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ProjectPythia · Oct 9, 2024 · 6fd7863 · 6fd7863
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diff --git a/_preview/1/README.html b/_preview/1/README.html
@@ -463,6 +463,7 @@ <h3>Working with Great Circles<a class="headerlink" href="#working-with-great-ci
 <li><p>Generating a great circle arc and path</p></li>
 <li><p>Midpoint (and additional intermediate points) of a great circle arc</p></li>
 <li><p>Length of a great circle arc (the distance between two points)</p></li>
+<li><p>Spherical distance to degrees</p></li>
 <li><p>Bearing of a great circle arc</p></li>
 <li><p>Compare great circle arc to rhumb line</p></li>
 <li><p>Antipodal point</p></li>

diff --git a/_preview/1/_sources/README.md b/_preview/1/_sources/README.md
@@ -49,6 +49,7 @@ Each section will make use of plotting to visually demonstrate concepts with `ma
 - Generating a great circle arc and path
 - Midpoint (and additional intermediate points) of a great circle arc
 - Length of a great circle arc (the distance between two points)
+- Spherical distance to degrees
 - Bearing of a great circle arc
 - Compare great circle arc to rhumb line
 - Antipodal point

diff --git a/_preview/1/_sources/notebooks/tutorials/arc_path.ipynb b/_preview/1/_sources/notebooks/tutorials/arc_path.ipynb
@@ -32,6 +32,7 @@
     "Great circles are circles that circumnavigate the globe\n",
     "\n",
     "1. Distance Between Points on a Great Circle Arc\n",
+    "1. Spherical distance to degrees\n",
     "1. Determine the Bearing of a Great Circle Arc\n",
     "1. Generating a Great Circle Arc with Intermediates Points\n",
     "1. Determine the Midpoint of a Great Circle Arc\n",
@@ -244,7 +245,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Distance Between Points on a Great Circle Arc\n"
+    "## Distance Between Points on a Great Circle Arc"
    ]
   },
   {
@@ -302,10 +303,11 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Haversine (TODO)\n",
-    "### Vincenty Sphere Great Circle Distance (TODO)\n",
-    "### Vincenty Ellipsoid Great Circle Distance (TODO)\n",
-    "### Meeus Great Circle Distance (TODO)"
+    "Additional distance measuerments\n",
+    "- Haversine (TODO)\n",
+    "- Vincenty Sphere Great Circle Distance (TODO)\n",
+    "- Vincenty Ellipsoid Great Circle Distance (TODO)\n",
+    "- Meeus Great Circle Distance (TODO)"
    ]
   },
   {
@@ -477,6 +479,61 @@
     "Compared to the distance from the associated airports in Denver and Boston ([DIA to Logan](https://www.greatcirclemap.com/?routes=DEN-BOS)) which has a distance of 2823 km"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Spherical distance to degrees\n",
+    "\n",
+    "Convert a distance from meters to degrees, measured along the great circle sphere with a radius of ~6371 km (mean radius of Earth)\n",
+    "\n",
+    "- See also: [ObsPy `kilometer2degrees()`](https://docs.obspy.org/packages/autogen/obspy.geodetics.base.kilometer2degrees.html)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 359,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2.6949458523585643\n",
+      "300.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "# assumes a spherical Earth\n",
+    "earth_radius = 6378.137 # km\n",
+    "\n",
+    "def km_to_degree_distance(distance_km=None):\n",
+    "    return distance_km / (2 * earth_radius * np.pi / 360)\n",
+    "\n",
+    "def degree_to_km_distance(distance_degree=None):\n",
+    "    return distance_degree * (2 * earth_radius * np.pi / 360)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 363,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "300 km to degrees = 2.6949458523585643 degrees\n",
+      "6.381307 degree to km = 710.3638458355522 km\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"300 km to degrees = {km_to_degree_distance(300)} degrees\")\n",
+    "print(f\"6.381307 degree to km = {degree_to_km_distance(6.381307)} km\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},

diff --git a/_preview/1/notebooks/notebook-template.html b/_preview/1/notebooks/notebook-template.html
@@ -529,8 +529,8 @@ <h5>of further and further<a class="headerlink" href="#of-further-and-further" t
 <section id="header-levels">
 <h6>header levels<a class="headerlink" href="#header-levels" title="Link to this heading"><i class="fas fa-link"></i></a></h6>
 <p>as well <span class="math notranslate nohighlight">\(m = a * t / h\)</span> text! Similarly, you have access to other <span class="math notranslate nohighlight">\(\LaTeX\)</span> equation <a class="reference external" href="https://jupyter-notebook.readthedocs.io/en/stable/examples/Notebook/Typesetting%20Equations.html"><strong>functionality</strong></a> via MathJax (demo below from link),</p>
-<div class="amsmath math notranslate nohighlight" id="equation-8db3ca5f-aeb4-400c-8cf9-2d4e9453f0d8">
-<span class="eqno">()<a class="headerlink" href="#equation-8db3ca5f-aeb4-400c-8cf9-2d4e9453f0d8" title="Permalink to this equation"><i class="fas fa-link"></i></a></span>\[\begin{align}
+<div class="amsmath math notranslate nohighlight" id="equation-0c56ba9a-af36-498d-80dc-9024e39173e0">
+<span class="eqno">()<a class="headerlink" href="#equation-0c56ba9a-af36-498d-80dc-9024e39173e0" title="Permalink to this equation"><i class="fas fa-link"></i></a></span>\[\begin{align}
 \dot{x} &amp; = \sigma(y-x) \\
 \dot{y} &amp; = \rho x - y - xz \\
 \dot{z} &amp; = -\beta z + xy

diff --git a/_preview/1/notebooks/tutorials/arc_path.html b/_preview/1/notebooks/tutorials/arc_path.html
@@ -422,6 +422,7 @@ <h2>Overview<a class="headerlink" href="#overview" title="Link to this heading">
 <p>Great circles are circles that circumnavigate the globe</p>
 <ol class="arabic simple">
 <li><p>Distance Between Points on a Great Circle Arc</p></li>
+<li><p>Spherical distance to degrees</p></li>
 <li><p>Determine the Bearing of a Great Circle Arc</p></li>
 <li><p>Generating a Great Circle Arc with Intermediates Points</p></li>
 <li><p>Determine the Midpoint of a Great Circle Arc</p></li>
@@ -650,18 +651,13 @@ <h3>Determine Distance Mathematically via Unit Sphere<a class="headerlink" href=
 </div>
 </div>
 </div>
-</section>
-<section id="haversine-todo">
-<h3>Haversine (TODO)<a class="headerlink" href="#haversine-todo" title="Link to this heading"><i class="fas fa-link"></i></a></h3>
-</section>
-<section id="vincenty-sphere-great-circle-distance-todo">
-<h3>Vincenty Sphere Great Circle Distance (TODO)<a class="headerlink" href="#vincenty-sphere-great-circle-distance-todo" title="Link to this heading"><i class="fas fa-link"></i></a></h3>
-</section>
-<section id="vincenty-ellipsoid-great-circle-distance-todo">
-<h3>Vincenty Ellipsoid Great Circle Distance (TODO)<a class="headerlink" href="#vincenty-ellipsoid-great-circle-distance-todo" title="Link to this heading"><i class="fas fa-link"></i></a></h3>
-</section>
-<section id="meeus-great-circle-distance-todo">
-<h3>Meeus Great Circle Distance (TODO)<a class="headerlink" href="#meeus-great-circle-distance-todo" title="Link to this heading"><i class="fas fa-link"></i></a></h3>
+<p>Additional distance measuerments</p>
+<ul class="simple">
+<li><p>Haversine (TODO)</p></li>
+<li><p>Vincenty Sphere Great Circle Distance (TODO)</p></li>
+<li><p>Vincenty Ellipsoid Great Circle Distance (TODO)</p></li>
+<li><p>Meeus Great Circle Distance (TODO)</p></li>
+</ul>
 </section>
 <section id="determine-distance-points-via-python-package-pyproj">
 <h3>Determine Distance Points via Python Package <code class="docutils literal notranslate"><span class="pre">pyproj</span></code><a class="headerlink" href="#determine-distance-points-via-python-package-pyproj" title="Link to this heading"><i class="fas fa-link"></i></a></h3>
@@ -788,6 +784,41 @@ <h3>Determine Distance Points via Python Package <code class="docutils literal n
 <p>Compared to the distance from the associated airports in Denver and Boston (<a class="reference external" href="https://www.greatcirclemap.com/?routes=DEN-BOS">DIA to Logan</a>) which has a distance of 2823 km</p>
 </section>
 </section>
+<section id="spherical-distance-to-degrees">
+<h2>Spherical distance to degrees<a class="headerlink" href="#spherical-distance-to-degrees" title="Link to this heading"><i class="fas fa-link"></i></a></h2>
+<p>Convert a distance from meters to degrees, measured along the great circle sphere with a radius of ~6371 km (mean radius of Earth)</p>
+<ul class="simple">
+<li><p>See also: <a class="reference external" href="https://docs.obspy.org/packages/autogen/obspy.geodetics.base.kilometer2degrees.html">ObsPy <code class="docutils literal notranslate"><span class="pre">kilometer2degrees()</span></code></a></p></li>
+</ul>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># assumes a spherical Earth</span>
+<span class="n">earth_radius</span> <span class="o">=</span> <span class="mf">6378.137</span> <span class="c1"># km</span>
+
+<span class="k">def</span> <span class="nf">km_to_degree_distance</span><span class="p">(</span><span class="n">distance_km</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">distance_km</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">earth_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">360</span><span class="p">)</span>
+
+<span class="k">def</span> <span class="nf">degree_to_km_distance</span><span class="p">(</span><span class="n">distance_degree</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">distance_degree</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">earth_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">360</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;300 km to degrees = </span><span class="si">{</span><span class="n">km_to_degree_distance</span><span class="p">(</span><span class="mi">300</span><span class="p">)</span><span class="si">}</span><span class="s2"> degrees&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;6.381307 degree to km = </span><span class="si">{</span><span class="n">degree_to_km_distance</span><span class="p">(</span><span class="mf">6.381307</span><span class="p">)</span><span class="si">}</span><span class="s2"> km&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>300 km to degrees = 2.6949458523585643 degrees
+6.381307 degree to km = 710.3638458355522 km
+</pre></div>
+</div>
+</div>
+</div>
+</section>
 <section id="determine-the-bearing-of-a-great-circle-arc">
 <h2>Determine the Bearing of a Great Circle Arc<a class="headerlink" href="#determine-the-bearing-of-a-great-circle-arc" title="Link to this heading"><i class="fas fa-link"></i></a></h2>
 <section id="determine-the-bearing-mathematically-via-unit-sphere">
@@ -1672,13 +1703,10 @@ <h2>Resources and references<a class="headerlink" href="#resources-and-reference
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#imports">Imports</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#distance-between-points-on-a-great-circle-arc">Distance Between Points on a Great Circle Arc</a><ul class="nav section-nav flex-column">
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#determine-distance-mathematically-via-unit-sphere">Determine Distance Mathematically via Unit Sphere</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#haversine-todo">Haversine (TODO)</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#vincenty-sphere-great-circle-distance-todo">Vincenty Sphere Great Circle Distance (TODO)</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#vincenty-ellipsoid-great-circle-distance-todo">Vincenty Ellipsoid Great Circle Distance (TODO)</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#meeus-great-circle-distance-todo">Meeus Great Circle Distance (TODO)</a></li>
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#determine-distance-points-via-python-package-pyproj">Determine Distance Points via Python Package <code class="docutils literal notranslate"><span class="pre">pyproj</span></code></a></li>
 </ul>
 </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#spherical-distance-to-degrees">Spherical distance to degrees</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#determine-the-bearing-of-a-great-circle-arc">Determine the Bearing of a Great Circle Arc</a><ul class="nav section-nav flex-column">
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#determine-the-bearing-mathematically-via-unit-sphere">Determine the Bearing Mathematically via Unit Sphere</a></li>
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#determine-the-bearing-via-python-package-pyproj">Determine the Bearing via Python Package <code class="docutils literal notranslate"><span class="pre">pyproj</span></code></a></li>

diff --git a/_preview/1/searchindex.js b/_preview/1/searchindex.js