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voronoi.py
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voronoi.py
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import numpy
from scipy.spatial import Voronoi
class VoronoiDiagram(object):
def __init__(self, vor, mapping):
self.vor = vor
self.mapping = mapping # cell_idx => voronoi_idx
self.center = {}
for cell_idx in self.mapping.keys():
region = self.get_region(cell_idx)
if len(region) == 0:
self.center[cell_idx] = None
else:
cell_x = list( map(lambda pt: pt[0], region) )
cell_y = list( map(lambda pt: pt[1], region) )
center_x = sum(cell_x) / len(cell_x)
center_y = sum(cell_y) / len(cell_y)
self.center[cell_idx] = (center_x, center_y)
self.cells_with_vertex = {}
for cell_idx in self.mapping.keys():
region = self.get_region(cell_idx, locations=False)
for vertex_id in [idx for idx in region if idx != -1]:
if vertex_id not in self.cells_with_vertex:
self.cells_with_vertex[vertex_id] = set()
self.cells_with_vertex[vertex_id].add(cell_idx)
def get_region(self, cell_idx, locations=True):
'''
Get the polygon that defines the region for the specified cell_id/region_id.
Returns a list of 2D points, or an empty list if the region isn't defined within
the Voronoi diagram; see more about when this happens here:
https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Voronoi.html
'''
v_idx = self.mapping[cell_idx]
region = [region for region in self.vor.regions[v_idx] if region != -1]
# if -1 in self.vor.regions[v_idx]:
# return [region for region in self.vor.regions[v_idx] if region != -1]
# print(self.vor.regions[v_idx])
# return []
if locations:
return list( map(lambda r: self.vor.vertices[r], region) )
# return list( map(lambda r: self.vor.vertices[r], self.vor.regions[v_idx]) )
else:
return region
def edges(self):
return list( filter(lambda ridge: -1 not in ridge, self.vor.ridge_vertices) )
def included_cells(self, vertex_id):
return list( self.cells_with_vertex[vertex_id] )
def vertex_location(self, vertex_id):
return self.vor.vertices[vertex_id]
def find_cell(self, x, y):
shortest_dist = 100.0
shortest_idx = -1
for cell_idx in self.mapping.keys():
center = self.center[cell_idx]
if center is not None:
dist = abs(x - center[0]) + abs(y - center[1])
if dist < shortest_dist:
shortest_dist = dist
shortest_idx = cell_idx
return shortest_idx
def outline(self, cell_idxs):
ridges = []
'''
get all allowed regions
for all ridge vertices
check if ridge is in exactly one region
'''
supported_regions = list( map(lambda idx: self.vor.regions[self.mapping[idx]], cell_idxs) )
regions_with_ridge = lambda ridge: list( filter(lambda region: ridge[0] in region and ridge[1] in region, supported_regions) )
for ridge in self.vor.ridge_vertices:
if len(regions_with_ridge(ridge)) == 1 and -1 not in ridge:
ridges.append(ridge)
# if sort:
# ridges = self.sort_ridges(ridges)
return list(map(lambda r: (self.vor.vertices[r[0]], self.vor.vertices[r[1]]), ridges))
def outline_polygons(self, cell_idxs):
ridges = []
'''
get all allowed regions
for all ridge vertices
check if ridge is in exactly one region
'''
supported_regions = list( map(lambda idx: self.vor.regions[self.mapping[idx]], cell_idxs) )
regions_with_ridge = lambda ridge: list( filter(lambda region: ridge[0] in region and ridge[1] in region, supported_regions) )
for ridge in self.vor.ridge_vertices:
if len(regions_with_ridge(ridge)) == 1 and -1 not in ridge:
ridges.append(ridge)
polygons = self.sort_ridges(ridges)
for polygon in polygons:
yield list(map(lambda r: (self.vor.vertices[r[0]], self.vor.vertices[r[1]]), polygon))
def sort_ridges(self, ridges):
polygons = []
polygon = [ ridges[0], ]
ridges.pop(0)
next_id = polygon[0][1]
# Store the starting vertex of the polygon. Once we get back, we need to pick a new
# polygon_start_id from the remaining vertices. This will cover landforms with multiple
# polygons, such as continents with both a coast and lakes.
polygon_start_id = next_id
remaining = len(ridges)
while len(ridges) > 0:
for idx, ridge in enumerate(ridges):
if ridge[0] == next_id:
polygon.append(ridge)
ridges.pop(idx)
next_id = ridge[1]
break
if ridge[1] == next_id:
polygon.append(ridge)
ridges.pop(idx)
next_id = ridge[0]
break
# Didn't remove a ridge. Switch to new polygon.
if len(ridges) == remaining:
polygons.append(polygon)
polygon = [ ridges[0], ]
ridges.pop(0)
next_id = polygon[-1][1]
remaining = len(ridges)
if len(polygon) > 0:
polygons.append(polygon)
return polygons
def generate(points, n_smooth=3):
vor = None
# Make several iterations, using the centroid of the polygons from the previous iteration
# as the new point cloud.
for _ in range(n_smooth):
vor = Voronoi(points)
new_points = numpy.zeros(points.shape)
for point_idx, region_id in enumerate(vor.point_region):
region = vor.regions[region_id]
# If the region is undefined, use the original point. If the region is defined,
# use the centroid of the polygon
if -1 in region:
new_points[point_idx] = points[point_idx]
else:
centroid = numpy.mean([vor.vertices[idx] for idx in region], 0)
if centroid[0] >= 0.0 and centroid[0] <= 1.0 and centroid[1] >= 0.0 and centroid[1] <= 1.0:
new_points[point_idx] = centroid
else:
new_points[point_idx] = points[point_idx]
points = new_points
return vor
def prebuilt_vor1():
points = numpy.array([
[0.40262444, 0.89010797],
[0.46321667, 0.38315214],
[0.44349672, 0.18688911],
[0.68745787, 0.69143624],
[0.81944654, 0.15131946],
[0.72458714, 0.22609854],
[0.09813275, 0.10948937],
[0.70126296, 0.75512688],
[0.94840268, 0.1245352 ],
[0.67502909, 0.67320131],
[0.51403338, 0.19046477],
[0.50371745, 0.11135518],
[0.82637509, 0.8662734 ],
[0.73357888, 0.17471943],
[0.03979779, 0.03844015],
[0.98681669, 0.93202815],
[0.37459058, 0.38567779],
[0.97938578, 0.79391543],
[0.72289236, 0.1089072 ],
[0.78337802, 0.73216984],
[0.19575816, 0.81631711],
[0.97356313, 0.82395971],
[0.10195127, 0.01111625],
[0.78762842, 0.95231354],
[0.4559196 , 0.01983087],
[0.94214394, 0.19983331],
[0.80805499, 0.75741924],
[0.01387654, 0.4010178 ],
[0.29149957, 0.11556165],
[0.66567361, 0.92751248],
[0.59049409, 0.32640914],
[0.38291789, 0.92962468],
[0.10056959, 0.56028808],
[0.78515087, 0.86267363],
[0.71865541, 0.22180088],
[0.05040245, 0.7702802 ],
[0.37084486, 0.36057732],
[0.64849443, 0.40721157],
[0.15563548, 0.90238154],
[0.58745176, 0.90352623],
[0.12489829, 0.32289921],
[0.34419703, 0.86792104],
[0.50676785, 0.40017397],
[0.50834899, 0.65523267],
[0.36487756, 0.62471309],
[0.39764789, 0.2181109 ],
[0.3011823 , 0.0222423 ],
[0.2143103 , 0.60207535],
[0.13990504, 0.17716391],
[0.90438299, 0.66031845],
[0.40423086, 0.56533161],
[0.79536783, 0.37672868],
[0.43392892, 0.32567715],
[0.17528278, 0.05660193],
[0.21399672, 0.68699174],
[0.47474729, 0.35745426],
[0.29068082, 0.59539884],
[0.36700722, 0.13542221],
[0.79564283, 0.95248314],
[0.68364939, 0.60702048],
[0.57251765, 0.6317786 ],
[0.21822423, 0.7171864 ],
[0.6573202 , 0.65521942],
[0.08380973, 0.23864449],
[0.73907708, 0.78899286],
[0.24951666, 0.50910092],
[0.48166857, 0.93009483],
[0.52880764, 0.76343148],
[0.14900537, 0.81545771],
[0.63578057, 0.69103053],
[0.66096026, 0.51938303],
[0.17768932, 0.78702168],
[0.89266581, 0.2582247 ],
[0.52915596, 0.67159946],
[0.6047453 , 0.26361231],
[0.76748022, 0.45862889],
[0.86477637, 0.44603271],
[0.82338454, 0.98428034],
[0.20278993, 0.06884434],
[0.15602841, 0.8087541 ],
[0.99733613, 0.98585632],
[0.23368683, 0.65465301],
[0.24976235, 0.38553243],
[0.76690454, 0.78862475],
[0.15056952, 0.96460832],
[0.23950245, 0.28971527],
[0.74287355, 0.06861326],
[0.63059252, 0.7292568 ],
[0.28497952, 0.94096798],
[0.29997593, 0.31476221],
[0.34970587, 0.84843535],
[0.09496377, 0.31222525],
[0.82098736, 0.52918112],
[0.92285489, 0.15623229],
[0.19687324, 0.55516564],
[0.45493029, 0.02460928],
[0.55018825, 0.75980363],
[0.33457664, 0.21343718],
[0.20419116, 0.13904349],
[0.27995101, 0.04775983],
])
return generate(points)