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<div class='docs'><h1>douglas_peucker.py</h1></div>
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<a class='octothorpe' href='#section-0'>#</a>
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<div class='code'>
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<div class="highlight"><pre></pre></div>
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<p>simplifies a line segment using the Douglas-Peucker algorithm.</p>
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<p>taken from
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http://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm#Pseudocode</p>
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<p>in order to preserve topology of the original polygons the algorithm
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- never removes the first or the last point of a line segment
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- flags all points as simplified after processing (so it won't be processed twice)</p>
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<div class="highlight"><pre><span class="k">def</span> <span class="nf">simplify_douglas_peucker</span><span class="p">(</span><span class="n">points</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">):</span></pre></div>
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<a class='octothorpe' href='#section-2'>#</a>
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<div class='code'>
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<div class="highlight"><pre> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">points</span><span class="p">)</span>
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<span class="n">kept</span> <span class="o">=</span> <span class="p">[]</span>
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<span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">4</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">points</span> <span class="c"># skip short lines</span>
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<span class="k">if</span> <span class="ow">not</span> <span class="n">points</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">simplified</span><span class="p">:</span>
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<span class="n">_douglas_peucker</span><span class="p">(</span><span class="n">points</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">kept</span></pre></div>
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<div class='section' id='section-3'>
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<a class='octothorpe' href='#section-3'>#</a>
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<p>print 'kept %d deleted %d' % (kept, deleted)</p>
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<div class='code'>
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<div class="highlight"><pre></pre></div>
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<p>inner part of Douglas-Peucker algorithm, called recursively</p>
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<div class="highlight"><pre><span class="k">def</span> <span class="nf">_douglas_peucker</span><span class="p">(</span><span class="n">points</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">end</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">):</span></pre></div>
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<a class='octothorpe' href='#section-5'>#</a>
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<div class='code'>
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<div class="highlight"><pre> <span class="n">dmax</span> <span class="o">=</span> <span class="mi">0</span>
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<span class="n">index</span> <span class="o">=</span> <span class="mi">0</span></pre></div>
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<a class='octothorpe' href='#section-6'>#</a>
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<p>Find the point with the maximum distance</p>
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<div class='code'>
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<div class="highlight"><pre> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">start</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">end</span><span class="p">):</span>
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<span class="n">x1</span><span class="p">,</span> <span class="n">y1</span> <span class="o">=</span> <span class="n">points</span><span class="p">[</span><span class="n">start</span><span class="p">]</span>
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<span class="n">x2</span><span class="p">,</span> <span class="n">y2</span> <span class="o">=</span> <span class="n">points</span><span class="p">[</span><span class="n">end</span><span class="p">]</span>
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<span class="k">if</span> <span class="n">x1</span> <span class="o">==</span> <span class="n">x2</span> <span class="ow">and</span> <span class="n">y1</span> <span class="o">==</span> <span class="n">y2</span><span class="p">:</span>
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<span class="k">return</span>
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<span class="n">x3</span><span class="p">,</span> <span class="n">y3</span> <span class="o">=</span> <span class="n">points</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
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<span class="n">d</span> <span class="o">=</span> <span class="n">_min_distance</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">x3</span><span class="p">,</span> <span class="n">y3</span><span class="p">)</span>
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<span class="k">if</span> <span class="n">d</span> <span class="o">></span> <span class="n">dmax</span><span class="p">:</span>
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<span class="n">index</span> <span class="o">=</span> <span class="n">i</span>
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<span class="n">dmax</span> <span class="o">=</span> <span class="n">d</span></pre></div>
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<div class='section' id='section-7'>
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<a class='octothorpe' href='#section-7'>#</a>
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<p>If max distance is greater than epsilon, recursively simplify</p>
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<div class='code'>
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<div class="highlight"><pre> <span class="k">if</span> <span class="n">dmax</span> <span class="o">>=</span> <span class="n">epsilon</span> <span class="ow">and</span> <span class="n">start</span> <span class="o"><</span> <span class="n">index</span> <span class="o"><</span> <span class="n">end</span><span class="p">:</span></pre></div>
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<a class='octothorpe' href='#section-8'>#</a>
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<p>recursivly call</p>
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<div class='code'>
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<div class="highlight"><pre> <span class="n">_douglas_peucker</span><span class="p">(</span><span class="n">points</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">index</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">)</span>
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<span class="n">_douglas_peucker</span><span class="p">(</span><span class="n">points</span><span class="p">,</span> <span class="n">index</span><span class="p">,</span> <span class="n">end</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span></pre></div>
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<a class='octothorpe' href='#section-9'>#</a>
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<p>remove any point but the first and last</p>
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<div class='code'>
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<div class="highlight"><pre> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="n">end</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
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<span class="n">points</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">deleted</span> <span class="o">=</span> <span class="n">i</span> <span class="o">==</span> <span class="n">start</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="n">end</span>
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<span class="n">points</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">simplified</span> <span class="o">=</span> <span class="bp">True</span></pre></div>
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<p>the perpendicular distance from a point (x3,y3) to the line from (x1,y1) to (x2,y2)
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taken from http://local.wasp.uwa.edu.au/~pbourke/geometry/pointline/</p>
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<div class='code'>
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<div class="highlight"><pre><span class="k">def</span> <span class="nf">_min_distance</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">x3</span><span class="p">,</span> <span class="n">y3</span><span class="p">):</span></pre></div>
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<div class="highlight"><pre> <span class="n">d</span> <span class="o">=</span> <span class="n">_dist</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">)</span>
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<span class="n">u</span> <span class="o">=</span> <span class="p">(</span><span class="n">x3</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">y3</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">d</span> <span class="o">*</span> <span class="n">d</span><span class="p">)</span>
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<span class="n">x</span> <span class="o">=</span> <span class="n">x1</span> <span class="o">+</span> <span class="n">u</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span>
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<span class="n">y</span> <span class="o">=</span> <span class="n">y1</span> <span class="o">+</span> <span class="n">u</span> <span class="o">*</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">_dist</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">x3</span><span class="p">,</span> <span class="n">y3</span><span class="p">)</span></pre></div>
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<p>eucledian distance between two points</p>
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<div class="highlight"><pre><span class="k">def</span> <span class="nf">_dist</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">):</span></pre></div>
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<div class="highlight"><pre> <span class="kn">import</span> <span class="nn">math</span>
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<span class="n">dx</span> <span class="o">=</span> <span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span>
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<span class="n">dy</span> <span class="o">=</span> <span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span>
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<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dx</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">+</span> <span class="n">dy</span> <span class="o">*</span> <span class="n">dy</span><span class="p">)</span>
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