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<div class="section" id="stereographic-projection">
<span id="stere"></span><h1>Stereographic Projection<a class="headerlink" href="#stereographic-projection" title="Permalink to this headline">ΒΆ</a></h1>
<p>A conformal projection. The green shapes drawn on the map are equal-area
circles on the surface of the earth. Known as “Tissot’s indicatrix”,
they can be used to show the angular and areal distortion of a map projection.
On a conformal projection, the shape of the circles is preserved, but the
area is not. On a equal-area projection, the area is preserved but the
shape is not.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">from</span> <span class="nn">mpl_toolkits.basemap</span> <span class="kn">import</span> <span class="n">Basemap</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="c"># setup stereographic basemap.</span>
<span class="c"># lat_ts is latitude of true scale.</span>
<span class="c"># lon_0,lat_0 is central point.</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">Basemap</span><span class="p">(</span><span class="n">width</span><span class="o">=</span><span class="mi">12000000</span><span class="p">,</span><span class="n">height</span><span class="o">=</span><span class="mi">8000000</span><span class="p">,</span>
<span class="n">resolution</span><span class="o">=</span><span class="s">'l'</span><span class="p">,</span><span class="n">projection</span><span class="o">=</span><span class="s">'stere'</span><span class="p">,</span>\
<span class="n">lat_ts</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span><span class="n">lat_0</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span><span class="n">lon_0</span><span class="o">=-</span><span class="mf">107.</span><span class="p">)</span>
<span class="n">m</span><span class="o">.</span><span class="n">drawcoastlines</span><span class="p">()</span>
<span class="n">m</span><span class="o">.</span><span class="n">fillcontinents</span><span class="p">(</span><span class="n">color</span><span class="o">=</span><span class="s">'coral'</span><span class="p">,</span><span class="n">lake_color</span><span class="o">=</span><span class="s">'aqua'</span><span class="p">)</span>
<span class="c"># draw parallels and meridians.</span>
<span class="n">m</span><span class="o">.</span><span class="n">drawparallels</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mf">80.</span><span class="p">,</span><span class="mf">81.</span><span class="p">,</span><span class="mf">20.</span><span class="p">))</span>
<span class="n">m</span><span class="o">.</span><span class="n">drawmeridians</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mf">180.</span><span class="p">,</span><span class="mf">181.</span><span class="p">,</span><span class="mf">20.</span><span class="p">))</span>
<span class="n">m</span><span class="o">.</span><span class="n">drawmapboundary</span><span class="p">(</span><span class="n">fill_color</span><span class="o">=</span><span class="s">'aqua'</span><span class="p">)</span>
<span class="c"># draw tissot's indicatrix to show distortion.</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span>
<span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">ymax</span><span class="o">/</span><span class="mi">20</span><span class="p">,</span><span class="mi">19</span><span class="o">*</span><span class="n">m</span><span class="o">.</span><span class="n">ymax</span><span class="o">/</span><span class="mi">20</span><span class="p">,</span><span class="mi">9</span><span class="p">):</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">xmax</span><span class="o">/</span><span class="mi">20</span><span class="p">,</span><span class="mi">19</span><span class="o">*</span><span class="n">m</span><span class="o">.</span><span class="n">xmax</span><span class="o">/</span><span class="mi">20</span><span class="p">,</span><span class="mi">12</span><span class="p">):</span>
<span class="n">lon</span><span class="p">,</span> <span class="n">lat</span> <span class="o">=</span> <span class="n">m</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span><span class="n">inverse</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">poly</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">tissot</span><span class="p">(</span><span class="n">lon</span><span class="p">,</span><span class="n">lat</span><span class="p">,</span><span class="mf">1.5</span><span class="p">,</span><span class="mi">100</span><span class="p">,</span>\
<span class="n">facecolor</span><span class="o">=</span><span class="s">'green'</span><span class="p">,</span><span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span><span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Stereographic Projection"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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<p>(<a class="reference external" href="../users/figures/stere.py">Source code</a>)</p>
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