838283890981543
+        lats[2530] = -87.908581687261687
+        lats[2531] = -87.978879415867283
+        lats[2532] = -88.049177069484486
+        lats[2533] = -88.119474639706425
+        lats[2534] = -88.189772116820762
+        lats[2535] = -88.26006948954614
+        lats[2536] = -88.330366744702559
+        lats[2537] = -88.40066386679355
+        lats[2538] = -88.470960837474877
+        lats[2539] = -88.541257634868515
+        lats[2540] = -88.611554232668382
+        lats[2541] = -88.681850598961759
+        lats[2542] = -88.752146694650691
+        lats[2543] = -88.822442471310097
+        lats[2544] = -88.892737868230952
+        lats[2545] = -88.96303280826325
+        lats[2546] = -89.033327191845927
+        lats[2547] = -89.103620888238879
+        lats[2548] = -89.173913722284126
+        lats[2549] = -89.24420545380525
+        lats[2550] = -89.314495744374256
+        lats[2551] = -89.3847841013921
+        lats[2552] = -89.45506977912261
+        lats[2553] = -89.525351592371393
+        lats[2554] = -89.595627537554492
+        lats[2555] = -89.6658939412157
+        lats[2556] = -89.736143271609578
+        lats[2557] = -89.806357319542244
+        lats[2558] = -89.876478353332288
+        lats[2559] = -89.946187715665616
+        return lats
+
+    def first_axis_vals(self):
+        if self._resolution == 1280:
+            return self.get_precomputed_values_N1280()
+        else:
+            precision = 1.0e-14
+            nval = self._resolution * 2
+            rad2deg = 180 / math.pi
+            convval = 1 - ((2 / math.pi) * (2 / math.pi)) * 0.25
+            vals = self.gauss_first_guess()
+            new_vals = [0] * nval
+            denom = math.sqrt(((nval + 0.5) * (nval + 0.5)) + convval)
+            for jval in range(self._resolution):
+                root = math.cos(vals[jval] / denom)
+                conv = 1
+                while abs(conv) >= precision:
+                    mem2 = 1
+                    mem1 = root
+                    for legi in range(nval):
+                        legfonc = ((2.0 * (legi + 1) - 1.0) * root * mem1 - legi * mem2) / (legi + 1)
+                        mem2 = mem1
+                        mem1 = legfonc
+                    conv = legfonc / ((nval * (mem2 - root * legfonc)) / (1.0 - (root * root)))
+                    root = root - conv
+                    # add maybe a max iter here to make sure we converge at some point
+                new_vals[jval] = math.asin(root) * rad2deg
+                new_vals[nval - 1 - jval] = -new_vals[jval]
+            return new_vals
+
+    def map_first_axis(self, lower, upper):
+        axis_lines = self._first_axis_vals
+        end_idx = bisect_left_cmp(axis_lines, lower, cmp=lambda x, y: x > y) + 1
+        start_idx = bisect_right_cmp(axis_lines, upper, cmp=lambda x, y: x > y)
+        return_vals = axis_lines[start_idx:end_idx]
+        return return_vals
+
+    def second_axis_vals(self, first_val):
+        first_axis_vals = self._first_axis_vals
+        tol = 1e-10
+        first_idx = bisect_left_cmp(first_axis_vals, first_val - tol, cmp=lambda x, y: x > y)
+        if first_idx >= self._resolution:
+            first_idx = (2 * self._resolution) - 1 - first_idx
+        first_idx = first_idx + 1
+        npoints = 4 * first_idx + 16
+        second_axis_spacing = 360 / npoints
+        second_axis_vals = [i * second_axis_spacing for i in range(npoints)]
+        return second_axis_vals
+
+    def second_axis_spacing(self, first_val):
+        first_axis_vals = self._first_axis_vals
+        tol = 1e-10
+        _first_idx = bisect_left_cmp(first_axis_vals, first_val - tol, cmp=lambda x, y: x > y)
+        first_idx = _first_idx
+        if first_idx >= self._resolution:
+            first_idx = (2 * self._resolution) - 1 - first_idx
+        first_idx = first_idx + 1
+        npoints = 4 * first_idx + 16
+        second_axis_spacing = 360 / npoints
+        return (second_axis_spacing, _first_idx + 1)
+
+    def map_second_axis(self, first_val, lower, upper):
+        second_axis_spacing, first_idx = self.second_axis_spacing(first_val)
+        start_idx = int(lower / second_axis_spacing)
+        end_idx = int(upper / second_axis_spacing) + 1
+        return_vals = [i * second_axis_spacing for i in range(start_idx, end_idx)]
+        return return_vals
+
+    def axes_idx_to_octahedral_idx(self, first_idx, second_idx):
+        # NOTE: for now this takes ~2e-4s per point, so taking significant time -> for 20k points, takes 4s
+        # Would it be better to store a dictionary of first_idx with cumulative number of points on that idx?
+        # Because this is what we are doing here, but we are calculating for each point...
+        # But then this would only work for special grid resolutions, so need to do like a O1280 version of this
+
+        # NOTE: OR somehow cache this for a given first_idx and then only modify the axis idx for second_idx when the
+        # first_idx changes
+        octa_idx = self._first_idx_map[first_idx - 1] + second_idx
+        return octa_idx
+
+    def create_first_idx_map(self):
+        first_idx_list = {}
+        idx = 0
+        for i in range(2 * self._resolution):
+            first_idx_list[i] = idx
+            if i <= self._resolution - 1:
+                idx += 20 + 4 * i
+            else:
+                i = i - self._resolution + 1
+                if i == 1:
+                    idx += 16 + 4 * self._resolution
+                else:
+                    i = i - 1
+                    idx += 16 + 4 * (self._resolution - i)
+        return first_idx_list
+
+    def find_second_axis_idx(self, first_val, second_val):
+        (second_axis_spacing, first_idx) = self.second_axis_spacing(first_val)
+        tol = 1e-8
+        if second_val / second_axis_spacing > int(second_val / second_axis_spacing) + 1 - tol:
+            second_idx = int(second_val / second_axis_spacing) + 1
+        else:
+            second_idx = int(second_val / second_axis_spacing)
+        return (first_idx, second_idx)
+
+    def unmap(self, first_val, second_val):
+        (first_idx, second_idx) = self.find_second_axis_idx(first_val, second_val)
+        octahedral_index = self.axes_idx_to_octahedral_idx(first_idx, second_idx)
+        return octahedral_index
diff --git a/polytope/datacube/transformations/mappers/reduced_ll.py b/polytope/datacube/transformations/mappers/reduced_ll.py
new file mode 100644
index 00000000..f056b232
--- /dev/null
+++ b/polytope/datacube/transformations/mappers/reduced_ll.py
@@ -0,0 +1,1504 @@
+import bisect
+
+from ..datacube_mappers import DatacubeMapper
+
+
+class ReducedLatLonMapper(DatacubeMapper):
+    def __init__(self, base_axis, mapped_axes, resolution):
+        self._mapped_axes = mapped_axes
+        self._base_axis = base_axis
+        self._resolution = resolution
+        self._axis_reversed = {mapped_axes[0]: False, mapped_axes[1]: False}
+        self._first_axis_vals = self.first_axis_vals()
+
+    def first_axis_vals(self):
+        resolution = 180 / (self._resolution - 1)
+        vals = [-90 + i * resolution for i in range(self._resolution)]
+        return vals
+
+    def map_first_axis(self, lower, upper):
+        axis_lines = self._first_axis_vals
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def lon_spacing(self):
+        if self._resolution == 1441:
+            return [
+                2,
+                6,
+                14,
+                20,
+                26,
+                32,
+                38,
+                44,
+                50,
+                58,
+                64,
+                70,
+                76,
+                82,
+                88,
+                94,
+                102,
+                108,
+                114,
+                120,
+                126,
+                132,
+                138,
+                144,
+                152,
+                158,
+                164,
+                170,
+                176,
+                182,
+                188,
+                196,
+                202,
+                208,
+                214,
+                220,
+                226,
+                232,
+                238,
+                246,
+                252,
+                258,
+                264,
+                270,
+                276,
+                282,
+                290,
+                296,
+                302,
+                308,
+                314,
+                320,
+                326,
+                332,
+                340,
+                346,
+                352,
+                358,
+                364,
+                370,
+                376,
+                382,
+                388,
+                396,
+                402,
+                408,
+                414,
+                420,
+                426,
+                432,
+                438,
+                444,
+                452,
+                458,
+                464,
+                470,
+                476,
+                482,
+                488,
+                494,
+                500,
+                506,
+                512,
+                520,
+                526,
+                532,
+                538,
+                544,
+                550,
+                556,
+                562,
+                568,
+                574,
+                580,
+                586,
+                594,
+                600,
+                606,
+                612,
+                618,
+                624,
+                630,
+                636,
+                642,
+                648,
+                654,
+                660,
+                666,
+                672,
+                678,
+                686,
+                692,
+                698,
+                704,
+                710,
+                716,
+                722,
+                728,
+                734,
+                740,
+                746,
+                752,
+                758,
+                764,
+                770,
+                776,
+                782,
+                788,
+                794,
+                800,
+                806,
+                812,
+                818,
+                824,
+                830,
+                836,
+                842,
+                848,
+                854,
+                860,
+                866,
+                872,
+                878,
+                884,
+                890,
+                896,
+                902,
+                908,
+                914,
+                920,
+                926,
+                932,
+                938,
+                944,
+                950,
+                956,
+                962,
+                968,
+                974,
+                980,
+                986,
+                992,
+                998,
+                1004,
+                1010,
+                1014,
+                1020,
+                1026,
+                1032,
+                1038,
+                1044,
+                1050,
+                1056,
+                1062,
+                1068,
+                1074,
+                1080,
+                1086,
+                1092,
+                1096,
+                1102,
+                1108,
+                1114,
+                1120,
+                1126,
+                1132,
+                1138,
+                1144,
+                1148,
+                1154,
+                1160,
+                1166,
+                1172,
+                1178,
+                1184,
+                1190,
+                1194,
+                1200,
+                1206,
+                1212,
+                1218,
+                1224,
+                1230,
+                1234,
+                1240,
+                1246,
+                1252,
+                1258,
+                1264,
+                1268,
+                1274,
+                1280,
+                1286,
+                1292,
+                1296,
+                1302,
+                1308,
+                1314,
+                1320,
+                1324,
+                1330,
+                1336,
+                1342,
+                1348,
+                1352,
+                1358,
+                1364,
+                1370,
+                1374,
+                1380,
+                1386,
+                1392,
+                1396,
+                1402,
+                1408,
+                1414,
+                1418,
+                1424,
+                1430,
+                1436,
+                1440,
+                1446,
+                1452,
+                1456,
+                1462,
+                1468,
+                1474,
+                1478,
+                1484,
+                1490,
+                1494,
+                1500,
+                1506,
+                1510,
+                1516,
+                1522,
+                1526,
+                1532,
+                1538,
+                1542,
+                1548,
+                1554,
+                1558,
+                1564,
+                1570,
+                1574,
+                1580,
+                1584,
+                1590,
+                1596,
+                1600,
+                1606,
+                1610,
+                1616,
+                1622,
+                1626,
+                1632,
+                1636,
+                1642,
+                1648,
+                1652,
+                1658,
+                1662,
+                1668,
+                1672,
+                1678,
+                1684,
+                1688,
+                1694,
+                1698,
+                1704,
+                1708,
+                1714,
+                1718,
+                1724,
+                1728,
+                1734,
+                1738,
+                1744,
+                1748,
+                1754,
+                1758,
+                1764,
+                1768,
+                1774,
+                1778,
+                1784,
+                1788,
+                1794,
+                1798,
+                1804,
+                1808,
+                1812,
+                1818,
+                1822,
+                1828,
+                1832,
+                1838,
+                1842,
+                1846,
+                1852,
+                1856,
+                1862,
+                1866,
+                1870,
+                1876,
+                1880,
+                1886,
+                1890,
+                1894,
+                1900,
+                1904,
+                1908,
+                1914,
+                1918,
+                1922,
+                1928,
+                1932,
+                1936,
+                1942,
+                1946,
+                1950,
+                1956,
+                1960,
+                1964,
+                1970,
+                1974,
+                1978,
+                1982,
+                1988,
+                1992,
+                1996,
+                2002,
+                2006,
+                2010,
+                2014,
+                2020,
+                2024,
+                2028,
+                2032,
+                2036,
+                2042,
+                2046,
+                2050,
+                2054,
+                2060,
+                2064,
+                2068,
+                2072,
+                2076,
+                2080,
+                2086,
+                2090,
+                2094,
+                2098,
+                2102,
+                2106,
+                2112,
+                2116,
+                2120,
+                2124,
+                2128,
+                2132,
+                2136,
+                2140,
+                2144,
+                2150,
+                2154,
+                2158,
+                2162,
+                2166,
+                2170,
+                2174,
+                2178,
+                2182,
+                2186,
+                2190,
+                2194,
+                2198,
+                2202,
+                2206,
+                2210,
+                2214,
+                2218,
+                2222,
+                2226,
+                2230,
+                2234,
+                2238,
+                2242,
+                2246,
+                2250,
+                2254,
+                2258,
+                2262,
+                2266,
+                2270,
+                2274,
+                2278,
+                2282,
+                2286,
+                2290,
+                2292,
+                2296,
+                2300,
+                2304,
+                2308,
+                2312,
+                2316,
+                2320,
+                2324,
+                2326,
+                2330,
+                2334,
+                2338,
+                2342,
+                2346,
+                2348,
+                2352,
+                2356,
+                2360,
+                2364,
+                2366,
+                2370,
+                2374,
+                2378,
+                2382,
+                2384,
+                2388,
+                2392,
+                2396,
+                2398,
+                2402,
+                2406,
+                2410,
+                2412,
+                2416,
+                2420,
+                2422,
+                2426,
+                2430,
+                2432,
+                2436,
+                2440,
+                2442,
+                2446,
+                2450,
+                2452,
+                2456,
+                2460,
+                2462,
+                2466,
+                2470,
+                2472,
+                2476,
+                2478,
+                2482,
+                2486,
+                2488,
+                2492,
+                2494,
+                2498,
+                2500,
+                2504,
+                2508,
+                2510,
+                2514,
+                2516,
+                2520,
+                2522,
+                2526,
+                2528,
+                2532,
+                2534,
+                2538,
+                2540,
+                2544,
+                2546,
+                2550,
+                2552,
+                2556,
+                2558,
+                2560,
+                2564,
+                2566,
+                2570,
+                2572,
+                2576,
+                2578,
+                2580,
+                2584,
+                2586,
+                2590,
+                2592,
+                2594,
+                2598,
+                2600,
+                2602,
+                2606,
+                2608,
+                2610,
+                2614,
+                2616,
+                2618,
+                2622,
+                2624,
+                2626,
+                2628,
+                2632,
+                2634,
+                2636,
+                2640,
+                2642,
+                2644,
+                2646,
+                2650,
+                2652,
+                2654,
+                2656,
+                2658,
+                2662,
+                2664,
+                2666,
+                2668,
+                2670,
+                2674,
+                2676,
+                2678,
+                2680,
+                2682,
+                2684,
+                2686,
+                2690,
+                2692,
+                2694,
+                2696,
+                2698,
+                2700,
+                2702,
+                2704,
+                2706,
+                2708,
+                2712,
+                2714,
+                2716,
+                2718,
+                2720,
+                2722,
+                2724,
+                2726,
+                2728,
+                2730,
+                2732,
+                2734,
+                2736,
+                2738,
+                2740,
+                2742,
+                2744,
+                2746,
+                2748,
+                2750,
+                2750,
+                2752,
+                2754,
+                2756,
+                2758,
+                2760,
+                2762,
+                2764,
+                2766,
+                2768,
+                2768,
+                2770,
+                2772,
+                2774,
+                2776,
+                2778,
+                2780,
+                2780,
+                2782,
+                2784,
+                2786,
+                2788,
+                2788,
+                2790,
+                2792,
+                2794,
+                2794,
+                2796,
+                2798,
+                2800,
+                2800,
+                2802,
+                2804,
+                2806,
+                2806,
+                2808,
+                2810,
+                2810,
+                2812,
+                2814,
+                2814,
+                2816,
+                2818,
+                2818,
+                2820,
+                2822,
+                2822,
+                2824,
+                2826,
+                2826,
+                2828,
+                2828,
+                2830,
+                2832,
+                2832,
+                2834,
+                2834,
+                2836,
+                2836,
+                2838,
+                2838,
+                2840,
+                2842,
+                2842,
+                2844,
+                2844,
+                2846,
+                2846,
+                2846,
+                2848,
+                2848,
+                2850,
+                2850,
+                2852,
+                2852,
+                2854,
+                2854,
+                2856,
+                2856,
+                2856,
+                2858,
+                2858,
+                2860,
+                2860,
+                2860,
+                2862,
+                2862,
+                2862,
+                2864,
+                2864,
+                2864,
+                2866,
+                2866,
+                2866,
+                2868,
+                2868,
+                2868,
+                2868,
+                2870,
+                2870,
+                2870,
+                2872,
+                2872,
+                2872,
+                2872,
+                2874,
+                2874,
+                2874,
+                2874,
+                2874,
+                2876,
+                2876,
+                2876,
+                2876,
+                2876,
+                2876,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2880,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2878,
+                2876,
+                2876,
+                2876,
+                2876,
+                2876,
+                2876,
+                2874,
+                2874,
+                2874,
+                2874,
+                2874,
+                2872,
+                2872,
+                2872,
+                2872,
+                2870,
+                2870,
+                2870,
+                2868,
+                2868,
+                2868,
+                2868,
+                2866,
+                2866,
+                2866,
+                2864,
+                2864,
+                2864,
+                2862,
+                2862,
+                2862,
+                2860,
+                2860,
+                2860,
+                2858,
+                2858,
+                2856,
+                2856,
+                2856,
+                2854,
+                2854,
+                2852,
+                2852,
+                2850,
+                2850,
+                2848,
+                2848,
+                2846,
+                2846,
+                2846,
+                2844,
+                2844,
+                2842,
+                2842,
+                2840,
+                2838,
+                2838,
+                2836,
+                2836,
+                2834,
+                2834,
+                2832,
+                2832,
+                2830,
+                2828,
+                2828,
+                2826,
+                2826,
+                2824,
+                2822,
+                2822,
+                2820,
+                2818,
+                2818,
+                2816,
+                2814,
+                2814,
+                2812,
+                2810,
+                2810,
+                2808,
+                2806,
+                2806,
+                2804,
+                2802,
+                2800,
+                2800,
+                2798,
+                2796,
+                2794,
+                2794,
+                2792,
+                2790,
+                2788,
+                2788,
+                2786,
+                2784,
+                2782,
+                2780,
+                2780,
+                2778,
+                2776,
+                2774,
+                2772,
+                2770,
+                2768,
+                2768,
+                2766,
+                2764,
+                2762,
+                2760,
+                2758,
+                2756,
+                2754,
+                2752,
+                2750,
+                2750,
+                2748,
+                2746,
+                2744,
+                2742,
+                2740,
+                2738,
+                2736,
+                2734,
+                2732,
+                2730,
+                2728,
+                2726,
+                2724,
+                2722,
+                2720,
+                2718,
+                2716,
+                2714,
+                2712,
+                2708,
+                2706,
+                2704,
+                2702,
+                2700,
+                2698,
+                2696,
+                2694,
+                2692,
+                2690,
+                2686,
+                2684,
+                2682,
+                2680,
+                2678,
+                2676,
+                2674,
+                2670,
+                2668,
+                2666,
+                2664,
+                2662,
+                2658,
+                2656,
+                2654,
+                2652,
+                2650,
+                2646,
+                2644,
+                2642,
+                2640,
+                2636,
+                2634,
+                2632,
+                2628,
+                2626,
+                2624,
+                2622,
+                2618,
+                2616,
+                2614,
+                2610,
+                2608,
+                2606,
+                2602,
+                2600,
+                2598,
+                2594,
+                2592,
+                2590,
+                2586,
+                2584,
+                2580,
+                2578,
+                2576,
+                2572,
+                2570,
+                2566,
+                2564,
+                2560,
+                2558,
+                2556,
+                2552,
+                2550,
+                2546,
+                2544,
+                2540,
+                2538,
+                2534,
+                2532,
+                2528,
+                2526,
+                2522,
+                2520,
+                2516,
+                2514,
+                2510,
+                2508,
+                2504,
+                2500,
+                2498,
+                2494,
+                2492,
+                2488,
+                2486,
+                2482,
+                2478,
+                2476,
+                2472,
+                2470,
+                2466,
+                2462,
+                2460,
+                2456,
+                2452,
+                2450,
+                2446,
+                2442,
+                2440,
+                2436,
+                2432,
+                2430,
+                2426,
+                2422,
+                2420,
+                2416,
+                2412,
+                2410,
+                2406,
+                2402,
+                2398,
+                2396,
+                2392,
+                2388,
+                2384,
+                2382,
+                2378,
+                2374,
+                2370,
+                2366,
+                2364,
+                2360,
+                2356,
+                2352,
+                2348,
+                2346,
+                2342,
+                2338,
+                2334,
+                2330,
+                2326,
+                2324,
+                2320,
+                2316,
+                2312,
+                2308,
+                2304,
+                2300,
+                2296,
+                2292,
+                2290,
+                2286,
+                2282,
+                2278,
+                2274,
+                2270,
+                2266,
+                2262,
+                2258,
+                2254,
+                2250,
+                2246,
+                2242,
+                2238,
+                2234,
+                2230,
+                2226,
+                2222,
+                2218,
+                2214,
+                2210,
+                2206,
+                2202,
+                2198,
+                2194,
+                2190,
+                2186,
+                2182,
+                2178,
+                2174,
+                2170,
+                2166,
+                2162,
+                2158,
+                2154,
+                2150,
+                2144,
+                2140,
+                2136,
+                2132,
+                2128,
+                2124,
+                2120,
+                2116,
+                2112,
+                2106,
+                2102,
+                2098,
+                2094,
+                2090,
+                2086,
+                2080,
+                2076,
+                2072,
+                2068,
+                2064,
+                2060,
+                2054,
+                2050,
+                2046,
+                2042,
+                2036,
+                2032,
+                2028,
+                2024,
+                2020,
+                2014,
+                2010,
+                2006,
+                2002,
+                1996,
+                1992,
+                1988,
+                1982,
+                1978,
+                1974,
+                1970,
+                1964,
+                1960,
+                1956,
+                1950,
+                1946,
+                1942,
+                1936,
+                1932,
+                1928,
+                1922,
+                1918,
+                1914,
+                1908,
+                1904,
+                1900,
+                1894,
+                1890,
+                1886,
+                1880,
+                1876,
+                1870,
+                1866,
+                1862,
+                1856,
+                1852,
+                1846,
+                1842,
+                1838,
+                1832,
+                1828,
+                1822,
+                1818,
+                1812,
+                1808,
+                1804,
+                1798,
+                1794,
+                1788,
+                1784,
+                1778,
+                1774,
+                1768,
+                1764,
+                1758,
+                1754,
+                1748,
+                1744,
+                1738,
+                1734,
+                1728,
+                1724,
+                1718,
+                1714,
+                1708,
+                1704,
+                1698,
+                1694,
+                1688,
+                1684,
+                1678,
+                1672,
+                1668,
+                1662,
+                1658,
+                1652,
+                1648,
+                1642,
+                1636,
+                1632,
+                1626,
+                1622,
+                1616,
+                1610,
+                1606,
+                1600,
+                1596,
+                1590,
+                1584,
+                1580,
+                1574,
+                1570,
+                1564,
+                1558,
+                1554,
+                1548,
+                1542,
+                1538,
+                1532,
+                1526,
+                1522,
+                1516,
+                1510,
+                1506,
+                1500,
+                1494,
+                1490,
+                1484,
+                1478,
+                1474,
+                1468,
+                1462,
+                1456,
+                1452,
+                1446,
+                1440,
+                1436,
+                1430,
+                1424,
+                1418,
+                1414,
+                1408,
+                1402,
+                1396,
+                1392,
+                1386,
+                1380,
+                1374,
+                1370,
+                1364,
+                1358,
+                1352,
+                1348,
+                1342,
+                1336,
+                1330,
+                1324,
+                1320,
+                1314,
+                1308,
+                1302,
+                1296,
+                1292,
+                1286,
+                1280,
+                1274,
+                1268,
+                1264,
+                1258,
+                1252,
+                1246,
+                1240,
+                1234,
+                1230,
+                1224,
+                1218,
+                1212,
+                1206,
+                1200,
+                1194,
+                1190,
+                1184,
+                1178,
+                1172,
+                1166,
+                1160,
+                1154,
+                1148,
+                1144,
+                1138,
+                1132,
+                1126,
+                1120,
+                1114,
+                1108,
+                1102,
+                1096,
+                1092,
+                1086,
+                1080,
+                1074,
+                1068,
+                1062,
+                1056,
+                1050,
+                1044,
+                1038,
+                1032,
+                1026,
+                1020,
+                1014,
+                1010,
+                1004,
+                998,
+                992,
+                986,
+                980,
+                974,
+                968,
+                962,
+                956,
+                950,
+                944,
+                938,
+                932,
+                926,
+                920,
+                914,
+                908,
+                902,
+                896,
+                890,
+                884,
+                878,
+                872,
+                866,
+                860,
+                854,
+                848,
+                842,
+                836,
+                830,
+                824,
+                818,
+                812,
+                806,
+                800,
+                794,
+                788,
+                782,
+                776,
+                770,
+                764,
+                758,
+                752,
+                746,
+                740,
+                734,
+                728,
+                722,
+                716,
+                710,
+                704,
+                698,
+                692,
+                686,
+                678,
+                672,
+                666,
+                660,
+                654,
+                648,
+                642,
+                636,
+                630,
+                624,
+                618,
+                612,
+                606,
+                600,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+                0,
+            ]
+
+    def second_axis_vals(self, first_val):
+        first_idx = self._first_axis_vals.index(first_val)
+        Ny = self.lon_spacing()[first_idx]
+        second_spacing = 360 / Ny
+        return [i * second_spacing for i in range(Ny)]
+
+    def map_second_axis(self, first_val, lower, upper):
+        axis_lines = self.second_axis_vals(first_val)
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def axes_idx_to_reduced_ll_idx(self, first_idx, second_idx):
+        Ny_array = self.lon_spacing()
+        idx = 0
+        for i in range(self._resolution):
+            if i != first_idx:
+                idx += Ny_array[i]
+            else:
+                idx += second_idx
+                return idx
+
+    def find_second_idx(self, first_val, second_val):
+        tol = 1e-10
+        second_axis_vals = self.second_axis_vals(first_val)
+        second_idx = bisect.bisect_left(second_axis_vals, second_val - tol)
+        return second_idx
+
+    def unmap(self, first_val, second_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        first_idx = self._first_axis_vals.index(first_val)
+        second_val = [i for i in self.second_axis_vals(first_val) if second_val - tol <= i <= second_val + tol][0]
+        second_idx = self.second_axis_vals(first_val).index(second_val)
+        reduced_ll_index = self.axes_idx_to_reduced_ll_idx(first_idx, second_idx)
+        return reduced_ll_index
diff --git a/polytope/datacube/transformations/mappers/regular.py b/polytope/datacube/transformations/mappers/regular.py
new file mode 100644
index 00000000..3b0598a0
--- /dev/null
+++ b/polytope/datacube/transformations/mappers/regular.py
@@ -0,0 +1,56 @@
+import bisect
+
+from ..datacube_mappers import DatacubeMapper
+
+
+class RegularGridMapper(DatacubeMapper):
+    def __init__(self, base_axis, mapped_axes, resolution):
+        self._mapped_axes = mapped_axes
+        self._base_axis = base_axis
+        self._resolution = resolution
+        self.deg_increment = 90 / self._resolution
+        self._axis_reversed = {mapped_axes[0]: True, mapped_axes[1]: False}
+        self._first_axis_vals = self.first_axis_vals()
+
+    def first_axis_vals(self):
+        first_ax_vals = [90 - i * self.deg_increment for i in range(2 * self._resolution)]
+        return first_ax_vals
+
+    def map_first_axis(self, lower, upper):
+        axis_lines = self._first_axis_vals
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def second_axis_vals(self, first_val):
+        second_ax_vals = [i * self.deg_increment for i in range(4 * self._resolution)]
+        return second_ax_vals
+
+    def map_second_axis(self, first_val, lower, upper):
+        axis_lines = self.second_axis_vals(first_val)
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def axes_idx_to_regular_idx(self, first_idx, second_idx):
+        final_idx = first_idx * 4 * self._resolution + second_idx
+        return final_idx
+
+    def find_second_idx(self, first_val, second_val):
+        tol = 1e-10
+        second_axis_vals = self.second_axis_vals(first_val)
+        second_idx = bisect.bisect_left(second_axis_vals, second_val - tol)
+        return second_idx
+
+    def unmap_first_val_to_start_line_idx(self, first_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        first_idx = self._first_axis_vals.index(first_val)
+        return first_idx * 4 * self._resolution
+
+    def unmap(self, first_val, second_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        first_idx = self._first_axis_vals.index(first_val)
+        second_val = [i for i in self.second_axis_vals(first_val) if second_val - tol <= i <= second_val + tol][0]
+        second_idx = self.second_axis_vals(first_val).index(second_val)
+        final_index = self.axes_idx_to_regular_idx(first_idx, second_idx)
+        return final_index
diff --git a/tests/test_ecmwf_oper_data_fdb.py b/tests/test_ecmwf_oper_data_fdb.py
index 7ec4a465..ebea9d99 100644
--- a/tests/test_ecmwf_oper_data_fdb.py
+++ b/tests/test_ecmwf_oper_data_fdb.py
@@ -16,7 +16,7 @@ def setup_method(self, method):
             "date": {"merge": {"with": "time", "linkers": ["T", "00"]}},
             "step": {"type_change": "int"},
         }
-        self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "step": 0, "type": "fc"}
+        self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "type": "fc", "stream": "oper"}
         self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
         self.slicer = HullSlicer()
         self.API = Polytope(datacube=self.fdbdatacube, engine=self.slicer, axis_options=self.options)
diff --git a/tests/test_fdb_datacube.py b/tests/test_fdb_datacube.py
index a7c54816..bf4452a3 100644
--- a/tests/test_fdb_datacube.py
+++ b/tests/test_fdb_datacube.py
@@ -20,7 +20,7 @@ def setup_method(self, method):
             "step": {"type_change": "int"},
             "number": {"type_change": "int"},
         }
-        self.config = {"class": "od", "expver": "0001", "levtype": "sfc"}
+        self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "stream": "oper"}
         self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
         self.slicer = HullSlicer()
         self.API = Polytope(datacube=self.fdbdatacube, engine=self.slicer, axis_options=self.options)
@@ -38,7 +38,6 @@ def test_fdb_datacube(self):
             Select("class", ["od"]),
             Select("stream", ["oper"]),
             Select("type", ["an"]),
-            Select("number", [1]),
             Box(["latitude", "longitude"], [0, 0], [0.2, 0.2]),
         )
         result = self.API.retrieve(request)
diff --git a/tests/test_mappers.py b/tests/test_mappers.py
index b9a39477..b3661822 100644
--- a/tests/test_mappers.py
+++ b/tests/test_mappers.py
@@ -1,4 +1,4 @@
-from polytope.datacube.transformations.datacube_mappers import OctahedralGridMapper
+from polytope.datacube.transformations.mappers.octahedral import OctahedralGridMapper
 
 
 class TestMapper:
diff --git a/tests/test_slice_date_range_fdb.py b/tests/test_slice_date_range_fdb.py
index 624a77fe..319bc2c2 100644
--- a/tests/test_slice_date_range_fdb.py
+++ b/tests/test_slice_date_range_fdb.py
@@ -17,7 +17,7 @@ def setup_method(self, method):
             "step": {"type_change": "int"},
             "number": {"type_change": "int"},
         }
-        self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "step": "0"}
+        self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "stream": "oper"}
         self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
         self.slicer = HullSlicer()
         self.API = Polytope(datacube=self.fdbdatacube, engine=self.slicer, axis_options=self.options)
@@ -27,7 +27,6 @@ def setup_method(self, method):
     def test_fdb_datacube(self):
         request = Request(
             Select("step", [0]),
-            Select("number", [1]),
             Select("levtype", ["sfc"]),
             Span("date", pd.Timestamp("20230625T120000"), pd.Timestamp("20230626T120000")),
             Select("domain", ["g"]),
@@ -36,7 +35,6 @@ def test_fdb_datacube(self):
             Select("class", ["od"]),
             Select("stream", ["oper"]),
             Select("type", ["an"]),
-            Select("number", [1]),
             Box(["latitude", "longitude"], [0, 0], [0.2, 0.2]),
         )
         result = self.API.retrieve(request)
diff --git a/tests/test_slice_date_range_fdb_v2.py b/tests/test_slice_date_range_fdb_v2.py
index 24ae1a9a..63ce5e67 100644
--- a/tests/test_slice_date_range_fdb_v2.py
+++ b/tests/test_slice_date_range_fdb_v2.py
@@ -16,7 +16,7 @@ def setup_method(self, method):
             "date": {"merge": {"with": "time", "linkers": ["T", "00"]}},
             "step": {"type_change": "int"},
         }
-        self.config = {"class": "ea", "expver": "0001", "levtype": "pl", "step": 0}
+        self.config = {"class": "ea", "expver": "0001", "levtype": "pl", "stream": "enda"}
         self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
         self.slicer = HullSlicer()
         self.API = Polytope(datacube=self.fdbdatacube, engine=self.slicer, axis_options=self.options)

From 8566ff6c5f3f5fafb1c640b226c05c8d2c865f32 Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Mon, 22 Jan 2024 13:21:12 +0100
Subject: [PATCH 02/12] add decorators in individual transformation files

---
 polytope/datacube/datacube_axis.py            | 534 +-----------------
 .../transformations/datacube_cyclic.py        | 187 ++++++
 .../transformations/datacube_mappers.py       | 106 ++++
 .../transformations/datacube_merger.py        |  76 +++
 .../datacube_null_transformation.py           |  24 +
 .../transformations/datacube_reverse.py       |  65 +++
 .../transformations/datacube_type_change.py   |  71 +++
 7 files changed, 534 insertions(+), 529 deletions(-)

diff --git a/polytope/datacube/datacube_axis.py b/polytope/datacube/datacube_axis.py
index 5c78c22f..129581d0 100644
--- a/polytope/datacube/datacube_axis.py
+++ b/polytope/datacube/datacube_axis.py
@@ -1,5 +1,3 @@
-import bisect
-import math
 from abc import ABC, abstractmethod
 from copy import deepcopy
 from typing import Any, List
@@ -7,533 +5,11 @@
 import numpy as np
 import pandas as pd
 
-from ..utility.list_tools import bisect_left_cmp, bisect_right_cmp
-
-
-def cyclic(cls):
-    if cls.is_cyclic:
-        from .transformations.datacube_cyclic import DatacubeAxisCyclic
-
-        def update_range():
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisCyclic):
-                    transformation = transform
-                    cls.range = transformation.range
-
-        def to_intervals(range):
-            update_range()
-            if range[0] == -math.inf:
-                range[0] = cls.range[0]
-            if range[1] == math.inf:
-                range[1] = cls.range[1]
-            axis_lower = cls.range[0]
-            axis_upper = cls.range[1]
-            axis_range = axis_upper - axis_lower
-            lower = range[0]
-            upper = range[1]
-            intervals = []
-            if lower < axis_upper:
-                # In this case, we want to go from lower to the first remapped cyclic axis upper
-                # or the asked upper range value.
-                # For example, if we have cyclic range [0,360] and we want to break [-270,180] into intervals,
-                # we first want to obtain [-270, 0] as the first range, where 0 is the remapped cyclic axis upper
-                # but if we wanted to break [-270, -180] into intervals, we would want to get [-270,-180],
-                # where -180 is the asked upper range value.
-                loops = int((axis_upper - lower) / axis_range)
-                remapped_up = axis_upper - (loops) * axis_range
-                new_upper = min(upper, remapped_up)
-            else:
-                # In this case, since lower >= axis_upper, we need to either go to the asked upper range
-                # or we need to go to the first remapped cyclic axis upper which is higher than lower
-                new_upper = min(axis_upper + axis_range, upper)
-                while new_upper < lower:
-                    new_upper = min(new_upper + axis_range, upper)
-            intervals.append([lower, new_upper])
-            # Now that we have established what the first interval should be, we should just jump from cyclic range
-            # to cyclic range until we hit the asked upper range value.
-            new_up = deepcopy(new_upper)
-            while new_up < upper:
-                new_upper = new_up
-                new_up = min(upper, new_upper + axis_range)
-                intervals.append([new_upper, new_up])
-            # Once we have added all the in-between ranges, we need to add the last interval
-            intervals.append([new_up, upper])
-            return intervals
-
-        def _remap_range_to_axis_range(range):
-            update_range()
-            axis_lower = cls.range[0]
-            axis_upper = cls.range[1]
-            axis_range = axis_upper - axis_lower
-            lower = range[0]
-            upper = range[1]
-            if lower < axis_lower:
-                # In this case we need to calculate the number of loops between the axis lower
-                # and the lower to recenter the lower
-                loops = int((axis_lower - lower - cls.tol) / axis_range)
-                return_lower = lower + (loops + 1) * axis_range
-                return_upper = upper + (loops + 1) * axis_range
-            elif lower >= axis_upper:
-                # In this case we need to calculate the number of loops between the axis upper
-                # and the lower to recenter the lower
-                loops = int((lower - axis_upper) / axis_range)
-                return_lower = lower - (loops + 1) * axis_range
-                return_upper = upper - (loops + 1) * axis_range
-            else:
-                # In this case, the lower value is already in the right range
-                return_lower = lower
-                return_upper = upper
-            return [return_lower, return_upper]
-
-        def _remap_val_to_axis_range(value):
-            return_range = _remap_range_to_axis_range([value, value])
-            return return_range[0]
-
-        def remap(range: List):
-            update_range()
-            if cls.range[0] - cls.tol <= range[0] <= cls.range[1] + cls.tol:
-                if cls.range[0] - cls.tol <= range[1] <= cls.range[1] + cls.tol:
-                    # If we are already in the cyclic range, return it
-                    return [range]
-            elif abs(range[0] - range[1]) <= 2 * cls.tol:
-                # If we have a range that is just one point, then it should still be counted
-                # and so we should take a small interval around it to find values inbetween
-                range = [
-                    _remap_val_to_axis_range(range[0]) - cls.tol,
-                    _remap_val_to_axis_range(range[0]) + cls.tol,
-                ]
-                return [range]
-            range_intervals = cls.to_intervals(range)
-            ranges = []
-            for interval in range_intervals:
-                if abs(interval[0] - interval[1]) > 0:
-                    # If the interval is not just a single point, we remap it to the axis range
-                    range = _remap_range_to_axis_range([interval[0], interval[1]])
-                    up = range[1]
-                    low = range[0]
-                    if up < low:
-                        # Make sure we remap in the right order
-                        ranges.append([up - cls.tol, low + cls.tol])
-                    else:
-                        ranges.append([low - cls.tol, up + cls.tol])
-            return ranges
-
-        old_find_indexes = cls.find_indexes
-
-        def find_indexes(path, datacube):
-            return old_find_indexes(path, datacube)
-
-        old_unmap_path_key = cls.unmap_path_key
-
-        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
-            value = key_value_path[cls.name]
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisCyclic):
-                    if cls.name == transform.name:
-                        new_val = _remap_val_to_axis_range(value)
-                        key_value_path[cls.name] = new_val
-            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
-            return (key_value_path, leaf_path, unwanted_path)
-
-        old_unmap_to_datacube = cls.unmap_to_datacube
-
-        def unmap_to_datacube(path, unmapped_path):
-            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
-            return (path, unmapped_path)
-
-        old_find_indices_between = cls.find_indices_between
-
-        def find_indices_between(index_ranges, low, up, datacube, method=None):
-            update_range()
-            indexes_between_ranges = []
-
-            if method != "surrounding":
-                return old_find_indices_between(index_ranges, low, up, datacube, method)
-            else:
-                for indexes in index_ranges:
-                    if cls.name in datacube.complete_axes:
-                        start = indexes.searchsorted(low, "left")
-                        end = indexes.searchsorted(up, "right")
-                    else:
-                        start = bisect.bisect_left(indexes, low)
-                        end = bisect.bisect_right(indexes, up)
-
-                    if start - 1 < 0:
-                        index_val_found = indexes[-1:][0]
-                        indexes_between_ranges.append([index_val_found])
-                    if end + 1 > len(indexes):
-                        index_val_found = indexes[:2][0]
-                        indexes_between_ranges.append([index_val_found])
-                    start = max(start - 1, 0)
-                    end = min(end + 1, len(indexes))
-                    if cls.name in datacube.complete_axes:
-                        indexes_between = indexes[start:end].to_list()
-                    else:
-                        indexes_between = indexes[start:end]
-                    indexes_between_ranges.append(indexes_between)
-                return indexes_between_ranges
-
-        def offset(range):
-            # We first unpad the range by the axis tolerance to make sure that
-            # we find the wanted range of the cyclic axis since we padded by the axis tolerance before.
-            # Also, it's safer that we find the offset of a value inside the range instead of on the border
-            unpadded_range = [range[0] + 1.5 * cls.tol, range[1] - 1.5 * cls.tol]
-            cyclic_range = _remap_range_to_axis_range(unpadded_range)
-            offset = unpadded_range[0] - cyclic_range[0]
-            return offset
-
-        cls.to_intervals = to_intervals
-        cls.remap = remap
-        cls.offset = offset
-        cls.find_indexes = find_indexes
-        cls.unmap_to_datacube = unmap_to_datacube
-        cls.find_indices_between = find_indices_between
-        cls.unmap_path_key = unmap_path_key
-
-    return cls
-
-
-def mapper(cls):
-    from .transformations.datacube_mappers import DatacubeMapper
-
-    if cls.has_mapper:
-
-        def find_indexes(path, datacube):
-            # first, find the relevant transformation object that is a mapping in the cls.transformation dico
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeMapper):
-                    transformation = transform
-                    if cls.name == transformation._mapped_axes()[0]:
-                        return transformation.first_axis_vals()
-                    if cls.name == transformation._mapped_axes()[1]:
-                        first_val = path[transformation._mapped_axes()[0]]
-                        return transformation.second_axis_vals(first_val)
-
-        old_unmap_to_datacube = cls.unmap_to_datacube
-
-        def unmap_to_datacube(path, unmapped_path):
-            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeMapper):
-                    if cls.name == transform._mapped_axes()[0]:
-                        # if we are on the first axis, then need to add the first val to unmapped_path
-                        first_val = path.get(cls.name, None)
-                        path.pop(cls.name, None)
-                        if cls.name not in unmapped_path:
-                            # if for some reason, the unmapped_path already has the first axis val, then don't update
-                            unmapped_path[cls.name] = first_val
-                    if cls.name == transform._mapped_axes()[1]:
-                        # if we are on the second axis, then the val of the first axis is stored
-                        # inside unmapped_path so can get it from there
-                        second_val = path.get(cls.name, None)
-                        path.pop(cls.name, None)
-                        first_val = unmapped_path.get(transform._mapped_axes()[0], None)
-                        unmapped_path.pop(transform._mapped_axes()[0], None)
-                        # if the first_val was not in the unmapped_path, then it's still in path
-                        if first_val is None:
-                            first_val = path.get(transform._mapped_axes()[0], None)
-                            path.pop(transform._mapped_axes()[0], None)
-                        if first_val is not None and second_val is not None:
-                            unmapped_idx = transform.unmap(first_val, second_val)
-                            unmapped_path[transform.old_axis] = unmapped_idx
-            return (path, unmapped_path)
-
-        old_unmap_path_key = cls.unmap_path_key
-
-        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
-            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
-            value = key_value_path[cls.name]
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeMapper):
-                    if cls.name == transform._mapped_axes()[0]:
-                        unwanted_val = key_value_path[transform._mapped_axes()[0]]
-                        unwanted_path[cls.name] = unwanted_val
-                    if cls.name == transform._mapped_axes()[1]:
-                        first_val = unwanted_path[transform._mapped_axes()[0]]
-                        unmapped_idx = transform.unmap(first_val, value)
-                        leaf_path.pop(transform._mapped_axes()[0], None)
-                        key_value_path.pop(cls.name)
-                        key_value_path[transform.old_axis] = unmapped_idx
-            return (key_value_path, leaf_path, unwanted_path)
-
-        def find_indices_between(index_ranges, low, up, datacube, method=None):
-            # TODO: add method for snappping
-            indexes_between_ranges = []
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeMapper):
-                    transformation = transform
-                    if cls.name in transformation._mapped_axes():
-                        for idxs in index_ranges:
-                            if method == "surrounding":
-                                axis_reversed = transform._axis_reversed[cls.name]
-                                if not axis_reversed:
-                                    start = bisect.bisect_left(idxs, low)
-                                    end = bisect.bisect_right(idxs, up)
-                                else:
-                                    # TODO: do the custom bisect
-                                    end = bisect_left_cmp(idxs, low, cmp=lambda x, y: x > y) + 1
-                                    start = bisect_right_cmp(idxs, up, cmp=lambda x, y: x > y)
-                                start = max(start - 1, 0)
-                                end = min(end + 1, len(idxs))
-                                indexes_between = idxs[start:end]
-                                indexes_between_ranges.append(indexes_between)
-                            else:
-                                axis_reversed = transform._axis_reversed[cls.name]
-                                if not axis_reversed:
-                                    lower_idx = bisect.bisect_left(idxs, low)
-                                    upper_idx = bisect.bisect_right(idxs, up)
-                                    indexes_between = idxs[lower_idx:upper_idx]
-                                else:
-                                    # TODO: do the custom bisect
-                                    end_idx = bisect_left_cmp(idxs, low, cmp=lambda x, y: x > y) + 1
-                                    start_idx = bisect_right_cmp(idxs, up, cmp=lambda x, y: x > y)
-                                    indexes_between = idxs[start_idx:end_idx]
-                                indexes_between_ranges.append(indexes_between)
-            return indexes_between_ranges
-
-        cls.find_indexes = find_indexes
-        cls.unmap_to_datacube = unmap_to_datacube
-        cls.find_indices_between = find_indices_between
-        cls.unmap_path_key = unmap_path_key
-
-    return cls
-
-
-def merge(cls):
-    from .transformations.datacube_merger import DatacubeAxisMerger
-
-    if cls.has_merger:
-
-        def find_indexes(path, datacube):
-            # first, find the relevant transformation object that is a mapping in the cls.transformation dico
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisMerger):
-                    transformation = transform
-                    if cls.name == transformation._first_axis:
-                        return transformation.merged_values(datacube)
-
-        old_unmap_path_key = cls.unmap_path_key
-
-        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
-            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
-            new_key_value_path = {}
-            value = key_value_path[cls.name]
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisMerger):
-                    if cls.name == transform._first_axis:
-                        (first_val, second_val) = transform.unmerge(value)
-                        new_key_value_path[transform._first_axis] = first_val
-                        new_key_value_path[transform._second_axis] = second_val
-            return (new_key_value_path, leaf_path, unwanted_path)
-
-        old_unmap_to_datacube = cls.unmap_to_datacube
-
-        def unmap_to_datacube(path, unmapped_path):
-            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisMerger):
-                    transformation = transform
-                    if cls.name == transformation._first_axis:
-                        old_val = path.get(cls.name, None)
-                        (first_val, second_val) = transformation.unmerge(old_val)
-                        path.pop(cls.name, None)
-                        path[transformation._first_axis] = first_val
-                        path[transformation._second_axis] = second_val
-            return (path, unmapped_path)
-
-        def find_indices_between(index_ranges, low, up, datacube, method=None):
-            # TODO: add method for snappping
-            indexes_between_ranges = []
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisMerger):
-                    transformation = transform
-                    if cls.name in transformation._mapped_axes():
-                        for indexes in index_ranges:
-                            if method == "surrounding":
-                                start = indexes.index(low)
-                                end = indexes.index(up)
-                                start = max(start - 1, 0)
-                                end = min(end + 1, len(indexes))
-                                indexes_between = indexes[start:end]
-                                indexes_between_ranges.append(indexes_between)
-                            else:
-                                lower_idx = bisect.bisect_left(indexes, low)
-                                upper_idx = bisect.bisect_right(indexes, up)
-                                indexes_between = indexes[lower_idx:upper_idx]
-                                indexes_between_ranges.append(indexes_between)
-            return indexes_between_ranges
-
-        def remap(range):
-            return [range]
-
-        cls.remap = remap
-        cls.find_indexes = find_indexes
-        cls.unmap_to_datacube = unmap_to_datacube
-        cls.find_indices_between = find_indices_between
-        cls.unmap_path_key = unmap_path_key
-
-    return cls
-
-
-def reverse(cls):
-    from .transformations.datacube_reverse import DatacubeAxisReverse
-
-    if cls.reorder:
-
-        def find_indexes(path, datacube):
-            # first, find the relevant transformation object that is a mapping in the cls.transformation dico
-            subarray = datacube.dataarray.sel(path, method="nearest")
-            unordered_indices = datacube.datacube_natural_indexes(cls, subarray)
-            if cls.name in datacube.complete_axes:
-                ordered_indices = unordered_indices.sort_values()
-            else:
-                ordered_indices = unordered_indices
-            return ordered_indices
-
-        def find_indices_between(index_ranges, low, up, datacube, method=None):
-            # TODO: add method for snappping
-            indexes_between_ranges = []
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisReverse):
-                    transformation = transform
-                    if cls.name == transformation.name:
-                        for indexes in index_ranges:
-                            if cls.name in datacube.complete_axes:
-                                # Find the range of indexes between lower and upper
-                                # https://pandas.pydata.org/docs/reference/api/pandas.Index.searchsorted.html
-                                # Assumes the indexes are already sorted (could sort to be sure) and monotonically
-                                # increasing
-                                if method == "surrounding":
-                                    start = indexes.searchsorted(low, "left")
-                                    end = indexes.searchsorted(up, "right")
-                                    start = max(start - 1, 0)
-                                    end = min(end + 1, len(indexes))
-                                    indexes_between = indexes[start:end].to_list()
-                                    indexes_between_ranges.append(indexes_between)
-                                else:
-                                    start = indexes.searchsorted(low, "left")
-                                    end = indexes.searchsorted(up, "right")
-                                    indexes_between = indexes[start:end].to_list()
-                                    indexes_between_ranges.append(indexes_between)
-                            else:
-                                if method == "surrounding":
-                                    start = indexes.index(low)
-                                    end = indexes.index(up)
-                                    start = max(start - 1, 0)
-                                    end = min(end + 1, len(indexes))
-                                    indexes_between = indexes[start:end]
-                                    indexes_between_ranges.append(indexes_between)
-                                else:
-                                    lower_idx = bisect.bisect_left(indexes, low)
-                                    upper_idx = bisect.bisect_right(indexes, up)
-                                    indexes_between = indexes[lower_idx:upper_idx]
-                                    indexes_between_ranges.append(indexes_between)
-            return indexes_between_ranges
-
-        def remap(range):
-            return [range]
-
-        cls.remap = remap
-        cls.find_indexes = find_indexes
-        cls.find_indices_between = find_indices_between
-
-    return cls
-
-
-def type_change(cls):
-    from .transformations.datacube_type_change import DatacubeAxisTypeChange
-
-    if cls.type_change:
-        old_find_indexes = cls.find_indexes
-
-        def find_indexes(path, datacube):
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisTypeChange):
-                    transformation = transform
-                    if cls.name == transformation.name:
-                        original_vals = old_find_indexes(path, datacube)
-                        return transformation.change_val_type(cls.name, original_vals)
-
-        old_unmap_path_key = cls.unmap_path_key
-
-        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
-            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
-            value = key_value_path[cls.name]
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisTypeChange):
-                    if cls.name == transform.name:
-                        unchanged_val = transform.make_str(value)
-                        key_value_path[cls.name] = unchanged_val
-            return (key_value_path, leaf_path, unwanted_path)
-
-        def unmap_to_datacube(path, unmapped_path):
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisTypeChange):
-                    transformation = transform
-                    if cls.name == transformation.name:
-                        changed_val = path.get(cls.name, None)
-                        unchanged_val = transformation.make_str(changed_val)
-                        if cls.name in path:
-                            path.pop(cls.name, None)
-                            unmapped_path[cls.name] = unchanged_val
-            return (path, unmapped_path)
-
-        def find_indices_between(index_ranges, low, up, datacube, method=None):
-            # TODO: add method for snappping
-            indexes_between_ranges = []
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisTypeChange):
-                    transformation = transform
-                    if cls.name == transformation.name:
-                        for indexes in index_ranges:
-                            if method == "surrounding":
-                                start = indexes.index(low)
-                                end = indexes.index(up)
-                                start = max(start - 1, 0)
-                                end = min(end + 1, len(indexes))
-                                indexes_between = indexes[start:end]
-                                indexes_between_ranges.append(indexes_between)
-                            else:
-                                lower_idx = bisect.bisect_left(indexes, low)
-                                upper_idx = bisect.bisect_right(indexes, up)
-                                indexes_between = indexes[lower_idx:upper_idx]
-                                indexes_between_ranges.append(indexes_between)
-            return indexes_between_ranges
-
-        def remap(range):
-            return [range]
-
-        cls.remap = remap
-        cls.find_indexes = find_indexes
-        cls.unmap_to_datacube = unmap_to_datacube
-        cls.find_indices_between = find_indices_between
-        cls.unmap_path_key = unmap_path_key
-
-    return cls
-
-
-def null(cls):
-    if cls.type_change:
-        old_find_indexes = cls.find_indexes
-
-        def find_indexes(path, datacube):
-            return old_find_indexes(path, datacube)
-
-        def find_indices_between(index_ranges, low, up, datacube, method=None):
-            indexes_between_ranges = []
-            for indexes in index_ranges:
-                indexes_between = [i for i in indexes if low <= i <= up]
-                indexes_between_ranges.append(indexes_between)
-            return indexes_between_ranges
-
-        def remap(range):
-            return [range]
-
-        cls.remap = remap
-        cls.find_indexes = find_indexes
-        cls.find_indices_between = find_indices_between
-
-    return cls
+from .transformations.datacube_cyclic import cyclic
+from .transformations.datacube_mappers import mapper
+from .transformations.datacube_merger import merge
+from .transformations.datacube_reverse import reverse
+from .transformations.datacube_type_change import type_change
 
 
 class DatacubeAxis(ABC):
diff --git a/polytope/datacube/transformations/datacube_cyclic.py b/polytope/datacube/transformations/datacube_cyclic.py
index 802285c3..ba93de2e 100644
--- a/polytope/datacube/transformations/datacube_cyclic.py
+++ b/polytope/datacube/transformations/datacube_cyclic.py
@@ -1,3 +1,8 @@
+import bisect
+import math
+from copy import deepcopy
+from typing import List
+
 from .datacube_transformations import DatacubeAxisTransformation
 
 
@@ -23,3 +28,185 @@ def blocked_axes(self):
 
     def unwanted_axes(self):
         return []
+
+
+def cyclic(cls):
+    if cls.is_cyclic:
+
+        def update_range():
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisCyclic):
+                    transformation = transform
+                    cls.range = transformation.range
+
+        def to_intervals(range):
+            update_range()
+            if range[0] == -math.inf:
+                range[0] = cls.range[0]
+            if range[1] == math.inf:
+                range[1] = cls.range[1]
+            axis_lower = cls.range[0]
+            axis_upper = cls.range[1]
+            axis_range = axis_upper - axis_lower
+            lower = range[0]
+            upper = range[1]
+            intervals = []
+            if lower < axis_upper:
+                # In this case, we want to go from lower to the first remapped cyclic axis upper
+                # or the asked upper range value.
+                # For example, if we have cyclic range [0,360] and we want to break [-270,180] into intervals,
+                # we first want to obtain [-270, 0] as the first range, where 0 is the remapped cyclic axis upper
+                # but if we wanted to break [-270, -180] into intervals, we would want to get [-270,-180],
+                # where -180 is the asked upper range value.
+                loops = int((axis_upper - lower) / axis_range)
+                remapped_up = axis_upper - (loops) * axis_range
+                new_upper = min(upper, remapped_up)
+            else:
+                # In this case, since lower >= axis_upper, we need to either go to the asked upper range
+                # or we need to go to the first remapped cyclic axis upper which is higher than lower
+                new_upper = min(axis_upper + axis_range, upper)
+                while new_upper < lower:
+                    new_upper = min(new_upper + axis_range, upper)
+            intervals.append([lower, new_upper])
+            # Now that we have established what the first interval should be, we should just jump from cyclic range
+            # to cyclic range until we hit the asked upper range value.
+            new_up = deepcopy(new_upper)
+            while new_up < upper:
+                new_upper = new_up
+                new_up = min(upper, new_upper + axis_range)
+                intervals.append([new_upper, new_up])
+            # Once we have added all the in-between ranges, we need to add the last interval
+            intervals.append([new_up, upper])
+            return intervals
+
+        def _remap_range_to_axis_range(range):
+            update_range()
+            axis_lower = cls.range[0]
+            axis_upper = cls.range[1]
+            axis_range = axis_upper - axis_lower
+            lower = range[0]
+            upper = range[1]
+            if lower < axis_lower:
+                # In this case we need to calculate the number of loops between the axis lower
+                # and the lower to recenter the lower
+                loops = int((axis_lower - lower - cls.tol) / axis_range)
+                return_lower = lower + (loops + 1) * axis_range
+                return_upper = upper + (loops + 1) * axis_range
+            elif lower >= axis_upper:
+                # In this case we need to calculate the number of loops between the axis upper
+                # and the lower to recenter the lower
+                loops = int((lower - axis_upper) / axis_range)
+                return_lower = lower - (loops + 1) * axis_range
+                return_upper = upper - (loops + 1) * axis_range
+            else:
+                # In this case, the lower value is already in the right range
+                return_lower = lower
+                return_upper = upper
+            return [return_lower, return_upper]
+
+        def _remap_val_to_axis_range(value):
+            return_range = _remap_range_to_axis_range([value, value])
+            return return_range[0]
+
+        def remap(range: List):
+            update_range()
+            if cls.range[0] - cls.tol <= range[0] <= cls.range[1] + cls.tol:
+                if cls.range[0] - cls.tol <= range[1] <= cls.range[1] + cls.tol:
+                    # If we are already in the cyclic range, return it
+                    return [range]
+            elif abs(range[0] - range[1]) <= 2 * cls.tol:
+                # If we have a range that is just one point, then it should still be counted
+                # and so we should take a small interval around it to find values inbetween
+                range = [
+                    _remap_val_to_axis_range(range[0]) - cls.tol,
+                    _remap_val_to_axis_range(range[0]) + cls.tol,
+                ]
+                return [range]
+            range_intervals = cls.to_intervals(range)
+            ranges = []
+            for interval in range_intervals:
+                if abs(interval[0] - interval[1]) > 0:
+                    # If the interval is not just a single point, we remap it to the axis range
+                    range = _remap_range_to_axis_range([interval[0], interval[1]])
+                    up = range[1]
+                    low = range[0]
+                    if up < low:
+                        # Make sure we remap in the right order
+                        ranges.append([up - cls.tol, low + cls.tol])
+                    else:
+                        ranges.append([low - cls.tol, up + cls.tol])
+            return ranges
+
+        old_find_indexes = cls.find_indexes
+
+        def find_indexes(path, datacube):
+            return old_find_indexes(path, datacube)
+
+        old_unmap_path_key = cls.unmap_path_key
+
+        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
+            value = key_value_path[cls.name]
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisCyclic):
+                    if cls.name == transform.name:
+                        new_val = _remap_val_to_axis_range(value)
+                        key_value_path[cls.name] = new_val
+            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
+            return (key_value_path, leaf_path, unwanted_path)
+
+        old_unmap_to_datacube = cls.unmap_to_datacube
+
+        def unmap_to_datacube(path, unmapped_path):
+            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
+            return (path, unmapped_path)
+
+        old_find_indices_between = cls.find_indices_between
+
+        def find_indices_between(index_ranges, low, up, datacube, method=None):
+            update_range()
+            indexes_between_ranges = []
+
+            if method != "surrounding":
+                return old_find_indices_between(index_ranges, low, up, datacube, method)
+            else:
+                for indexes in index_ranges:
+                    if cls.name in datacube.complete_axes:
+                        start = indexes.searchsorted(low, "left")
+                        end = indexes.searchsorted(up, "right")
+                    else:
+                        start = bisect.bisect_left(indexes, low)
+                        end = bisect.bisect_right(indexes, up)
+
+                    if start - 1 < 0:
+                        index_val_found = indexes[-1:][0]
+                        indexes_between_ranges.append([index_val_found])
+                    if end + 1 > len(indexes):
+                        index_val_found = indexes[:2][0]
+                        indexes_between_ranges.append([index_val_found])
+                    start = max(start - 1, 0)
+                    end = min(end + 1, len(indexes))
+                    if cls.name in datacube.complete_axes:
+                        indexes_between = indexes[start:end].to_list()
+                    else:
+                        indexes_between = indexes[start:end]
+                    indexes_between_ranges.append(indexes_between)
+                return indexes_between_ranges
+
+        def offset(range):
+            # We first unpad the range by the axis tolerance to make sure that
+            # we find the wanted range of the cyclic axis since we padded by the axis tolerance before.
+            # Also, it's safer that we find the offset of a value inside the range instead of on the border
+            unpadded_range = [range[0] + 1.5 * cls.tol, range[1] - 1.5 * cls.tol]
+            cyclic_range = _remap_range_to_axis_range(unpadded_range)
+            offset = unpadded_range[0] - cyclic_range[0]
+            return offset
+
+        cls.to_intervals = to_intervals
+        cls.remap = remap
+        cls.offset = offset
+        cls.find_indexes = find_indexes
+        cls.unmap_to_datacube = unmap_to_datacube
+        cls.find_indices_between = find_indices_between
+        cls.unmap_path_key = unmap_path_key
+
+    return cls
diff --git a/polytope/datacube/transformations/datacube_mappers.py b/polytope/datacube/transformations/datacube_mappers.py
index 2e94c649..d410f991 100644
--- a/polytope/datacube/transformations/datacube_mappers.py
+++ b/polytope/datacube/transformations/datacube_mappers.py
@@ -1,6 +1,8 @@
+import bisect
 from copy import deepcopy
 from importlib import import_module
 
+from ...utility.list_tools import bisect_left_cmp, bisect_right_cmp
 from .datacube_transformations import DatacubeAxisTransformation
 
 
@@ -79,3 +81,107 @@ def unmap(self, first_val, second_val):
     "regular": "RegularGridMapper",
     "reduced_ll": "ReducedLatLonMapper",
 }
+
+
+def mapper(cls):
+    if cls.has_mapper:
+
+        def find_indexes(path, datacube):
+            # first, find the relevant transformation object that is a mapping in the cls.transformation dico
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeMapper):
+                    transformation = transform
+                    if cls.name == transformation._mapped_axes()[0]:
+                        return transformation.first_axis_vals()
+                    if cls.name == transformation._mapped_axes()[1]:
+                        first_val = path[transformation._mapped_axes()[0]]
+                        return transformation.second_axis_vals(first_val)
+
+        old_unmap_to_datacube = cls.unmap_to_datacube
+
+        def unmap_to_datacube(path, unmapped_path):
+            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeMapper):
+                    if cls.name == transform._mapped_axes()[0]:
+                        # if we are on the first axis, then need to add the first val to unmapped_path
+                        first_val = path.get(cls.name, None)
+                        path.pop(cls.name, None)
+                        if cls.name not in unmapped_path:
+                            # if for some reason, the unmapped_path already has the first axis val, then don't update
+                            unmapped_path[cls.name] = first_val
+                    if cls.name == transform._mapped_axes()[1]:
+                        # if we are on the second axis, then the val of the first axis is stored
+                        # inside unmapped_path so can get it from there
+                        second_val = path.get(cls.name, None)
+                        path.pop(cls.name, None)
+                        first_val = unmapped_path.get(transform._mapped_axes()[0], None)
+                        unmapped_path.pop(transform._mapped_axes()[0], None)
+                        # if the first_val was not in the unmapped_path, then it's still in path
+                        if first_val is None:
+                            first_val = path.get(transform._mapped_axes()[0], None)
+                            path.pop(transform._mapped_axes()[0], None)
+                        if first_val is not None and second_val is not None:
+                            unmapped_idx = transform.unmap(first_val, second_val)
+                            unmapped_path[transform.old_axis] = unmapped_idx
+            return (path, unmapped_path)
+
+        old_unmap_path_key = cls.unmap_path_key
+
+        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
+            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
+            value = key_value_path[cls.name]
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeMapper):
+                    if cls.name == transform._mapped_axes()[0]:
+                        unwanted_val = key_value_path[transform._mapped_axes()[0]]
+                        unwanted_path[cls.name] = unwanted_val
+                    if cls.name == transform._mapped_axes()[1]:
+                        first_val = unwanted_path[transform._mapped_axes()[0]]
+                        unmapped_idx = transform.unmap(first_val, value)
+                        leaf_path.pop(transform._mapped_axes()[0], None)
+                        key_value_path.pop(cls.name)
+                        key_value_path[transform.old_axis] = unmapped_idx
+            return (key_value_path, leaf_path, unwanted_path)
+
+        def find_indices_between(index_ranges, low, up, datacube, method=None):
+            # TODO: add method for snappping
+            indexes_between_ranges = []
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeMapper):
+                    transformation = transform
+                    if cls.name in transformation._mapped_axes():
+                        for idxs in index_ranges:
+                            if method == "surrounding":
+                                axis_reversed = transform._axis_reversed[cls.name]
+                                if not axis_reversed:
+                                    start = bisect.bisect_left(idxs, low)
+                                    end = bisect.bisect_right(idxs, up)
+                                else:
+                                    # TODO: do the custom bisect
+                                    end = bisect_left_cmp(idxs, low, cmp=lambda x, y: x > y) + 1
+                                    start = bisect_right_cmp(idxs, up, cmp=lambda x, y: x > y)
+                                start = max(start - 1, 0)
+                                end = min(end + 1, len(idxs))
+                                indexes_between = idxs[start:end]
+                                indexes_between_ranges.append(indexes_between)
+                            else:
+                                axis_reversed = transform._axis_reversed[cls.name]
+                                if not axis_reversed:
+                                    lower_idx = bisect.bisect_left(idxs, low)
+                                    upper_idx = bisect.bisect_right(idxs, up)
+                                    indexes_between = idxs[lower_idx:upper_idx]
+                                else:
+                                    # TODO: do the custom bisect
+                                    end_idx = bisect_left_cmp(idxs, low, cmp=lambda x, y: x > y) + 1
+                                    start_idx = bisect_right_cmp(idxs, up, cmp=lambda x, y: x > y)
+                                    indexes_between = idxs[start_idx:end_idx]
+                                indexes_between_ranges.append(indexes_between)
+            return indexes_between_ranges
+
+        cls.find_indexes = find_indexes
+        cls.unmap_to_datacube = unmap_to_datacube
+        cls.find_indices_between = find_indices_between
+        cls.unmap_path_key = unmap_path_key
+
+    return cls
diff --git a/polytope/datacube/transformations/datacube_merger.py b/polytope/datacube/transformations/datacube_merger.py
index d6027867..883ea964 100644
--- a/polytope/datacube/transformations/datacube_merger.py
+++ b/polytope/datacube/transformations/datacube_merger.py
@@ -1,3 +1,5 @@
+import bisect
+
 import numpy as np
 import pandas as pd
 
@@ -61,3 +63,77 @@ def unmerge(self, merged_val):
     def change_val_type(self, axis_name, values):
         new_values = pd.to_datetime(values)
         return new_values
+
+
+def merge(cls):
+    if cls.has_merger:
+
+        def find_indexes(path, datacube):
+            # first, find the relevant transformation object that is a mapping in the cls.transformation dico
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisMerger):
+                    transformation = transform
+                    if cls.name == transformation._first_axis:
+                        return transformation.merged_values(datacube)
+
+        old_unmap_path_key = cls.unmap_path_key
+
+        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
+            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
+            new_key_value_path = {}
+            value = key_value_path[cls.name]
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisMerger):
+                    if cls.name == transform._first_axis:
+                        (first_val, second_val) = transform.unmerge(value)
+                        new_key_value_path[transform._first_axis] = first_val
+                        new_key_value_path[transform._second_axis] = second_val
+            return (new_key_value_path, leaf_path, unwanted_path)
+
+        old_unmap_to_datacube = cls.unmap_to_datacube
+
+        def unmap_to_datacube(path, unmapped_path):
+            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisMerger):
+                    transformation = transform
+                    if cls.name == transformation._first_axis:
+                        old_val = path.get(cls.name, None)
+                        (first_val, second_val) = transformation.unmerge(old_val)
+                        path.pop(cls.name, None)
+                        path[transformation._first_axis] = first_val
+                        path[transformation._second_axis] = second_val
+            return (path, unmapped_path)
+
+        def find_indices_between(index_ranges, low, up, datacube, method=None):
+            # TODO: add method for snappping
+            indexes_between_ranges = []
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisMerger):
+                    transformation = transform
+                    if cls.name in transformation._mapped_axes():
+                        for indexes in index_ranges:
+                            if method == "surrounding":
+                                start = indexes.index(low)
+                                end = indexes.index(up)
+                                start = max(start - 1, 0)
+                                end = min(end + 1, len(indexes))
+                                indexes_between = indexes[start:end]
+                                indexes_between_ranges.append(indexes_between)
+                            else:
+                                lower_idx = bisect.bisect_left(indexes, low)
+                                upper_idx = bisect.bisect_right(indexes, up)
+                                indexes_between = indexes[lower_idx:upper_idx]
+                                indexes_between_ranges.append(indexes_between)
+            return indexes_between_ranges
+
+        def remap(range):
+            return [range]
+
+        cls.remap = remap
+        cls.find_indexes = find_indexes
+        cls.unmap_to_datacube = unmap_to_datacube
+        cls.find_indices_between = find_indices_between
+        cls.unmap_path_key = unmap_path_key
+
+    return cls
diff --git a/polytope/datacube/transformations/datacube_null_transformation.py b/polytope/datacube/transformations/datacube_null_transformation.py
index 55c94277..66af3f3a 100644
--- a/polytope/datacube/transformations/datacube_null_transformation.py
+++ b/polytope/datacube/transformations/datacube_null_transformation.py
@@ -20,3 +20,27 @@ def blocked_axes(self):
 
     def unwanted_axes(self):
         return []
+
+
+def null(cls):
+    if cls.type_change:
+        old_find_indexes = cls.find_indexes
+
+        def find_indexes(path, datacube):
+            return old_find_indexes(path, datacube)
+
+        def find_indices_between(index_ranges, low, up, datacube, method=None):
+            indexes_between_ranges = []
+            for indexes in index_ranges:
+                indexes_between = [i for i in indexes if low <= i <= up]
+                indexes_between_ranges.append(indexes_between)
+            return indexes_between_ranges
+
+        def remap(range):
+            return [range]
+
+        cls.remap = remap
+        cls.find_indexes = find_indexes
+        cls.find_indices_between = find_indices_between
+
+    return cls
diff --git a/polytope/datacube/transformations/datacube_reverse.py b/polytope/datacube/transformations/datacube_reverse.py
index 6a556907..0e03006a 100644
--- a/polytope/datacube/transformations/datacube_reverse.py
+++ b/polytope/datacube/transformations/datacube_reverse.py
@@ -1,3 +1,5 @@
+import bisect
+
 from .datacube_transformations import DatacubeAxisTransformation
 
 
@@ -20,3 +22,66 @@ def blocked_axes(self):
 
     def unwanted_axes(self):
         return []
+
+
+def reverse(cls):
+    if cls.reorder:
+
+        def find_indexes(path, datacube):
+            # first, find the relevant transformation object that is a mapping in the cls.transformation dico
+            subarray = datacube.dataarray.sel(path, method="nearest")
+            unordered_indices = datacube.datacube_natural_indexes(cls, subarray)
+            if cls.name in datacube.complete_axes:
+                ordered_indices = unordered_indices.sort_values()
+            else:
+                ordered_indices = unordered_indices
+            return ordered_indices
+
+        def find_indices_between(index_ranges, low, up, datacube, method=None):
+            # TODO: add method for snappping
+            indexes_between_ranges = []
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisReverse):
+                    transformation = transform
+                    if cls.name == transformation.name:
+                        for indexes in index_ranges:
+                            if cls.name in datacube.complete_axes:
+                                # Find the range of indexes between lower and upper
+                                # https://pandas.pydata.org/docs/reference/api/pandas.Index.searchsorted.html
+                                # Assumes the indexes are already sorted (could sort to be sure) and monotonically
+                                # increasing
+                                if method == "surrounding":
+                                    start = indexes.searchsorted(low, "left")
+                                    end = indexes.searchsorted(up, "right")
+                                    start = max(start - 1, 0)
+                                    end = min(end + 1, len(indexes))
+                                    indexes_between = indexes[start:end].to_list()
+                                    indexes_between_ranges.append(indexes_between)
+                                else:
+                                    start = indexes.searchsorted(low, "left")
+                                    end = indexes.searchsorted(up, "right")
+                                    indexes_between = indexes[start:end].to_list()
+                                    indexes_between_ranges.append(indexes_between)
+                            else:
+                                if method == "surrounding":
+                                    start = indexes.index(low)
+                                    end = indexes.index(up)
+                                    start = max(start - 1, 0)
+                                    end = min(end + 1, len(indexes))
+                                    indexes_between = indexes[start:end]
+                                    indexes_between_ranges.append(indexes_between)
+                                else:
+                                    lower_idx = bisect.bisect_left(indexes, low)
+                                    upper_idx = bisect.bisect_right(indexes, up)
+                                    indexes_between = indexes[lower_idx:upper_idx]
+                                    indexes_between_ranges.append(indexes_between)
+            return indexes_between_ranges
+
+        def remap(range):
+            return [range]
+
+        cls.remap = remap
+        cls.find_indexes = find_indexes
+        cls.find_indices_between = find_indices_between
+
+    return cls
diff --git a/polytope/datacube/transformations/datacube_type_change.py b/polytope/datacube/transformations/datacube_type_change.py
index cdc046b7..1813efe2 100644
--- a/polytope/datacube/transformations/datacube_type_change.py
+++ b/polytope/datacube/transformations/datacube_type_change.py
@@ -1,3 +1,4 @@
+import bisect
 from copy import deepcopy
 from importlib import import_module
 
@@ -51,3 +52,73 @@ def make_str(self, value):
 
 
 _type_to_datacube_type_change_lookup = {"int": "TypeChangeStrToInt"}
+
+
+def type_change(cls):
+    if cls.type_change:
+        old_find_indexes = cls.find_indexes
+
+        def find_indexes(path, datacube):
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisTypeChange):
+                    transformation = transform
+                    if cls.name == transformation.name:
+                        original_vals = old_find_indexes(path, datacube)
+                        return transformation.change_val_type(cls.name, original_vals)
+
+        old_unmap_path_key = cls.unmap_path_key
+
+        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
+            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
+            value = key_value_path[cls.name]
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisTypeChange):
+                    if cls.name == transform.name:
+                        unchanged_val = transform.make_str(value)
+                        key_value_path[cls.name] = unchanged_val
+            return (key_value_path, leaf_path, unwanted_path)
+
+        def unmap_to_datacube(path, unmapped_path):
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisTypeChange):
+                    transformation = transform
+                    if cls.name == transformation.name:
+                        changed_val = path.get(cls.name, None)
+                        unchanged_val = transformation.make_str(changed_val)
+                        if cls.name in path:
+                            path.pop(cls.name, None)
+                            unmapped_path[cls.name] = unchanged_val
+            return (path, unmapped_path)
+
+        def find_indices_between(index_ranges, low, up, datacube, method=None):
+            # TODO: add method for snappping
+            indexes_between_ranges = []
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisTypeChange):
+                    transformation = transform
+                    if cls.name == transformation.name:
+                        for indexes in index_ranges:
+                            if method == "surrounding":
+                                start = indexes.index(low)
+                                end = indexes.index(up)
+                                start = max(start - 1, 0)
+                                end = min(end + 1, len(indexes))
+                                indexes_between = indexes[start:end]
+                                indexes_between_ranges.append(indexes_between)
+                            else:
+                                lower_idx = bisect.bisect_left(indexes, low)
+                                upper_idx = bisect.bisect_right(indexes, up)
+                                indexes_between = indexes[lower_idx:upper_idx]
+                                indexes_between_ranges.append(indexes_between)
+            return indexes_between_ranges
+
+        def remap(range):
+            return [range]
+
+        cls.remap = remap
+        cls.find_indexes = find_indexes
+        cls.unmap_to_datacube = unmap_to_datacube
+        cls.find_indices_between = find_indices_between
+        cls.unmap_path_key = unmap_path_key
+
+    return cls

From 8eeb0b5087aa7ece5ad406db06e6e0564b43fe6e Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Mon, 22 Jan 2024 16:15:27 +0100
Subject: [PATCH 03/12] refactor some transformations

---
 polytope/datacube/datacube_axis.py            |   4 +-
 .../datacube_cyclic/cyclic_axis_decorator.py  | 188 ++++++++++++++++++
 .../{ => datacube_cyclic}/datacube_cyclic.py  |   2 +-
 .../datacube_mappers/datacube_mappers.py      |  81 ++++++++
 .../mapper_axis_decorator.py}                 |  83 +-------
 .../mapper_types}/healpix.py                  |   0
 .../mapper_types}/octahedral.py               |   2 +-
 .../mapper_types}/reduced_ll.py               |   0
 .../mapper_types}/regular.py                  |   0
 .../datacube_transformations.py               |   4 +-
 tests/test_mappers.py                         |   4 +-
 11 files changed, 280 insertions(+), 88 deletions(-)
 create mode 100644 polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py
 rename polytope/datacube/transformations/{ => datacube_cyclic}/datacube_cyclic.py (99%)
 create mode 100644 polytope/datacube/transformations/datacube_mappers/datacube_mappers.py
 rename polytope/datacube/transformations/{datacube_mappers.py => datacube_mappers/mapper_axis_decorator.py} (67%)
 rename polytope/datacube/transformations/{mappers => datacube_mappers/mapper_types}/healpix.py (100%)
 rename polytope/datacube/transformations/{mappers => datacube_mappers/mapper_types}/octahedral.py (99%)
 rename polytope/datacube/transformations/{mappers => datacube_mappers/mapper_types}/reduced_ll.py (100%)
 rename polytope/datacube/transformations/{mappers => datacube_mappers/mapper_types}/regular.py (100%)

diff --git a/polytope/datacube/datacube_axis.py b/polytope/datacube/datacube_axis.py
index 129581d0..2e88fb26 100644
--- a/polytope/datacube/datacube_axis.py
+++ b/polytope/datacube/datacube_axis.py
@@ -5,8 +5,8 @@
 import numpy as np
 import pandas as pd
 
-from .transformations.datacube_cyclic import cyclic
-from .transformations.datacube_mappers import mapper
+from .transformations.datacube_cyclic.cyclic_axis_decorator import cyclic
+from .transformations.datacube_mappers.mapper_axis_decorator import mapper
 from .transformations.datacube_merger import merge
 from .transformations.datacube_reverse import reverse
 from .transformations.datacube_type_change import type_change
diff --git a/polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py b/polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py
new file mode 100644
index 00000000..8b1cf292
--- /dev/null
+++ b/polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py
@@ -0,0 +1,188 @@
+import bisect
+import math
+from copy import deepcopy
+from typing import List
+
+from .datacube_cyclic import DatacubeAxisCyclic
+
+
+def cyclic(cls):
+    if cls.is_cyclic:
+
+        def update_range():
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisCyclic):
+                    transformation = transform
+                    cls.range = transformation.range
+
+        def to_intervals(range):
+            update_range()
+            if range[0] == -math.inf:
+                range[0] = cls.range[0]
+            if range[1] == math.inf:
+                range[1] = cls.range[1]
+            axis_lower = cls.range[0]
+            axis_upper = cls.range[1]
+            axis_range = axis_upper - axis_lower
+            lower = range[0]
+            upper = range[1]
+            intervals = []
+            if lower < axis_upper:
+                # In this case, we want to go from lower to the first remapped cyclic axis upper
+                # or the asked upper range value.
+                # For example, if we have cyclic range [0,360] and we want to break [-270,180] into intervals,
+                # we first want to obtain [-270, 0] as the first range, where 0 is the remapped cyclic axis upper
+                # but if we wanted to break [-270, -180] into intervals, we would want to get [-270,-180],
+                # where -180 is the asked upper range value.
+                loops = int((axis_upper - lower) / axis_range)
+                remapped_up = axis_upper - (loops) * axis_range
+                new_upper = min(upper, remapped_up)
+            else:
+                # In this case, since lower >= axis_upper, we need to either go to the asked upper range
+                # or we need to go to the first remapped cyclic axis upper which is higher than lower
+                new_upper = min(axis_upper + axis_range, upper)
+                while new_upper < lower:
+                    new_upper = min(new_upper + axis_range, upper)
+            intervals.append([lower, new_upper])
+            # Now that we have established what the first interval should be, we should just jump from cyclic range
+            # to cyclic range until we hit the asked upper range value.
+            new_up = deepcopy(new_upper)
+            while new_up < upper:
+                new_upper = new_up
+                new_up = min(upper, new_upper + axis_range)
+                intervals.append([new_upper, new_up])
+            # Once we have added all the in-between ranges, we need to add the last interval
+            intervals.append([new_up, upper])
+            return intervals
+
+        def _remap_range_to_axis_range(range):
+            update_range()
+            axis_lower = cls.range[0]
+            axis_upper = cls.range[1]
+            axis_range = axis_upper - axis_lower
+            lower = range[0]
+            upper = range[1]
+            if lower < axis_lower:
+                # In this case we need to calculate the number of loops between the axis lower
+                # and the lower to recenter the lower
+                loops = int((axis_lower - lower - cls.tol) / axis_range)
+                return_lower = lower + (loops + 1) * axis_range
+                return_upper = upper + (loops + 1) * axis_range
+            elif lower >= axis_upper:
+                # In this case we need to calculate the number of loops between the axis upper
+                # and the lower to recenter the lower
+                loops = int((lower - axis_upper) / axis_range)
+                return_lower = lower - (loops + 1) * axis_range
+                return_upper = upper - (loops + 1) * axis_range
+            else:
+                # In this case, the lower value is already in the right range
+                return_lower = lower
+                return_upper = upper
+            return [return_lower, return_upper]
+
+        def _remap_val_to_axis_range(value):
+            return_range = _remap_range_to_axis_range([value, value])
+            return return_range[0]
+
+        def remap(range: List):
+            update_range()
+            if cls.range[0] - cls.tol <= range[0] <= cls.range[1] + cls.tol:
+                if cls.range[0] - cls.tol <= range[1] <= cls.range[1] + cls.tol:
+                    # If we are already in the cyclic range, return it
+                    return [range]
+            elif abs(range[0] - range[1]) <= 2 * cls.tol:
+                # If we have a range that is just one point, then it should still be counted
+                # and so we should take a small interval around it to find values inbetween
+                range = [
+                    _remap_val_to_axis_range(range[0]) - cls.tol,
+                    _remap_val_to_axis_range(range[0]) + cls.tol,
+                ]
+                return [range]
+            range_intervals = cls.to_intervals(range)
+            ranges = []
+            for interval in range_intervals:
+                if abs(interval[0] - interval[1]) > 0:
+                    # If the interval is not just a single point, we remap it to the axis range
+                    range = _remap_range_to_axis_range([interval[0], interval[1]])
+                    up = range[1]
+                    low = range[0]
+                    if up < low:
+                        # Make sure we remap in the right order
+                        ranges.append([up - cls.tol, low + cls.tol])
+                    else:
+                        ranges.append([low - cls.tol, up + cls.tol])
+            return ranges
+
+        old_find_indexes = cls.find_indexes
+
+        def find_indexes(path, datacube):
+            return old_find_indexes(path, datacube)
+
+        old_unmap_path_key = cls.unmap_path_key
+
+        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
+            value = key_value_path[cls.name]
+            for transform in cls.transformations:
+                if isinstance(transform, DatacubeAxisCyclic):
+                    if cls.name == transform.name:
+                        new_val = _remap_val_to_axis_range(value)
+                        key_value_path[cls.name] = new_val
+            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
+            return (key_value_path, leaf_path, unwanted_path)
+
+        old_unmap_to_datacube = cls.unmap_to_datacube
+
+        def unmap_to_datacube(path, unmapped_path):
+            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
+            return (path, unmapped_path)
+
+        old_find_indices_between = cls.find_indices_between
+
+        def find_indices_between(index_ranges, low, up, datacube, method=None):
+            update_range()
+            indexes_between_ranges = []
+
+            if method != "surrounding":
+                return old_find_indices_between(index_ranges, low, up, datacube, method)
+            else:
+                for indexes in index_ranges:
+                    if cls.name in datacube.complete_axes:
+                        start = indexes.searchsorted(low, "left")
+                        end = indexes.searchsorted(up, "right")
+                    else:
+                        start = bisect.bisect_left(indexes, low)
+                        end = bisect.bisect_right(indexes, up)
+
+                    if start - 1 < 0:
+                        index_val_found = indexes[-1:][0]
+                        indexes_between_ranges.append([index_val_found])
+                    if end + 1 > len(indexes):
+                        index_val_found = indexes[:2][0]
+                        indexes_between_ranges.append([index_val_found])
+                    start = max(start - 1, 0)
+                    end = min(end + 1, len(indexes))
+                    if cls.name in datacube.complete_axes:
+                        indexes_between = indexes[start:end].to_list()
+                    else:
+                        indexes_between = indexes[start:end]
+                    indexes_between_ranges.append(indexes_between)
+                return indexes_between_ranges
+
+        def offset(range):
+            # We first unpad the range by the axis tolerance to make sure that
+            # we find the wanted range of the cyclic axis since we padded by the axis tolerance before.
+            # Also, it's safer that we find the offset of a value inside the range instead of on the border
+            unpadded_range = [range[0] + 1.5 * cls.tol, range[1] - 1.5 * cls.tol]
+            cyclic_range = _remap_range_to_axis_range(unpadded_range)
+            offset = unpadded_range[0] - cyclic_range[0]
+            return offset
+
+        cls.to_intervals = to_intervals
+        cls.remap = remap
+        cls.offset = offset
+        cls.find_indexes = find_indexes
+        cls.unmap_to_datacube = unmap_to_datacube
+        cls.find_indices_between = find_indices_between
+        cls.unmap_path_key = unmap_path_key
+
+    return cls
diff --git a/polytope/datacube/transformations/datacube_cyclic.py b/polytope/datacube/transformations/datacube_cyclic/datacube_cyclic.py
similarity index 99%
rename from polytope/datacube/transformations/datacube_cyclic.py
rename to polytope/datacube/transformations/datacube_cyclic/datacube_cyclic.py
index ba93de2e..fd4da7ae 100644
--- a/polytope/datacube/transformations/datacube_cyclic.py
+++ b/polytope/datacube/transformations/datacube_cyclic/datacube_cyclic.py
@@ -3,7 +3,7 @@
 from copy import deepcopy
 from typing import List
 
-from .datacube_transformations import DatacubeAxisTransformation
+from ..datacube_transformations import DatacubeAxisTransformation
 
 
 class DatacubeAxisCyclic(DatacubeAxisTransformation):
diff --git a/polytope/datacube/transformations/datacube_mappers/datacube_mappers.py b/polytope/datacube/transformations/datacube_mappers/datacube_mappers.py
new file mode 100644
index 00000000..c42d04a7
--- /dev/null
+++ b/polytope/datacube/transformations/datacube_mappers/datacube_mappers.py
@@ -0,0 +1,81 @@
+from copy import deepcopy
+from importlib import import_module
+
+from ..datacube_transformations import DatacubeAxisTransformation
+
+
+class DatacubeMapper(DatacubeAxisTransformation):
+    # Needs to implements DatacubeAxisTransformation methods
+
+    def __init__(self, name, mapper_options):
+        self.transformation_options = mapper_options
+        self.grid_type = mapper_options["type"]
+        self.grid_resolution = mapper_options["resolution"]
+        self.grid_axes = mapper_options["axes"]
+        self.old_axis = name
+        self._final_transformation = self.generate_final_transformation()
+        self._final_mapped_axes = self._final_transformation._mapped_axes
+        self._axis_reversed = self._final_transformation._axis_reversed
+
+    def generate_final_transformation(self):
+        map_type = _type_to_datacube_mapper_lookup[self.grid_type]
+        module = import_module("polytope.datacube.transformations.datacube_mappers.mapper_types." + self.grid_type)
+        constructor = getattr(module, map_type)
+        transformation = deepcopy(constructor(self.old_axis, self.grid_axes, self.grid_resolution))
+        return transformation
+
+    def blocked_axes(self):
+        return []
+
+    def unwanted_axes(self):
+        return [self._final_mapped_axes[0]]
+
+    def transformation_axes_final(self):
+        final_axes = self._final_mapped_axes
+        return final_axes
+
+    # Needs to also implement its own methods
+
+    def change_val_type(self, axis_name, values):
+        # the new axis_vals created will be floats
+        return [0.0]
+
+    def _mapped_axes(self):
+        # NOTE: Each of the mapper method needs to call it's sub mapper method
+        final_axes = self._final_mapped_axes
+        return final_axes
+
+    def _base_axis(self):
+        pass
+
+    def _resolution(self):
+        pass
+
+    def first_axis_vals(self):
+        return self._final_transformation.first_axis_vals()
+
+    def second_axis_vals(self, first_val):
+        return self._final_transformation.second_axis_vals(first_val)
+
+    def map_first_axis(self, lower, upper):
+        return self._final_transformation.map_first_axis(lower, upper)
+
+    def map_second_axis(self, first_val, lower, upper):
+        return self._final_transformation.map_second_axis(first_val, lower, upper)
+
+    def find_second_idx(self, first_val, second_val):
+        return self._final_transformation.find_second_idx(first_val, second_val)
+
+    def unmap_first_val_to_start_line_idx(self, first_val):
+        return self._final_transformation.unmap_first_val_to_start_line_idx(first_val)
+
+    def unmap(self, first_val, second_val):
+        return self._final_transformation.unmap(first_val, second_val)
+
+
+_type_to_datacube_mapper_lookup = {
+    "octahedral": "OctahedralGridMapper",
+    "healpix": "HealpixGridMapper",
+    "regular": "RegularGridMapper",
+    "reduced_ll": "ReducedLatLonMapper",
+}
diff --git a/polytope/datacube/transformations/datacube_mappers.py b/polytope/datacube/transformations/datacube_mappers/mapper_axis_decorator.py
similarity index 67%
rename from polytope/datacube/transformations/datacube_mappers.py
rename to polytope/datacube/transformations/datacube_mappers/mapper_axis_decorator.py
index d410f991..30f95b61 100644
--- a/polytope/datacube/transformations/datacube_mappers.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_axis_decorator.py
@@ -1,86 +1,7 @@
 import bisect
-from copy import deepcopy
-from importlib import import_module
 
-from ...utility.list_tools import bisect_left_cmp, bisect_right_cmp
-from .datacube_transformations import DatacubeAxisTransformation
-
-
-class DatacubeMapper(DatacubeAxisTransformation):
-    # Needs to implements DatacubeAxisTransformation methods
-
-    def __init__(self, name, mapper_options):
-        self.transformation_options = mapper_options
-        self.grid_type = mapper_options["type"]
-        self.grid_resolution = mapper_options["resolution"]
-        self.grid_axes = mapper_options["axes"]
-        self.old_axis = name
-        self._final_transformation = self.generate_final_transformation()
-        self._final_mapped_axes = self._final_transformation._mapped_axes
-        self._axis_reversed = self._final_transformation._axis_reversed
-
-    def generate_final_transformation(self):
-        map_type = _type_to_datacube_mapper_lookup[self.grid_type]
-        module = import_module("polytope.datacube.transformations.mappers." + self.grid_type)
-        constructor = getattr(module, map_type)
-        transformation = deepcopy(constructor(self.old_axis, self.grid_axes, self.grid_resolution))
-        return transformation
-
-    def blocked_axes(self):
-        return []
-
-    def unwanted_axes(self):
-        return [self._final_mapped_axes[0]]
-
-    def transformation_axes_final(self):
-        final_axes = self._final_mapped_axes
-        return final_axes
-
-    # Needs to also implement its own methods
-
-    def change_val_type(self, axis_name, values):
-        # the new axis_vals created will be floats
-        return [0.0]
-
-    def _mapped_axes(self):
-        # NOTE: Each of the mapper method needs to call it's sub mapper method
-        final_axes = self._final_mapped_axes
-        return final_axes
-
-    def _base_axis(self):
-        pass
-
-    def _resolution(self):
-        pass
-
-    def first_axis_vals(self):
-        return self._final_transformation.first_axis_vals()
-
-    def second_axis_vals(self, first_val):
-        return self._final_transformation.second_axis_vals(first_val)
-
-    def map_first_axis(self, lower, upper):
-        return self._final_transformation.map_first_axis(lower, upper)
-
-    def map_second_axis(self, first_val, lower, upper):
-        return self._final_transformation.map_second_axis(first_val, lower, upper)
-
-    def find_second_idx(self, first_val, second_val):
-        return self._final_transformation.find_second_idx(first_val, second_val)
-
-    def unmap_first_val_to_start_line_idx(self, first_val):
-        return self._final_transformation.unmap_first_val_to_start_line_idx(first_val)
-
-    def unmap(self, first_val, second_val):
-        return self._final_transformation.unmap(first_val, second_val)
-
-
-_type_to_datacube_mapper_lookup = {
-    "octahedral": "OctahedralGridMapper",
-    "healpix": "HealpixGridMapper",
-    "regular": "RegularGridMapper",
-    "reduced_ll": "ReducedLatLonMapper",
-}
+from ....utility.list_tools import bisect_left_cmp, bisect_right_cmp
+from .datacube_mappers import DatacubeMapper
 
 
 def mapper(cls):
diff --git a/polytope/datacube/transformations/mappers/healpix.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/healpix.py
similarity index 100%
rename from polytope/datacube/transformations/mappers/healpix.py
rename to polytope/datacube/transformations/datacube_mappers/mapper_types/healpix.py
diff --git a/polytope/datacube/transformations/mappers/octahedral.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/octahedral.py
similarity index 99%
rename from polytope/datacube/transformations/mappers/octahedral.py
rename to polytope/datacube/transformations/datacube_mappers/mapper_types/octahedral.py
index 1c24703d..b2a3159b 100644
--- a/polytope/datacube/transformations/mappers/octahedral.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_types/octahedral.py
@@ -1,6 +1,6 @@
 import math
 
-from ....utility.list_tools import bisect_left_cmp, bisect_right_cmp
+from .....utility.list_tools import bisect_left_cmp, bisect_right_cmp
 from ..datacube_mappers import DatacubeMapper
 
 
diff --git a/polytope/datacube/transformations/mappers/reduced_ll.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/reduced_ll.py
similarity index 100%
rename from polytope/datacube/transformations/mappers/reduced_ll.py
rename to polytope/datacube/transformations/datacube_mappers/mapper_types/reduced_ll.py
diff --git a/polytope/datacube/transformations/mappers/regular.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/regular.py
similarity index 100%
rename from polytope/datacube/transformations/mappers/regular.py
rename to polytope/datacube/transformations/datacube_mappers/mapper_types/regular.py
diff --git a/polytope/datacube/transformations/datacube_transformations.py b/polytope/datacube/transformations/datacube_transformations.py
index 900ad16b..4bd07a2d 100644
--- a/polytope/datacube/transformations/datacube_transformations.py
+++ b/polytope/datacube/transformations/datacube_transformations.py
@@ -54,8 +54,8 @@ def change_val_type(self, axis_name, values):
 }
 
 _type_to_transformation_file_lookup = {
-    "mapper": "mappers",
-    "cyclic": "cyclic",
+    "mapper": "mappers.datacube_mappers",
+    "cyclic": "cyclic.datacube_cyclic",
     "merge": "merger",
     "reverse": "reverse",
     "type_change": "type_change",
diff --git a/tests/test_mappers.py b/tests/test_mappers.py
index b3661822..1231f19d 100644
--- a/tests/test_mappers.py
+++ b/tests/test_mappers.py
@@ -1,4 +1,6 @@
-from polytope.datacube.transformations.mappers.octahedral import OctahedralGridMapper
+from polytope.datacube.transformations.datacube_mappers.mapper_types.octahedral import (
+    OctahedralGridMapper,
+)
 
 
 class TestMapper:

From 38f2ade35c410b08abef454f3f30cebc24a90a49 Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Thu, 25 Jan 2024 10:23:22 +0100
Subject: [PATCH 04/12] change structure of transformations

---
 polytope/datacube/datacube_axis.py            |   6 +-
 .../datacube_cyclic/datacube_cyclic.py        | 187 ------------------
 .../datacube_merger/datacube_merger.py        |  63 ++++++
 .../merger_axis_decorator.py}                 |  64 +-----
 .../datacube_null_transformation.py           |  22 +++
 .../null_axis_decorator.py}                   |  24 ---
 .../datacube_reverse/datacube_reverse.py      |  22 +++
 .../reverse_axis_decorator.py}                |  23 +--
 .../datacube_transformations.py               |   8 +-
 .../datacube_type_change.py                   |  53 +++++
 .../type_change_axis_decorator.py}            |  53 +----
 11 files changed, 170 insertions(+), 355 deletions(-)
 create mode 100644 polytope/datacube/transformations/datacube_merger/datacube_merger.py
 rename polytope/datacube/transformations/{datacube_merger.py => datacube_merger/merger_axis_decorator.py} (61%)
 create mode 100644 polytope/datacube/transformations/datacube_null_transformation/datacube_null_transformation.py
 rename polytope/datacube/transformations/{datacube_null_transformation.py => datacube_null_transformation/null_axis_decorator.py} (56%)
 create mode 100644 polytope/datacube/transformations/datacube_reverse/datacube_reverse.py
 rename polytope/datacube/transformations/{datacube_reverse.py => datacube_reverse/reverse_axis_decorator.py} (86%)
 create mode 100644 polytope/datacube/transformations/datacube_type_change/datacube_type_change.py
 rename polytope/datacube/transformations/{datacube_type_change.py => datacube_type_change/type_change_axis_decorator.py} (66%)

diff --git a/polytope/datacube/datacube_axis.py b/polytope/datacube/datacube_axis.py
index 2e88fb26..7f9806e8 100644
--- a/polytope/datacube/datacube_axis.py
+++ b/polytope/datacube/datacube_axis.py
@@ -7,9 +7,9 @@
 
 from .transformations.datacube_cyclic.cyclic_axis_decorator import cyclic
 from .transformations.datacube_mappers.mapper_axis_decorator import mapper
-from .transformations.datacube_merger import merge
-from .transformations.datacube_reverse import reverse
-from .transformations.datacube_type_change import type_change
+from .transformations.datacube_merger.merger_axis_decorator import merge
+from .transformations.datacube_reverse.reverse_axis_decorator import reverse
+from .transformations.datacube_type_change.type_change_axis_decorator import type_change
 
 
 class DatacubeAxis(ABC):
diff --git a/polytope/datacube/transformations/datacube_cyclic/datacube_cyclic.py b/polytope/datacube/transformations/datacube_cyclic/datacube_cyclic.py
index fd4da7ae..86113aa2 100644
--- a/polytope/datacube/transformations/datacube_cyclic/datacube_cyclic.py
+++ b/polytope/datacube/transformations/datacube_cyclic/datacube_cyclic.py
@@ -1,8 +1,3 @@
-import bisect
-import math
-from copy import deepcopy
-from typing import List
-
 from ..datacube_transformations import DatacubeAxisTransformation
 
 
@@ -28,185 +23,3 @@ def blocked_axes(self):
 
     def unwanted_axes(self):
         return []
-
-
-def cyclic(cls):
-    if cls.is_cyclic:
-
-        def update_range():
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisCyclic):
-                    transformation = transform
-                    cls.range = transformation.range
-
-        def to_intervals(range):
-            update_range()
-            if range[0] == -math.inf:
-                range[0] = cls.range[0]
-            if range[1] == math.inf:
-                range[1] = cls.range[1]
-            axis_lower = cls.range[0]
-            axis_upper = cls.range[1]
-            axis_range = axis_upper - axis_lower
-            lower = range[0]
-            upper = range[1]
-            intervals = []
-            if lower < axis_upper:
-                # In this case, we want to go from lower to the first remapped cyclic axis upper
-                # or the asked upper range value.
-                # For example, if we have cyclic range [0,360] and we want to break [-270,180] into intervals,
-                # we first want to obtain [-270, 0] as the first range, where 0 is the remapped cyclic axis upper
-                # but if we wanted to break [-270, -180] into intervals, we would want to get [-270,-180],
-                # where -180 is the asked upper range value.
-                loops = int((axis_upper - lower) / axis_range)
-                remapped_up = axis_upper - (loops) * axis_range
-                new_upper = min(upper, remapped_up)
-            else:
-                # In this case, since lower >= axis_upper, we need to either go to the asked upper range
-                # or we need to go to the first remapped cyclic axis upper which is higher than lower
-                new_upper = min(axis_upper + axis_range, upper)
-                while new_upper < lower:
-                    new_upper = min(new_upper + axis_range, upper)
-            intervals.append([lower, new_upper])
-            # Now that we have established what the first interval should be, we should just jump from cyclic range
-            # to cyclic range until we hit the asked upper range value.
-            new_up = deepcopy(new_upper)
-            while new_up < upper:
-                new_upper = new_up
-                new_up = min(upper, new_upper + axis_range)
-                intervals.append([new_upper, new_up])
-            # Once we have added all the in-between ranges, we need to add the last interval
-            intervals.append([new_up, upper])
-            return intervals
-
-        def _remap_range_to_axis_range(range):
-            update_range()
-            axis_lower = cls.range[0]
-            axis_upper = cls.range[1]
-            axis_range = axis_upper - axis_lower
-            lower = range[0]
-            upper = range[1]
-            if lower < axis_lower:
-                # In this case we need to calculate the number of loops between the axis lower
-                # and the lower to recenter the lower
-                loops = int((axis_lower - lower - cls.tol) / axis_range)
-                return_lower = lower + (loops + 1) * axis_range
-                return_upper = upper + (loops + 1) * axis_range
-            elif lower >= axis_upper:
-                # In this case we need to calculate the number of loops between the axis upper
-                # and the lower to recenter the lower
-                loops = int((lower - axis_upper) / axis_range)
-                return_lower = lower - (loops + 1) * axis_range
-                return_upper = upper - (loops + 1) * axis_range
-            else:
-                # In this case, the lower value is already in the right range
-                return_lower = lower
-                return_upper = upper
-            return [return_lower, return_upper]
-
-        def _remap_val_to_axis_range(value):
-            return_range = _remap_range_to_axis_range([value, value])
-            return return_range[0]
-
-        def remap(range: List):
-            update_range()
-            if cls.range[0] - cls.tol <= range[0] <= cls.range[1] + cls.tol:
-                if cls.range[0] - cls.tol <= range[1] <= cls.range[1] + cls.tol:
-                    # If we are already in the cyclic range, return it
-                    return [range]
-            elif abs(range[0] - range[1]) <= 2 * cls.tol:
-                # If we have a range that is just one point, then it should still be counted
-                # and so we should take a small interval around it to find values inbetween
-                range = [
-                    _remap_val_to_axis_range(range[0]) - cls.tol,
-                    _remap_val_to_axis_range(range[0]) + cls.tol,
-                ]
-                return [range]
-            range_intervals = cls.to_intervals(range)
-            ranges = []
-            for interval in range_intervals:
-                if abs(interval[0] - interval[1]) > 0:
-                    # If the interval is not just a single point, we remap it to the axis range
-                    range = _remap_range_to_axis_range([interval[0], interval[1]])
-                    up = range[1]
-                    low = range[0]
-                    if up < low:
-                        # Make sure we remap in the right order
-                        ranges.append([up - cls.tol, low + cls.tol])
-                    else:
-                        ranges.append([low - cls.tol, up + cls.tol])
-            return ranges
-
-        old_find_indexes = cls.find_indexes
-
-        def find_indexes(path, datacube):
-            return old_find_indexes(path, datacube)
-
-        old_unmap_path_key = cls.unmap_path_key
-
-        def unmap_path_key(key_value_path, leaf_path, unwanted_path):
-            value = key_value_path[cls.name]
-            for transform in cls.transformations:
-                if isinstance(transform, DatacubeAxisCyclic):
-                    if cls.name == transform.name:
-                        new_val = _remap_val_to_axis_range(value)
-                        key_value_path[cls.name] = new_val
-            key_value_path, leaf_path, unwanted_path = old_unmap_path_key(key_value_path, leaf_path, unwanted_path)
-            return (key_value_path, leaf_path, unwanted_path)
-
-        old_unmap_to_datacube = cls.unmap_to_datacube
-
-        def unmap_to_datacube(path, unmapped_path):
-            (path, unmapped_path) = old_unmap_to_datacube(path, unmapped_path)
-            return (path, unmapped_path)
-
-        old_find_indices_between = cls.find_indices_between
-
-        def find_indices_between(index_ranges, low, up, datacube, method=None):
-            update_range()
-            indexes_between_ranges = []
-
-            if method != "surrounding":
-                return old_find_indices_between(index_ranges, low, up, datacube, method)
-            else:
-                for indexes in index_ranges:
-                    if cls.name in datacube.complete_axes:
-                        start = indexes.searchsorted(low, "left")
-                        end = indexes.searchsorted(up, "right")
-                    else:
-                        start = bisect.bisect_left(indexes, low)
-                        end = bisect.bisect_right(indexes, up)
-
-                    if start - 1 < 0:
-                        index_val_found = indexes[-1:][0]
-                        indexes_between_ranges.append([index_val_found])
-                    if end + 1 > len(indexes):
-                        index_val_found = indexes[:2][0]
-                        indexes_between_ranges.append([index_val_found])
-                    start = max(start - 1, 0)
-                    end = min(end + 1, len(indexes))
-                    if cls.name in datacube.complete_axes:
-                        indexes_between = indexes[start:end].to_list()
-                    else:
-                        indexes_between = indexes[start:end]
-                    indexes_between_ranges.append(indexes_between)
-                return indexes_between_ranges
-
-        def offset(range):
-            # We first unpad the range by the axis tolerance to make sure that
-            # we find the wanted range of the cyclic axis since we padded by the axis tolerance before.
-            # Also, it's safer that we find the offset of a value inside the range instead of on the border
-            unpadded_range = [range[0] + 1.5 * cls.tol, range[1] - 1.5 * cls.tol]
-            cyclic_range = _remap_range_to_axis_range(unpadded_range)
-            offset = unpadded_range[0] - cyclic_range[0]
-            return offset
-
-        cls.to_intervals = to_intervals
-        cls.remap = remap
-        cls.offset = offset
-        cls.find_indexes = find_indexes
-        cls.unmap_to_datacube = unmap_to_datacube
-        cls.find_indices_between = find_indices_between
-        cls.unmap_path_key = unmap_path_key
-
-    return cls
diff --git a/polytope/datacube/transformations/datacube_merger/datacube_merger.py b/polytope/datacube/transformations/datacube_merger/datacube_merger.py
new file mode 100644
index 00000000..ecd53372
--- /dev/null
+++ b/polytope/datacube/transformations/datacube_merger/datacube_merger.py
@@ -0,0 +1,63 @@
+import numpy as np
+import pandas as pd
+
+from ..datacube_transformations import DatacubeAxisTransformation
+
+
+class DatacubeAxisMerger(DatacubeAxisTransformation):
+    def __init__(self, name, merge_options):
+        self.transformation_options = merge_options
+        self.name = name
+        self._first_axis = name
+        self._second_axis = merge_options["with"]
+        self._linkers = merge_options["linkers"]
+
+    def blocked_axes(self):
+        return [self._second_axis]
+
+    def unwanted_axes(self):
+        return []
+
+    def _mapped_axes(self):
+        return self._first_axis
+
+    def merged_values(self, datacube):
+        first_ax_vals = datacube.ax_vals(self.name)
+        second_ax_name = self._second_axis
+        second_ax_vals = datacube.ax_vals(second_ax_name)
+        linkers = self._linkers
+        merged_values = []
+        for i in range(len(first_ax_vals)):
+            first_val = first_ax_vals[i]
+            for j in range(len(second_ax_vals)):
+                second_val = second_ax_vals[j]
+                # TODO: check that the first and second val are strings
+                val_to_add = pd.to_datetime("".join([first_val, linkers[0], second_val, linkers[1]]))
+                val_to_add = val_to_add.to_numpy()
+                val_to_add = val_to_add.astype("datetime64[s]")
+                merged_values.append(val_to_add)
+        merged_values = np.array(merged_values)
+        return merged_values
+
+    def transformation_axes_final(self):
+        return [self._first_axis]
+
+    def generate_final_transformation(self):
+        return self
+
+    def unmerge(self, merged_val):
+        merged_val = str(merged_val)
+        first_idx = merged_val.find(self._linkers[0])
+        first_val = merged_val[:first_idx]
+        first_linker_size = len(self._linkers[0])
+        second_linked_size = len(self._linkers[1])
+        second_val = merged_val[first_idx + first_linker_size : -second_linked_size]
+
+        # TODO: maybe replacing like this is too specific to time/dates?
+        first_val = str(first_val).replace("-", "")
+        second_val = second_val.replace(":", "")
+        return (first_val, second_val)
+
+    def change_val_type(self, axis_name, values):
+        new_values = pd.to_datetime(values)
+        return new_values
diff --git a/polytope/datacube/transformations/datacube_merger.py b/polytope/datacube/transformations/datacube_merger/merger_axis_decorator.py
similarity index 61%
rename from polytope/datacube/transformations/datacube_merger.py
rename to polytope/datacube/transformations/datacube_merger/merger_axis_decorator.py
index 883ea964..eeb0cbe7 100644
--- a/polytope/datacube/transformations/datacube_merger.py
+++ b/polytope/datacube/transformations/datacube_merger/merger_axis_decorator.py
@@ -1,68 +1,6 @@
 import bisect
 
-import numpy as np
-import pandas as pd
-
-from .datacube_transformations import DatacubeAxisTransformation
-
-
-class DatacubeAxisMerger(DatacubeAxisTransformation):
-    def __init__(self, name, merge_options):
-        self.transformation_options = merge_options
-        self.name = name
-        self._first_axis = name
-        self._second_axis = merge_options["with"]
-        self._linkers = merge_options["linkers"]
-
-    def blocked_axes(self):
-        return [self._second_axis]
-
-    def unwanted_axes(self):
-        return []
-
-    def _mapped_axes(self):
-        return self._first_axis
-
-    def merged_values(self, datacube):
-        first_ax_vals = datacube.ax_vals(self.name)
-        second_ax_name = self._second_axis
-        second_ax_vals = datacube.ax_vals(second_ax_name)
-        linkers = self._linkers
-        merged_values = []
-        for i in range(len(first_ax_vals)):
-            first_val = first_ax_vals[i]
-            for j in range(len(second_ax_vals)):
-                second_val = second_ax_vals[j]
-                # TODO: check that the first and second val are strings
-                val_to_add = pd.to_datetime("".join([first_val, linkers[0], second_val, linkers[1]]))
-                val_to_add = val_to_add.to_numpy()
-                val_to_add = val_to_add.astype("datetime64[s]")
-                merged_values.append(val_to_add)
-        merged_values = np.array(merged_values)
-        return merged_values
-
-    def transformation_axes_final(self):
-        return [self._first_axis]
-
-    def generate_final_transformation(self):
-        return self
-
-    def unmerge(self, merged_val):
-        merged_val = str(merged_val)
-        first_idx = merged_val.find(self._linkers[0])
-        first_val = merged_val[:first_idx]
-        first_linker_size = len(self._linkers[0])
-        second_linked_size = len(self._linkers[1])
-        second_val = merged_val[first_idx + first_linker_size : -second_linked_size]
-
-        # TODO: maybe replacing like this is too specific to time/dates?
-        first_val = str(first_val).replace("-", "")
-        second_val = second_val.replace(":", "")
-        return (first_val, second_val)
-
-    def change_val_type(self, axis_name, values):
-        new_values = pd.to_datetime(values)
-        return new_values
+from .datacube_merger import DatacubeAxisMerger
 
 
 def merge(cls):
diff --git a/polytope/datacube/transformations/datacube_null_transformation/datacube_null_transformation.py b/polytope/datacube/transformations/datacube_null_transformation/datacube_null_transformation.py
new file mode 100644
index 00000000..43dccbbe
--- /dev/null
+++ b/polytope/datacube/transformations/datacube_null_transformation/datacube_null_transformation.py
@@ -0,0 +1,22 @@
+from ..datacube_transformations import DatacubeAxisTransformation
+
+
+class DatacubeNullTransformation(DatacubeAxisTransformation):
+    def __init__(self, name, mapper_options):
+        self.name = name
+        self.transformation_options = mapper_options
+
+    def generate_final_transformation(self):
+        return self
+
+    def transformation_axes_final(self):
+        return [self.name]
+
+    def change_val_type(self, axis_name, values):
+        return values
+
+    def blocked_axes(self):
+        return []
+
+    def unwanted_axes(self):
+        return []
diff --git a/polytope/datacube/transformations/datacube_null_transformation.py b/polytope/datacube/transformations/datacube_null_transformation/null_axis_decorator.py
similarity index 56%
rename from polytope/datacube/transformations/datacube_null_transformation.py
rename to polytope/datacube/transformations/datacube_null_transformation/null_axis_decorator.py
index 66af3f3a..10e2644d 100644
--- a/polytope/datacube/transformations/datacube_null_transformation.py
+++ b/polytope/datacube/transformations/datacube_null_transformation/null_axis_decorator.py
@@ -1,27 +1,3 @@
-from .datacube_transformations import DatacubeAxisTransformation
-
-
-class DatacubeNullTransformation(DatacubeAxisTransformation):
-    def __init__(self, name, mapper_options):
-        self.name = name
-        self.transformation_options = mapper_options
-
-    def generate_final_transformation(self):
-        return self
-
-    def transformation_axes_final(self):
-        return [self.name]
-
-    def change_val_type(self, axis_name, values):
-        return values
-
-    def blocked_axes(self):
-        return []
-
-    def unwanted_axes(self):
-        return []
-
-
 def null(cls):
     if cls.type_change:
         old_find_indexes = cls.find_indexes
diff --git a/polytope/datacube/transformations/datacube_reverse/datacube_reverse.py b/polytope/datacube/transformations/datacube_reverse/datacube_reverse.py
new file mode 100644
index 00000000..6e60de87
--- /dev/null
+++ b/polytope/datacube/transformations/datacube_reverse/datacube_reverse.py
@@ -0,0 +1,22 @@
+from ..datacube_transformations import DatacubeAxisTransformation
+
+
+class DatacubeAxisReverse(DatacubeAxisTransformation):
+    def __init__(self, name, mapper_options):
+        self.name = name
+        self.transformation_options = mapper_options
+
+    def generate_final_transformation(self):
+        return self
+
+    def transformation_axes_final(self):
+        return [self.name]
+
+    def change_val_type(self, axis_name, values):
+        return values
+
+    def blocked_axes(self):
+        return []
+
+    def unwanted_axes(self):
+        return []
diff --git a/polytope/datacube/transformations/datacube_reverse.py b/polytope/datacube/transformations/datacube_reverse/reverse_axis_decorator.py
similarity index 86%
rename from polytope/datacube/transformations/datacube_reverse.py
rename to polytope/datacube/transformations/datacube_reverse/reverse_axis_decorator.py
index 0e03006a..2e5eff96 100644
--- a/polytope/datacube/transformations/datacube_reverse.py
+++ b/polytope/datacube/transformations/datacube_reverse/reverse_axis_decorator.py
@@ -1,27 +1,6 @@
 import bisect
 
-from .datacube_transformations import DatacubeAxisTransformation
-
-
-class DatacubeAxisReverse(DatacubeAxisTransformation):
-    def __init__(self, name, mapper_options):
-        self.name = name
-        self.transformation_options = mapper_options
-
-    def generate_final_transformation(self):
-        return self
-
-    def transformation_axes_final(self):
-        return [self.name]
-
-    def change_val_type(self, axis_name, values):
-        return values
-
-    def blocked_axes(self):
-        return []
-
-    def unwanted_axes(self):
-        return []
+from .datacube_reverse import DatacubeAxisReverse
 
 
 def reverse(cls):
diff --git a/polytope/datacube/transformations/datacube_transformations.py b/polytope/datacube/transformations/datacube_transformations.py
index 4bd07a2d..2077f346 100644
--- a/polytope/datacube/transformations/datacube_transformations.py
+++ b/polytope/datacube/transformations/datacube_transformations.py
@@ -8,8 +8,8 @@ class DatacubeAxisTransformation(ABC):
     def create_transform(name, transformation_type_key, transformation_options):
         transformation_type = _type_to_datacube_transformation_lookup[transformation_type_key]
         transformation_file_name = _type_to_transformation_file_lookup[transformation_type_key]
-
-        module = import_module("polytope.datacube.transformations.datacube_" + transformation_file_name)
+        file_name = ".datacube_" + transformation_file_name
+        module = import_module("polytope.datacube.transformations" + file_name + file_name)
         constructor = getattr(module, transformation_type)
         transformation_type_option = transformation_options[transformation_type_key]
         new_transformation = deepcopy(constructor(name, transformation_type_option))
@@ -54,8 +54,8 @@ def change_val_type(self, axis_name, values):
 }
 
 _type_to_transformation_file_lookup = {
-    "mapper": "mappers.datacube_mappers",
-    "cyclic": "cyclic.datacube_cyclic",
+    "mapper": "mappers",
+    "cyclic": "cyclic",
     "merge": "merger",
     "reverse": "reverse",
     "type_change": "type_change",
diff --git a/polytope/datacube/transformations/datacube_type_change/datacube_type_change.py b/polytope/datacube/transformations/datacube_type_change/datacube_type_change.py
new file mode 100644
index 00000000..8ba2ef0f
--- /dev/null
+++ b/polytope/datacube/transformations/datacube_type_change/datacube_type_change.py
@@ -0,0 +1,53 @@
+from copy import deepcopy
+from importlib import import_module
+
+from ..datacube_transformations import DatacubeAxisTransformation
+
+
+class DatacubeAxisTypeChange(DatacubeAxisTransformation):
+    # The transformation here will be to point the old axes to the new cyclic axes
+
+    def __init__(self, name, type_options):
+        self.name = name
+        self.transformation_options = type_options
+        self.new_type = type_options
+        self._final_transformation = self.generate_final_transformation()
+
+    def generate_final_transformation(self):
+        map_type = _type_to_datacube_type_change_lookup[self.new_type]
+        module = import_module("polytope.datacube.transformations.datacube_type_change.datacube_type_change")
+        constructor = getattr(module, map_type)
+        transformation = deepcopy(constructor(self.name, self.new_type))
+        return transformation
+
+    def transformation_axes_final(self):
+        return [self._final_transformation.axis_name]
+
+    def change_val_type(self, axis_name, values):
+        return_idx = [self._final_transformation.transform_type(val) for val in values]
+        return_idx.sort()
+        return return_idx
+
+    def make_str(self, value):
+        return self._final_transformation.make_str(value)
+
+    def blocked_axes(self):
+        return []
+
+    def unwanted_axes(self):
+        return []
+
+
+class TypeChangeStrToInt(DatacubeAxisTypeChange):
+    def __init__(self, axis_name, new_type):
+        self.axis_name = axis_name
+        self._new_type = new_type
+
+    def transform_type(self, value):
+        return int(value)
+
+    def make_str(self, value):
+        return str(value)
+
+
+_type_to_datacube_type_change_lookup = {"int": "TypeChangeStrToInt"}
diff --git a/polytope/datacube/transformations/datacube_type_change.py b/polytope/datacube/transformations/datacube_type_change/type_change_axis_decorator.py
similarity index 66%
rename from polytope/datacube/transformations/datacube_type_change.py
rename to polytope/datacube/transformations/datacube_type_change/type_change_axis_decorator.py
index 1813efe2..10c9a95a 100644
--- a/polytope/datacube/transformations/datacube_type_change.py
+++ b/polytope/datacube/transformations/datacube_type_change/type_change_axis_decorator.py
@@ -1,57 +1,6 @@
 import bisect
-from copy import deepcopy
-from importlib import import_module
 
-from .datacube_transformations import DatacubeAxisTransformation
-
-
-class DatacubeAxisTypeChange(DatacubeAxisTransformation):
-    # The transformation here will be to point the old axes to the new cyclic axes
-
-    def __init__(self, name, type_options):
-        self.name = name
-        self.transformation_options = type_options
-        self.new_type = type_options
-        self._final_transformation = self.generate_final_transformation()
-
-    def generate_final_transformation(self):
-        map_type = _type_to_datacube_type_change_lookup[self.new_type]
-        module = import_module("polytope.datacube.transformations.datacube_type_change")
-        constructor = getattr(module, map_type)
-        transformation = deepcopy(constructor(self.name, self.new_type))
-        return transformation
-
-    def transformation_axes_final(self):
-        return [self._final_transformation.axis_name]
-
-    def change_val_type(self, axis_name, values):
-        return_idx = [self._final_transformation.transform_type(val) for val in values]
-        return_idx.sort()
-        return return_idx
-
-    def make_str(self, value):
-        return self._final_transformation.make_str(value)
-
-    def blocked_axes(self):
-        return []
-
-    def unwanted_axes(self):
-        return []
-
-
-class TypeChangeStrToInt(DatacubeAxisTypeChange):
-    def __init__(self, axis_name, new_type):
-        self.axis_name = axis_name
-        self._new_type = new_type
-
-    def transform_type(self, value):
-        return int(value)
-
-    def make_str(self, value):
-        return str(value)
-
-
-_type_to_datacube_type_change_lookup = {"int": "TypeChangeStrToInt"}
+from .datacube_type_change import DatacubeAxisTypeChange
 
 
 def type_change(cls):

From 9ddbbd87d8a39d35290bb7ee289198bfde323b3c Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Mon, 29 Jan 2024 12:18:11 +0000
Subject: [PATCH 05/12] add local regular grid mapper

---
 .../datacube_mappers/datacube_mappers.py      |  6 +-
 .../datacube_mappers/mapper_types/healpix.py  |  3 +-
 .../mapper_types/local_regular.py             | 69 +++++++++++++++++++
 .../mapper_types/octahedral.py                |  3 +-
 .../mapper_types/reduced_ll.py                |  3 +-
 .../datacube_mappers/mapper_types/regular.py  |  3 +-
 6 files changed, 82 insertions(+), 5 deletions(-)
 create mode 100644 polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py

diff --git a/polytope/datacube/transformations/datacube_mappers/datacube_mappers.py b/polytope/datacube/transformations/datacube_mappers/datacube_mappers.py
index c42d04a7..a2034bfb 100644
--- a/polytope/datacube/transformations/datacube_mappers/datacube_mappers.py
+++ b/polytope/datacube/transformations/datacube_mappers/datacube_mappers.py
@@ -12,6 +12,9 @@ def __init__(self, name, mapper_options):
         self.grid_type = mapper_options["type"]
         self.grid_resolution = mapper_options["resolution"]
         self.grid_axes = mapper_options["axes"]
+        self.local_area = []
+        if "local" in mapper_options.keys():
+            self.local_area = mapper_options["local"]
         self.old_axis = name
         self._final_transformation = self.generate_final_transformation()
         self._final_mapped_axes = self._final_transformation._mapped_axes
@@ -21,7 +24,7 @@ def generate_final_transformation(self):
         map_type = _type_to_datacube_mapper_lookup[self.grid_type]
         module = import_module("polytope.datacube.transformations.datacube_mappers.mapper_types." + self.grid_type)
         constructor = getattr(module, map_type)
-        transformation = deepcopy(constructor(self.old_axis, self.grid_axes, self.grid_resolution))
+        transformation = deepcopy(constructor(self.old_axis, self.grid_axes, self.grid_resolution, self.local_area))
         return transformation
 
     def blocked_axes(self):
@@ -78,4 +81,5 @@ def unmap(self, first_val, second_val):
     "healpix": "HealpixGridMapper",
     "regular": "RegularGridMapper",
     "reduced_ll": "ReducedLatLonMapper",
+    "local_regular": "LocalRegularGridMapper",
 }
diff --git a/polytope/datacube/transformations/datacube_mappers/mapper_types/healpix.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/healpix.py
index 627a1be9..8589ec71 100644
--- a/polytope/datacube/transformations/datacube_mappers/mapper_types/healpix.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_types/healpix.py
@@ -5,7 +5,8 @@
 
 
 class HealpixGridMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
+    def __init__(self, base_axis, mapped_axes, resolution, local_area=[]):
+        # TODO: if local area is not empty list, raise NotImplemented
         self._mapped_axes = mapped_axes
         self._base_axis = base_axis
         self._resolution = resolution
diff --git a/polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py
new file mode 100644
index 00000000..1c83c988
--- /dev/null
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py
@@ -0,0 +1,69 @@
+import bisect
+
+from ..datacube_mappers import DatacubeMapper
+
+
+class LocalRegularGridMapper(DatacubeMapper):
+    def __init__(self, base_axis, mapped_axes, resolution, local_area=[]):
+        # TODO: if local area is not empty list, raise NotImplemented
+        self._mapped_axes = mapped_axes
+        self._base_axis = base_axis
+        self._first_axis_min = local_area[0]
+        self._first_axis_max = local_area[1]
+        self._second_axis_min = local_area[2]
+        self._second_axis_max = local_area[3]
+        if not isinstance(resolution, list):
+            self.first_resolution = resolution
+            self.second_resolution = resolution
+        else:
+            self.first_resolution = resolution[0]
+            self.second_resolution = resolution[1]
+        self._first_deg_increment = (local_area[1] - local_area[0]) / self.first_resolution
+        self._second_deg_increment = (local_area[3] - local_area[2]) / self.second_resolution
+        self._axis_reversed = {mapped_axes[0]: True, mapped_axes[1]: False}
+        self._first_axis_vals = self.first_axis_vals()
+
+    def first_axis_vals(self):
+        first_ax_vals = [self._first_axis_max - i * self._first_deg_increment for i in range(self.first_resolution)]
+        return first_ax_vals
+
+    def map_first_axis(self, lower, upper):
+        axis_lines = self._first_axis_vals
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def second_axis_vals(self, first_val):
+        second_ax_vals = [
+            self._second_axis_min + i * self._second_deg_increment for i in range(4 * self.second_resolution)
+        ]
+        return second_ax_vals
+
+    def map_second_axis(self, first_val, lower, upper):
+        axis_lines = self.second_axis_vals(first_val)
+        return_vals = [val for val in axis_lines if lower <= val <= upper]
+        return return_vals
+
+    def axes_idx_to_regular_idx(self, first_idx, second_idx):
+        final_idx = first_idx * self.second_resolution + second_idx
+        return final_idx
+
+    def find_second_idx(self, first_val, second_val):
+        tol = 1e-10
+        second_axis_vals = self.second_axis_vals(first_val)
+        second_idx = bisect.bisect_left(second_axis_vals, second_val - tol)
+        return second_idx
+
+    def unmap_first_val_to_start_line_idx(self, first_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        first_idx = self._first_axis_vals.index(first_val)
+        return first_idx * self.second_resolution
+
+    def unmap(self, first_val, second_val):
+        tol = 1e-8
+        first_val = [i for i in self._first_axis_vals if first_val - tol <= i <= first_val + tol][0]
+        first_idx = self._first_axis_vals.index(first_val)
+        second_val = [i for i in self.second_axis_vals(first_val) if second_val - tol <= i <= second_val + tol][0]
+        second_idx = self.second_axis_vals(first_val).index(second_val)
+        final_index = self.axes_idx_to_regular_idx(first_idx, second_idx)
+        return final_index
diff --git a/polytope/datacube/transformations/datacube_mappers/mapper_types/octahedral.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/octahedral.py
index b2a3159b..730ac959 100644
--- a/polytope/datacube/transformations/datacube_mappers/mapper_types/octahedral.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_types/octahedral.py
@@ -5,7 +5,8 @@
 
 
 class OctahedralGridMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
+    def __init__(self, base_axis, mapped_axes, resolution, local_area=[]):
+        # TODO: if local area is not empty list, raise NotImplemented
         self._mapped_axes = mapped_axes
         self._base_axis = base_axis
         self._resolution = resolution
diff --git a/polytope/datacube/transformations/datacube_mappers/mapper_types/reduced_ll.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/reduced_ll.py
index f056b232..ece09b4a 100644
--- a/polytope/datacube/transformations/datacube_mappers/mapper_types/reduced_ll.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_types/reduced_ll.py
@@ -4,7 +4,8 @@
 
 
 class ReducedLatLonMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
+    def __init__(self, base_axis, mapped_axes, resolution, local_area=[]):
+        # TODO: if local area is not empty list, raise NotImplemented
         self._mapped_axes = mapped_axes
         self._base_axis = base_axis
         self._resolution = resolution
diff --git a/polytope/datacube/transformations/datacube_mappers/mapper_types/regular.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/regular.py
index 3b0598a0..c8f207fc 100644
--- a/polytope/datacube/transformations/datacube_mappers/mapper_types/regular.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_types/regular.py
@@ -4,7 +4,8 @@
 
 
 class RegularGridMapper(DatacubeMapper):
-    def __init__(self, base_axis, mapped_axes, resolution):
+    def __init__(self, base_axis, mapped_axes, resolution, local_area=[]):
+        # TODO: if local area is not empty list, raise NotImplemented
         self._mapped_axes = mapped_axes
         self._base_axis = base_axis
         self._resolution = resolution

From aeb86eb9fb7c56802d5ed1e11ad13fc1f8e2af39 Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Mon, 29 Jan 2024 12:56:52 +0000
Subject: [PATCH 06/12] add __init__ file

---
 polytope/datacube/transformations/__init__.py | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 polytope/datacube/transformations/__init__.py

diff --git a/polytope/datacube/transformations/__init__.py b/polytope/datacube/transformations/__init__.py
new file mode 100644
index 00000000..e69de29b

From d63d52dd679725f6fffee663fea4cc7ed9fbe0ee Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Mon, 29 Jan 2024 15:49:24 +0000
Subject: [PATCH 07/12] add nearest method to transformations

---
 polytope/datacube/index_tree.py                               | 2 +-
 .../transformations/datacube_cyclic/cyclic_axis_decorator.py  | 2 +-
 .../transformations/datacube_mappers/mapper_axis_decorator.py | 2 +-
 .../transformations/datacube_merger/merger_axis_decorator.py  | 2 +-
 .../datacube_reverse/reverse_axis_decorator.py                | 4 ++--
 .../datacube_type_change/type_change_axis_decorator.py        | 2 +-
 tests/test_point_nearest.py                                   | 2 +-
 7 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/polytope/datacube/index_tree.py b/polytope/datacube/index_tree.py
index b15e67fe..76ab48ab 100644
--- a/polytope/datacube/index_tree.py
+++ b/polytope/datacube/index_tree.py
@@ -1,6 +1,6 @@
 import json
-from typing import OrderedDict
 import logging
+from typing import OrderedDict
 
 from sortedcontainers import SortedList
 
diff --git a/polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py b/polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py
index 8b1cf292..76a2aa42 100644
--- a/polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py
+++ b/polytope/datacube/transformations/datacube_cyclic/cyclic_axis_decorator.py
@@ -142,7 +142,7 @@ def find_indices_between(index_ranges, low, up, datacube, method=None):
             update_range()
             indexes_between_ranges = []
 
-            if method != "surrounding":
+            if method != "surrounding" or method != "nearest":
                 return old_find_indices_between(index_ranges, low, up, datacube, method)
             else:
                 for indexes in index_ranges:
diff --git a/polytope/datacube/transformations/datacube_mappers/mapper_axis_decorator.py b/polytope/datacube/transformations/datacube_mappers/mapper_axis_decorator.py
index 30f95b61..99432186 100644
--- a/polytope/datacube/transformations/datacube_mappers/mapper_axis_decorator.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_axis_decorator.py
@@ -73,7 +73,7 @@ def find_indices_between(index_ranges, low, up, datacube, method=None):
                     transformation = transform
                     if cls.name in transformation._mapped_axes():
                         for idxs in index_ranges:
-                            if method == "surrounding":
+                            if method == "surrounding" or method == "nearest":
                                 axis_reversed = transform._axis_reversed[cls.name]
                                 if not axis_reversed:
                                     start = bisect.bisect_left(idxs, low)
diff --git a/polytope/datacube/transformations/datacube_merger/merger_axis_decorator.py b/polytope/datacube/transformations/datacube_merger/merger_axis_decorator.py
index eeb0cbe7..16d81639 100644
--- a/polytope/datacube/transformations/datacube_merger/merger_axis_decorator.py
+++ b/polytope/datacube/transformations/datacube_merger/merger_axis_decorator.py
@@ -51,7 +51,7 @@ def find_indices_between(index_ranges, low, up, datacube, method=None):
                     transformation = transform
                     if cls.name in transformation._mapped_axes():
                         for indexes in index_ranges:
-                            if method == "surrounding":
+                            if method == "surrounding" or method == "nearest":
                                 start = indexes.index(low)
                                 end = indexes.index(up)
                                 start = max(start - 1, 0)
diff --git a/polytope/datacube/transformations/datacube_reverse/reverse_axis_decorator.py b/polytope/datacube/transformations/datacube_reverse/reverse_axis_decorator.py
index 2e5eff96..18bc8bd6 100644
--- a/polytope/datacube/transformations/datacube_reverse/reverse_axis_decorator.py
+++ b/polytope/datacube/transformations/datacube_reverse/reverse_axis_decorator.py
@@ -29,7 +29,7 @@ def find_indices_between(index_ranges, low, up, datacube, method=None):
                                 # https://pandas.pydata.org/docs/reference/api/pandas.Index.searchsorted.html
                                 # Assumes the indexes are already sorted (could sort to be sure) and monotonically
                                 # increasing
-                                if method == "surrounding":
+                                if method == "surrounding" or method == "nearest":
                                     start = indexes.searchsorted(low, "left")
                                     end = indexes.searchsorted(up, "right")
                                     start = max(start - 1, 0)
@@ -42,7 +42,7 @@ def find_indices_between(index_ranges, low, up, datacube, method=None):
                                     indexes_between = indexes[start:end].to_list()
                                     indexes_between_ranges.append(indexes_between)
                             else:
-                                if method == "surrounding":
+                                if method == "surrounding" or method == "nearest":
                                     start = indexes.index(low)
                                     end = indexes.index(up)
                                     start = max(start - 1, 0)
diff --git a/polytope/datacube/transformations/datacube_type_change/type_change_axis_decorator.py b/polytope/datacube/transformations/datacube_type_change/type_change_axis_decorator.py
index 10c9a95a..0e366982 100644
--- a/polytope/datacube/transformations/datacube_type_change/type_change_axis_decorator.py
+++ b/polytope/datacube/transformations/datacube_type_change/type_change_axis_decorator.py
@@ -47,7 +47,7 @@ def find_indices_between(index_ranges, low, up, datacube, method=None):
                     transformation = transform
                     if cls.name == transformation.name:
                         for indexes in index_ranges:
-                            if method == "surrounding":
+                            if method == "surrounding" or method == "nearest":
                                 start = indexes.index(low)
                                 end = indexes.index(up)
                                 start = max(start - 1, 0)
diff --git a/tests/test_point_nearest.py b/tests/test_point_nearest.py
index 081050da..fa53b980 100644
--- a/tests/test_point_nearest.py
+++ b/tests/test_point_nearest.py
@@ -95,7 +95,7 @@ def test_fdb_datacube_true_point_3(self):
         result = self.API.retrieve(request)
         result.pprint()
         assert len(result.leaves) == 1
-        assert result.leaves[0].value == 0
+        assert result.leaves[0].value == 359.929906542056
         assert result.leaves[0].axis.name == "longitude"
 
     @pytest.mark.fdb

From 28328d8f9b17937a249df5ef3143d1fcbb5bb005 Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Thu, 1 Feb 2024 11:09:24 +0000
Subject: [PATCH 08/12] fix local grid mapper issues

---
 polytope/datacube/index_tree.py               |  7 +++
 .../mapper_types/local_regular.py             |  6 +--
 tests/test_local_regular_grid.py              | 48 +++++++++++++++++++
 3 files changed, 58 insertions(+), 3 deletions(-)
 create mode 100644 tests/test_local_regular_grid.py

diff --git a/polytope/datacube/index_tree.py b/polytope/datacube/index_tree.py
index 76ab48ab..b4ce3bce 100644
--- a/polytope/datacube/index_tree.py
+++ b/polytope/datacube/index_tree.py
@@ -46,6 +46,13 @@ def leaves_with_ancestors(self):
         self._collect_leaf_nodes(leaves)
         return leaves
 
+    def pprint_2(self, level=0):
+        if self.axis.name == "root":
+            print("\n")
+        print("\t" * level + "\u21b3" + str(self))
+        for child in self.children:
+            child.pprint_2(level + 1)
+
     def _collect_leaf_nodes_old(self, leaves):
         if len(self.children) == 0:
             leaves.append(self)
diff --git a/polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py b/polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py
index 1c83c988..a1514778 100644
--- a/polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py
+++ b/polytope/datacube/transformations/datacube_mappers/mapper_types/local_regular.py
@@ -24,7 +24,7 @@ def __init__(self, base_axis, mapped_axes, resolution, local_area=[]):
         self._first_axis_vals = self.first_axis_vals()
 
     def first_axis_vals(self):
-        first_ax_vals = [self._first_axis_max - i * self._first_deg_increment for i in range(self.first_resolution)]
+        first_ax_vals = [self._first_axis_max - i * self._first_deg_increment for i in range(self.first_resolution + 1)]
         return first_ax_vals
 
     def map_first_axis(self, lower, upper):
@@ -34,7 +34,7 @@ def map_first_axis(self, lower, upper):
 
     def second_axis_vals(self, first_val):
         second_ax_vals = [
-            self._second_axis_min + i * self._second_deg_increment for i in range(4 * self.second_resolution)
+            self._second_axis_min + i * self._second_deg_increment for i in range(self.second_resolution + 1)
         ]
         return second_ax_vals
 
@@ -44,7 +44,7 @@ def map_second_axis(self, first_val, lower, upper):
         return return_vals
 
     def axes_idx_to_regular_idx(self, first_idx, second_idx):
-        final_idx = first_idx * self.second_resolution + second_idx
+        final_idx = first_idx * (self.second_resolution + 1) + second_idx
         return final_idx
 
     def find_second_idx(self, first_val, second_val):
diff --git a/tests/test_local_regular_grid.py b/tests/test_local_regular_grid.py
new file mode 100644
index 00000000..e623c840
--- /dev/null
+++ b/tests/test_local_regular_grid.py
@@ -0,0 +1,48 @@
+import pandas as pd
+import pytest
+from earthkit import data
+
+from polytope.engine.hullslicer import HullSlicer
+from polytope.polytope import Polytope, Request
+from polytope.shapes import Point, Select
+
+
+class TestSlicingFDBDatacube:
+    def setup_method(self, method):
+        from polytope.datacube.backends.fdb import FDBDatacube
+
+        ds = data.from_source("file", "./local.grib")
+        self.latlon_array = ds.to_xarray().t2m
+        print(self.latlon_array)
+
+        # Create a dataarray with 3 labelled axes using different index types
+        self.options = {
+            "values": {"mapper": {"type": "local_regular", "resolution": [80, 80], "axes": ["latitude", "longitude"], "local": [-40, 40, -20, 60]}},
+            "date": {"merge": {"with": "time", "linkers": ["T", "00"]}},
+            "step": {"type_change": "int"},
+            "number": {"type_change": "int"},
+            "longitude": {"cyclic": [0, 360]},
+        }
+        self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "stream": "oper"}
+        self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
+        self.slicer = HullSlicer()
+        self.API = Polytope(datacube=self.fdbdatacube, engine=self.slicer, axis_options=self.options)
+
+    # Testing different shapes
+    @pytest.mark.fdb
+    def test_fdb_datacube(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["an"]),
+            Point(["latitude", "longitude"], [[0.16, 0.176]], method="nearest"),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1

From facc193e6fd649c1599716093fbddf85150398c1 Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Thu, 1 Feb 2024 11:16:13 +0000
Subject: [PATCH 09/12] fix local grid test

---
 tests/test_local_regular_grid.py | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/tests/test_local_regular_grid.py b/tests/test_local_regular_grid.py
index e623c840..03bcb22b 100644
--- a/tests/test_local_regular_grid.py
+++ b/tests/test_local_regular_grid.py
@@ -1,6 +1,5 @@
 import pandas as pd
 import pytest
-from earthkit import data
 
 from polytope.engine.hullslicer import HullSlicer
 from polytope.polytope import Polytope, Request
@@ -11,13 +10,16 @@ class TestSlicingFDBDatacube:
     def setup_method(self, method):
         from polytope.datacube.backends.fdb import FDBDatacube
 
-        ds = data.from_source("file", "./local.grib")
-        self.latlon_array = ds.to_xarray().t2m
-        print(self.latlon_array)
-
         # Create a dataarray with 3 labelled axes using different index types
         self.options = {
-            "values": {"mapper": {"type": "local_regular", "resolution": [80, 80], "axes": ["latitude", "longitude"], "local": [-40, 40, -20, 60]}},
+            "values": {
+                "mapper": {
+                    "type": "local_regular",
+                    "resolution": [80, 80],
+                    "axes": ["latitude", "longitude"],
+                    "local": [-40, 40, -20, 60],
+                }
+            },
             "date": {"merge": {"with": "time", "linkers": ["T", "00"]}},
             "step": {"type_change": "int"},
             "number": {"type_change": "int"},
@@ -40,9 +42,11 @@ def test_fdb_datacube(self):
             Select("param", ["167"]),
             Select("class", ["od"]),
             Select("stream", ["oper"]),
-            Select("type", ["an"]),
+            Select("type", ["fc"]),
             Point(["latitude", "longitude"], [[0.16, 0.176]], method="nearest"),
         )
         result = self.API.retrieve(request)
         result.pprint_2()
         assert len(result.leaves) == 1
+        assert result.leaves[0].flatten()["latitude"] == 0
+        assert result.leaves[0].flatten()["longitude"] == 0

From 19b490644f78198d65113cb8cc1a56f475302a76 Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Thu, 1 Feb 2024 13:43:58 +0000
Subject: [PATCH 10/12] test local grid with cyclicity

---
 tests/test_local_grid_cyclic.py  |  71 +++++++++++++
 tests/test_local_regular_grid.py | 177 ++++++++++++++++++++++++++++++-
 2 files changed, 247 insertions(+), 1 deletion(-)
 create mode 100644 tests/test_local_grid_cyclic.py

diff --git a/tests/test_local_grid_cyclic.py b/tests/test_local_grid_cyclic.py
new file mode 100644
index 00000000..cb1c57eb
--- /dev/null
+++ b/tests/test_local_grid_cyclic.py
@@ -0,0 +1,71 @@
+import pandas as pd
+import pytest
+
+from polytope.engine.hullslicer import HullSlicer
+from polytope.polytope import Polytope, Request
+from polytope.shapes import Point, Select
+
+
+class TestSlicingFDBDatacube:
+    def setup_method(self, method):
+        from polytope.datacube.backends.fdb import FDBDatacube
+
+        # Create a dataarray with 3 labelled axes using different index types
+        self.options = {
+            "values": {
+                "mapper": {
+                    "type": "local_regular",
+                    "resolution": [80, 80],
+                    "axes": ["latitude", "longitude"],
+                    "local": [-40, 40, -20, 60],
+                }
+            },
+            "date": {"merge": {"with": "time", "linkers": ["T", "00"]}},
+            "step": {"type_change": "int"},
+            "number": {"type_change": "int"},
+            "longitude": {"cyclic": [-180, 180]}
+        }
+        self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "stream": "oper"}
+        self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
+        self.slicer = HullSlicer()
+        self.API = Polytope(datacube=self.fdbdatacube, engine=self.slicer, axis_options=self.options)
+
+    # Testing different shapes
+    @pytest.mark.fdb
+    def test_fdb_datacube(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[-20, -20]]),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.leaves[0].flatten()["latitude"] == -20
+        assert result.leaves[0].flatten()["longitude"] == -20
+
+    def test_fdb_datacube_2(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[-20, 50+360]]),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.leaves[0].flatten()["latitude"] == -20
+        assert result.leaves[0].flatten()["longitude"] == 50
diff --git a/tests/test_local_regular_grid.py b/tests/test_local_regular_grid.py
index 03bcb22b..dfac410e 100644
--- a/tests/test_local_regular_grid.py
+++ b/tests/test_local_regular_grid.py
@@ -23,7 +23,6 @@ def setup_method(self, method):
             "date": {"merge": {"with": "time", "linkers": ["T", "00"]}},
             "step": {"type_change": "int"},
             "number": {"type_change": "int"},
-            "longitude": {"cyclic": [0, 360]},
         }
         self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "stream": "oper"}
         self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
@@ -50,3 +49,179 @@ def test_fdb_datacube(self):
         assert len(result.leaves) == 1
         assert result.leaves[0].flatten()["latitude"] == 0
         assert result.leaves[0].flatten()["longitude"] == 0
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[0.16, 61]], method="nearest"),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.leaves[0].flatten()["latitude"] == 0
+        assert result.leaves[0].flatten()["longitude"] == 60
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_2(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[41, 1]], method="nearest"),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.leaves[0].flatten()["latitude"] == 40
+        assert result.leaves[0].flatten()["longitude"] == 1
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_3(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[1, 61]]),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.is_root()
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_4(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[41, 1]]),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.is_root()
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_5(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[-41, 1]]),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.is_root()
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_6(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[-30, -21]]),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.is_root()
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_7(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[-41, 1]], method="nearest"),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.leaves[0].flatten()["latitude"] == -40
+        assert result.leaves[0].flatten()["longitude"] == 1
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_8(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[-30, -21]], method="nearest"),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 1
+        assert result.leaves[0].flatten()["latitude"] == -30
+        assert result.leaves[0].flatten()["longitude"] == -20
+
+    @pytest.mark.fdb
+    def test_point_outside_local_region_9(self):
+        request = Request(
+            Select("step", [0]),
+            Select("levtype", ["sfc"]),
+            Select("date", [pd.Timestamp("20240129T000000")]),
+            Select("domain", ["g"]),
+            Select("expver", ["0001"]),
+            Select("param", ["167"]),
+            Select("class", ["od"]),
+            Select("stream", ["oper"]),
+            Select("type", ["fc"]),
+            Point(["latitude", "longitude"], [[-30, -21]], method="surrounding"),
+        )
+        result = self.API.retrieve(request)
+        result.pprint_2()
+        assert len(result.leaves) == 3
+        assert result.leaves[0].flatten()["latitude"] == -31
+        assert result.leaves[0].flatten()["longitude"] == -20

From df2ca21a731b0a826b747ac2c2db0ab0622c545b Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Thu, 1 Feb 2024 13:45:31 +0000
Subject: [PATCH 11/12] black

---
 tests/test_local_grid_cyclic.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/test_local_grid_cyclic.py b/tests/test_local_grid_cyclic.py
index cb1c57eb..bf6f5713 100644
--- a/tests/test_local_grid_cyclic.py
+++ b/tests/test_local_grid_cyclic.py
@@ -23,7 +23,7 @@ def setup_method(self, method):
             "date": {"merge": {"with": "time", "linkers": ["T", "00"]}},
             "step": {"type_change": "int"},
             "number": {"type_change": "int"},
-            "longitude": {"cyclic": [-180, 180]}
+            "longitude": {"cyclic": [-180, 180]},
         }
         self.config = {"class": "od", "expver": "0001", "levtype": "sfc", "stream": "oper"}
         self.fdbdatacube = FDBDatacube(self.config, axis_options=self.options)
@@ -62,7 +62,7 @@ def test_fdb_datacube_2(self):
             Select("class", ["od"]),
             Select("stream", ["oper"]),
             Select("type", ["fc"]),
-            Point(["latitude", "longitude"], [[-20, 50+360]]),
+            Point(["latitude", "longitude"], [[-20, 50 + 360]]),
         )
         result = self.API.retrieve(request)
         result.pprint_2()

From c666d0fe428afad3772488acd2dc55a5f94fd242 Mon Sep 17 00:00:00 2001
From: Mathilde Leuridan <mathilde.leuridan@ecmwf.int>
Date: Thu, 1 Feb 2024 14:01:44 +0000
Subject: [PATCH 12/12] ignore pygribjump test

---
 tests/test_local_grid_cyclic.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/tests/test_local_grid_cyclic.py b/tests/test_local_grid_cyclic.py
index bf6f5713..02598632 100644
--- a/tests/test_local_grid_cyclic.py
+++ b/tests/test_local_grid_cyclic.py
@@ -51,6 +51,7 @@ def test_fdb_datacube(self):
         assert result.leaves[0].flatten()["latitude"] == -20
         assert result.leaves[0].flatten()["longitude"] == -20
 
+    @pytest.mark.fdb
     def test_fdb_datacube_2(self):
         request = Request(
             Select("step", [0]),