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<li><a class="reference internal" href="#">Path Tutorial</a><ul>
<li><a class="reference internal" href="#bezier-example">Bézier example</a></li>
<li><a class="reference internal" href="#compound-paths">Compound paths</a></li>
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<div class="section" id="path-tutorial">
<span id="id1"></span><h1>Path Tutorial<a class="headerlink" href="#path-tutorial" title="Permalink to this headline">¶</a></h1>
<p>The object underlying all of the <code class="xref py py-mod docutils literal"><span class="pre">matplotlib.patch</span></code> objects is
the <a class="reference internal" href="../api/path_api.html#matplotlib.path.Path" title="matplotlib.path.Path"><code class="xref py py-class docutils literal"><span class="pre">Path</span></code></a>, which supports the standard set of
moveto, lineto, curveto commands to draw simple and compound outlines
consisting of line segments and splines. The <code class="docutils literal"><span class="pre">Path</span></code> is instantiated
with a (N,2) array of (x,y) vertices, and a N-length array of path
codes. For example to draw the unit rectangle from (0,0) to (1,1), we
could use this code</p>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.path</span> <span class="kn">import</span> <span class="n">Path</span>
<span class="kn">import</span> <span class="nn">matplotlib.patches</span> <span class="kn">as</span> <span class="nn">patches</span>
<span class="n">verts</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">),</span> <span class="c"># left, bottom</span>
<span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">),</span> <span class="c"># left, top</span>
<span class="p">(</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">),</span> <span class="c"># right, top</span>
<span class="p">(</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">),</span> <span class="c"># right, bottom</span>
<span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">),</span> <span class="c"># ignored</span>
<span class="p">]</span>
<span class="n">codes</span> <span class="o">=</span> <span class="p">[</span><span class="n">Path</span><span class="o">.</span><span class="n">MOVETO</span><span class="p">,</span>
<span class="n">Path</span><span class="o">.</span><span class="n">LINETO</span><span class="p">,</span>
<span class="n">Path</span><span class="o">.</span><span class="n">LINETO</span><span class="p">,</span>
<span class="n">Path</span><span class="o">.</span><span class="n">LINETO</span><span class="p">,</span>
<span class="n">Path</span><span class="o">.</span><span class="n">CLOSEPOLY</span><span class="p">,</span>
<span class="p">]</span>
<span class="n">path</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="n">verts</span><span class="p">,</span> <span class="n">codes</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">patch</span> <span class="o">=</span> <span class="n">patches</span><span class="o">.</span><span class="n">PathPatch</span><span class="p">(</span><span class="n">path</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">'orange'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span><span class="p">(</span><span class="n">patch</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</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>
</div>
<p>(<a class="reference external" href="../users/path_tutorial-1.py">Source code</a>, <a class="reference external" href="../users/path_tutorial-1.png">png</a>, <a class="reference external" href="../users/path_tutorial-1.hires.png">hires.png</a>, <a class="reference external" href="../users/path_tutorial-1.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/path_tutorial-1.png" src="../_images/path_tutorial-1.png" />
</div>
<p>The following path codes are recognized</p>
<table border="1" class="docutils">
<colgroup>
<col width="9%" />
<col width="20%" />
<col width="71%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Code</th>
<th class="head">Vertices</th>
<th class="head">Description</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><code class="docutils literal"><span class="pre">STOP</span></code></td>
<td>1 (ignored)</td>
<td>A marker for the end of the entire path (currently not required and ignored)</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">MOVETO</span></code></td>
<td>1</td>
<td>Pick up the pen and move to the given vertex.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">LINETO</span></code></td>
<td>1</td>
<td>Draw a line from the current position to the given vertex.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">CURVE3</span></code></td>
<td>2 (1 control point, 1 endpoint)</td>
<td>Draw a quadratic Bézier curve from the current position, with the given control point, to the given end point.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">CURVE4</span></code></td>
<td>3 (2 control points, 1 endpoint)</td>
<td>Draw a cubic Bézier curve from the current position, with the given control points, to the given end point.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">CLOSEPOLY</span></code></td>
<td>1 (point itself is ignored)</td>
<td>Draw a line segment to the start point of the current polyline.</td>
</tr>
</tbody>
</table>
<div class="section" id="bezier-example">
<h2>Bézier example<a class="headerlink" href="#bezier-example" title="Permalink to this headline">¶</a></h2>
<p>Some of the path components require multiple vertices to specify them:
for example CURVE 3 is a <a class="reference external" href="http://en.wikipedia.org/wiki/B%C3%A9zier_curve">bézier</a> curve with one
control point and one end point, and CURVE4 has three vertices for the
two control points and the end point. The example below shows a
CURVE4 Bézier spline – the bézier curve will be contained in the
convex hull of the start point, the two control points, and the end
point</p>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.path</span> <span class="kn">import</span> <span class="n">Path</span>
<span class="kn">import</span> <span class="nn">matplotlib.patches</span> <span class="kn">as</span> <span class="nn">patches</span>
<span class="n">verts</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">),</span> <span class="c"># P0</span>
<span class="p">(</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">1.</span><span class="p">),</span> <span class="c"># P1</span>
<span class="p">(</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">),</span> <span class="c"># P2</span>
<span class="p">(</span><span class="mf">0.8</span><span class="p">,</span> <span class="mf">0.</span><span class="p">),</span> <span class="c"># P3</span>
<span class="p">]</span>
<span class="n">codes</span> <span class="o">=</span> <span class="p">[</span><span class="n">Path</span><span class="o">.</span><span class="n">MOVETO</span><span class="p">,</span>
<span class="n">Path</span><span class="o">.</span><span class="n">CURVE4</span><span class="p">,</span>
<span class="n">Path</span><span class="o">.</span><span class="n">CURVE4</span><span class="p">,</span>
<span class="n">Path</span><span class="o">.</span><span class="n">CURVE4</span><span class="p">,</span>
<span class="p">]</span>
<span class="n">path</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="n">verts</span><span class="p">,</span> <span class="n">codes</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">patch</span> <span class="o">=</span> <span class="n">patches</span><span class="o">.</span><span class="n">PathPatch</span><span class="p">(</span><span class="n">path</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">'none'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span><span class="p">(</span><span class="n">patch</span><span class="p">)</span>
<span class="n">xs</span><span class="p">,</span> <span class="n">ys</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">verts</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="s">'x--'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="s">'P0'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.15</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">,</span> <span class="s">'P1'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">1.05</span><span class="p">,</span> <span class="mf">0.85</span><span class="p">,</span> <span class="s">'P2'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.85</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="s">'P3'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">1.1</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>
</div>
<p>(<a class="reference external" href="../users/path_tutorial-2.py">Source code</a>, <a class="reference external" href="../users/path_tutorial-2.png">png</a>, <a class="reference external" href="../users/path_tutorial-2.hires.png">hires.png</a>, <a class="reference external" href="../users/path_tutorial-2.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/path_tutorial-2.png" src="../_images/path_tutorial-2.png" />
</div>
</div>
<div class="section" id="compound-paths">
<h2>Compound paths<a class="headerlink" href="#compound-paths" title="Permalink to this headline">¶</a></h2>
<p>All of the simple patch primitives in matplotlib, Rectangle, Circle,
Polygon, etc, are implemented with simple path. Plotting functions
like <a class="reference internal" href="../api/axes_api.html#matplotlib.axes.Axes.hist" title="matplotlib.axes.Axes.hist"><code class="xref py py-meth docutils literal"><span class="pre">hist()</span></code></a> and
<a class="reference internal" href="../api/axes_api.html#matplotlib.axes.Axes.bar" title="matplotlib.axes.Axes.bar"><code class="xref py py-meth docutils literal"><span class="pre">bar()</span></code></a>, which create a number of
primitives, eg a bunch of Rectangles, can usually be implemented more
efficiently using a compound path. The reason <code class="docutils literal"><span class="pre">bar</span></code> creates a list
of rectangles and not a compound path is largely historical: the
<a class="reference internal" href="../api/path_api.html#matplotlib.path.Path" title="matplotlib.path.Path"><code class="xref py py-class docutils literal"><span class="pre">Path</span></code></a> code is comparatively new and <code class="docutils literal"><span class="pre">bar</span></code>
predates it. While we could change it now, it would break old code,
so here we will cover how to create compound paths, replacing the
functionality in bar, in case you need to do so in your own code for
efficiency reasons, eg you are creating an animated bar plot.</p>
<p>We will make the histogram chart by creating a series of rectangles
for each histogram bar: the rectangle width is the bin width and the
rectangle height is the number of datapoints in that bin. First we’ll
create some random normally distributed data and compute the
histogram. Because numpy returns the bin edges and not centers, the
length of <code class="docutils literal"><span class="pre">bins</span></code> is 1 greater than the length of <code class="docutils literal"><span class="pre">n</span></code> in the
example below:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="c"># histogram our data with numpy</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1000</span><span class="p">)</span>
<span class="n">n</span><span class="p">,</span> <span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
</pre></div>
</div>
<p>We’ll now extract the corners of the rectangles. Each of the
<code class="docutils literal"><span class="pre">left</span></code>, <code class="docutils literal"><span class="pre">bottom</span></code>, etc, arrays below is <code class="docutils literal"><span class="pre">len(n)</span></code>, where <code class="docutils literal"><span class="pre">n</span></code> is
the array of counts for each histogram bar:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="c"># get the corners of the rectangles for the histogram</span>
<span class="n">left</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">right</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">bins</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
<span class="n">bottom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">left</span><span class="p">))</span>
<span class="n">top</span> <span class="o">=</span> <span class="n">bottom</span> <span class="o">+</span> <span class="n">n</span>
</pre></div>
</div>
<p>Now we have to construct our compound path, which will consist of a
series of <code class="docutils literal"><span class="pre">MOVETO</span></code>, <code class="docutils literal"><span class="pre">LINETO</span></code> and <code class="docutils literal"><span class="pre">CLOSEPOLY</span></code> for each rectangle.
For each rectangle, we need 5 vertices: 1 for the <code class="docutils literal"><span class="pre">MOVETO</span></code>, 3 for
the <code class="docutils literal"><span class="pre">LINETO</span></code>, and 1 for the <code class="docutils literal"><span class="pre">CLOSEPOLY</span></code>. As indicated in the
table above, the vertex for the closepoly is ignored but we still need
it to keep the codes aligned with the vertices:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">nverts</span> <span class="o">=</span> <span class="n">nrects</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="mi">3</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">verts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">nverts</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">codes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">nverts</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span> <span class="o">*</span> <span class="n">path</span><span class="o">.</span><span class="n">Path</span><span class="o">.</span><span class="n">LINETO</span>
<span class="n">codes</span><span class="p">[</span><span class="mi">0</span><span class="p">::</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">path</span><span class="o">.</span><span class="n">Path</span><span class="o">.</span><span class="n">MOVETO</span>
<span class="n">codes</span><span class="p">[</span><span class="mi">4</span><span class="p">::</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">path</span><span class="o">.</span><span class="n">Path</span><span class="o">.</span><span class="n">CLOSEPOLY</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">0</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">left</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">0</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">bottom</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">left</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">top</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">2</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">right</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">2</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">top</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">3</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">right</span>
<span class="n">verts</span><span class="p">[</span><span class="mi">3</span><span class="p">::</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">bottom</span>
</pre></div>
</div>
<p>All that remains is to create the path, attach it to a
<code class="xref py py-class docutils literal"><span class="pre">PathPatch</span></code>, and add it to our axes:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">barpath</span> <span class="o">=</span> <span class="n">path</span><span class="o">.</span><span class="n">Path</span><span class="p">(</span><span class="n">verts</span><span class="p">,</span> <span class="n">codes</span><span class="p">)</span>
<span class="n">patch</span> <span class="o">=</span> <span class="n">patches</span><span class="o">.</span><span class="n">PathPatch</span><span class="p">(</span><span class="n">barpath</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">edgecolor</span><span class="o">=</span><span class="s">'yellow'</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">ax</span><span class="o">.</span><span class="n">add_patch</span><span class="p">(</span><span class="n">patch</span><span class="p">)</span>
</pre></div>
</div>
<p>Here is the result</p>
<p>(<a class="reference external" href="../pyplots/compound_path_demo.py">Source code</a>, <a class="reference external" href="../pyplots/compound_path_demo.png">png</a>, <a class="reference external" href="../pyplots/compound_path_demo.hires.png">hires.png</a>, <a class="reference external" href="../pyplots/compound_path_demo.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/compound_path_demo.png" src="../_images/compound_path_demo.png" />
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