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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<li><a class="reference internal" href="#">path</a><ul>
<li><a class="reference internal" href="#module-matplotlib.path"><tt class="docutils literal"><span class="pre">matplotlib.path</span></tt></a></li>
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<div class="section" id="path">
<h1>path<a class="headerlink" href="#path" title="Permalink to this headline">¶</a></h1>
<div class="section" id="module-matplotlib.path">
<span id="matplotlib-path"></span><h2><a class="reference internal" href="#module-matplotlib.path" title="matplotlib.path"><tt class="xref py py-mod docutils literal"><span class="pre">matplotlib.path</span></tt></a><a class="headerlink" href="#module-matplotlib.path" title="Permalink to this headline">¶</a></h2>
<p>A module for dealing with the polylines used throughout matplotlib.</p>
<p>The primary class for polyline handling in matplotlib is <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a>.
Almost all vector drawing makes use of Paths somewhere in the drawing
pipeline.</p>
<p>Whilst a <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> instance itself cannot be drawn, there exists
<a class="reference internal" href="artist_api.html#matplotlib.artist.Artist" title="matplotlib.artist.Artist"><tt class="xref py py-class docutils literal"><span class="pre">Artist</span></tt></a> subclasses which can be used for
convenient Path visualisation - the two most frequently used of these are
<a class="reference internal" href="patches_api.html#matplotlib.patches.PathPatch" title="matplotlib.patches.PathPatch"><tt class="xref py py-class docutils literal"><span class="pre">PathPatch</span></tt></a> and
<a class="reference internal" href="collections_api.html#matplotlib.collections.PathCollection" title="matplotlib.collections.PathCollection"><tt class="xref py py-class docutils literal"><span class="pre">PathCollection</span></tt></a>.</p>
<dl class="class">
<dt id="matplotlib.path.Path">
<em class="property">class </em><tt class="descclassname">matplotlib.path.</tt><tt class="descname">Path</tt><span class="sig-paren">(</span><em>vertices</em>, <em>codes=None</em>, <em>_interpolation_steps=1</em>, <em>closed=False</em>, <em>readonly=False</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">object</span></tt></p>
<p><a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> represents a series of possibly disconnected,
possibly closed, line and curve segments.</p>
<dl class="docutils">
<dt>The underlying storage is made up of two parallel numpy arrays:</dt>
<dd><ul class="first last simple">
<li><em>vertices</em>: an Nx2 float array of vertices</li>
<li><em>codes</em>: an N-length uint8 array of vertex types</li>
</ul>
</dd>
</dl>
<p>These two arrays always have the same length in the first
dimension. For example, to represent a cubic curve, you must
provide three vertices as well as three codes <tt class="docutils literal"><span class="pre">CURVE3</span></tt>.</p>
<p>The code types are:</p>
<blockquote>
<div><ul>
<li><dl class="first docutils">
<dt><tt class="docutils literal"><span class="pre">STOP</span></tt> <span class="classifier-delimiter">:</span> <span class="classifier">1 vertex (ignored)</span></dt>
<dd><p class="first last">A marker for the end of the entire path (currently not
required and ignored)</p>
</dd>
</dl>
</li>
<li><dl class="first docutils">
<dt><tt class="docutils literal"><span class="pre">MOVETO</span></tt> <span class="classifier-delimiter">:</span> <span class="classifier">1 vertex</span></dt>
<dd><p class="first last">Pick up the pen and move to the given vertex.</p>
</dd>
</dl>
</li>
<li><dl class="first docutils">
<dt><tt class="docutils literal"><span class="pre">LINETO</span></tt> <span class="classifier-delimiter">:</span> <span class="classifier">1 vertex</span></dt>
<dd><p class="first last">Draw a line from the current position to the given vertex.</p>
</dd>
</dl>
</li>
<li><dl class="first docutils">
<dt><tt class="docutils literal"><span class="pre">CURVE3</span></tt> <span class="classifier-delimiter">:</span> <span class="classifier">1 control point, 1 endpoint</span></dt>
<dd><p class="first last">Draw a quadratic Bezier curve from the current position,
with the given control point, to the given end point.</p>
</dd>
</dl>
</li>
<li><dl class="first docutils">
<dt><tt class="docutils literal"><span class="pre">CURVE4</span></tt> <span class="classifier-delimiter">:</span> <span class="classifier">2 control points, 1 endpoint</span></dt>
<dd><p class="first last">Draw a cubic Bezier curve from the current position, with
the given control points, to the given end point.</p>
</dd>
</dl>
</li>
<li><dl class="first docutils">
<dt><tt class="docutils literal"><span class="pre">CLOSEPOLY</span></tt> <span class="classifier-delimiter">:</span> <span class="classifier">1 vertex (ignored)</span></dt>
<dd><p class="first last">Draw a line segment to the start point of the current
polyline.</p>
</dd>
</dl>
</li>
</ul>
</div></blockquote>
<p>Users of Path objects should not access the vertices and codes
arrays directly. Instead, they should use <a class="reference internal" href="#matplotlib.path.Path.iter_segments" title="matplotlib.path.Path.iter_segments"><tt class="xref py py-meth docutils literal"><span class="pre">iter_segments()</span></tt></a>
or <a class="reference internal" href="#matplotlib.path.Path.cleaned" title="matplotlib.path.Path.cleaned"><tt class="xref py py-meth docutils literal"><span class="pre">cleaned()</span></tt></a> to get the vertex/code pairs. This is important,
since many <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> objects, as an optimization, do not store a
<em>codes</em> at all, but have a default one provided for them by
<a class="reference internal" href="#matplotlib.path.Path.iter_segments" title="matplotlib.path.Path.iter_segments"><tt class="xref py py-meth docutils literal"><span class="pre">iter_segments()</span></tt></a>.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The vertices and codes arrays should be treated as
immutable – there are a number of optimizations and assumptions
made up front in the constructor that will not change when the
data changes.</p>
</div>
<p>Create a new path with the given vertices and codes.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>vertices</strong> : array_like</p>
<blockquote>
<div><p>The <tt class="docutils literal"><span class="pre">(n,</span> <span class="pre">2)</span></tt> float array, masked array or sequence of pairs
representing the vertices of the path.</p>
<p>If <em>vertices</em> contains masked values, they will be converted
to NaNs which are then handled correctly by the Agg
PathIterator and other consumers of path data, such as
<a class="reference internal" href="#matplotlib.path.Path.iter_segments" title="matplotlib.path.Path.iter_segments"><tt class="xref py py-meth docutils literal"><span class="pre">iter_segments()</span></tt></a>.</p>
</div></blockquote>
<p><strong>codes</strong> : {None, array_like}, optional</p>
<blockquote>
<div><p>n-length array integers representing the codes of the path.
If not None, codes must be the same length as vertices.
If None, <em>vertices</em> will be treated as a series of line segments.</p>
</div></blockquote>
<p><strong>_interpolation_steps</strong> : int, optional</p>
<blockquote>
<div><p>Used as a hint to certain projections, such as Polar, that this
path should be linearly interpolated immediately before drawing.
This attribute is primarily an implementation detail and is not
intended for public use.</p>
</div></blockquote>
<p><strong>closed</strong> : bool, optional</p>
<blockquote>
<div><p>If <em>codes</em> is None and closed is True, vertices will be treated as
line segments of a closed polygon.</p>
</div></blockquote>
<p><strong>readonly</strong> : bool, optional</p>
<blockquote class="last">
<div><p>Makes the path behave in an immutable way and sets the vertices
and codes as read-only arrays.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<dl class="attribute">
<dt id="matplotlib.path.Path.CLOSEPOLY">
<tt class="descname">CLOSEPOLY</tt><em class="property"> = 79</em><a class="headerlink" href="#matplotlib.path.Path.CLOSEPOLY" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.CURVE3">
<tt class="descname">CURVE3</tt><em class="property"> = 3</em><a class="headerlink" href="#matplotlib.path.Path.CURVE3" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.CURVE4">
<tt class="descname">CURVE4</tt><em class="property"> = 4</em><a class="headerlink" href="#matplotlib.path.Path.CURVE4" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.LINETO">
<tt class="descname">LINETO</tt><em class="property"> = 2</em><a class="headerlink" href="#matplotlib.path.Path.LINETO" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.MOVETO">
<tt class="descname">MOVETO</tt><em class="property"> = 1</em><a class="headerlink" href="#matplotlib.path.Path.MOVETO" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.NUM_VERTICES_FOR_CODE">
<tt class="descname">NUM_VERTICES_FOR_CODE</tt><em class="property"> = {0: 1, 1: 1, 2: 1, 3: 2, 4: 3, 79: 1}</em><a class="headerlink" href="#matplotlib.path.Path.NUM_VERTICES_FOR_CODE" title="Permalink to this definition">¶</a></dt>
<dd><p>A dictionary mapping Path codes to the number of vertices that the
code expects.</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.STOP">
<tt class="descname">STOP</tt><em class="property"> = 0</em><a class="headerlink" href="#matplotlib.path.Path.STOP" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.arc">
<em class="property">classmethod </em><tt class="descname">arc</tt><span class="sig-paren">(</span><em>theta1</em>, <em>theta2</em>, <em>n=None</em>, <em>is_wedge=False</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.arc" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an arc on the unit circle from angle
<em>theta1</em> to angle <em>theta2</em> (in degrees).</p>
<p>If <em>n</em> is provided, it is the number of spline segments to make.
If <em>n</em> is not provided, the number of spline segments is
determined based on the delta between <em>theta1</em> and <em>theta2</em>.</p>
<blockquote>
<div>Masionobe, L. 2003. <a class="reference external" href="http://www.spaceroots.org/documents/ellipse/index.html">Drawing an elliptical arc using
polylines, quadratic or cubic Bezier curves</a>.</div></blockquote>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.circle">
<em class="property">classmethod </em><tt class="descname">circle</tt><span class="sig-paren">(</span><em>center=(0.0</em>, <em>0.0)</em>, <em>radius=1.0</em>, <em>readonly=False</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.circle" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a Path representing a circle of a given radius and center.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>center</strong> : pair of floats</p>
<blockquote>
<div><p>The center of the circle. Default <tt class="docutils literal"><span class="pre">(0,</span> <span class="pre">0)</span></tt>.</p>
</div></blockquote>
<p><strong>radius</strong> : float</p>
<blockquote>
<div><p>The radius of the circle. Default is 1.</p>
</div></blockquote>
<p><strong>readonly</strong> : bool</p>
<blockquote class="last">
<div><p>Whether the created path should have the “readonly” argument
set when creating the Path instance.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The circle is approximated using cubic Bezier curves. This
uses 8 splines around the circle using the approach presented
here:</p>
<blockquote>
<div>Lancaster, Don. <a class="reference external" href="http://www.tinaja.com/glib/ellipse4.pdf">Approximating a Circle or an Ellipse Using Four
Bezier Cubic Splines</a>.</div></blockquote>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.cleaned">
<tt class="descname">cleaned</tt><span class="sig-paren">(</span><em>transform=None</em>, <em>remove_nans=False</em>, <em>clip=None</em>, <em>quantize=False</em>, <em>simplify=False</em>, <em>curves=False</em>, <em>stroke_width=1.0</em>, <em>snap=False</em>, <em>sketch=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.cleaned" title="Permalink to this definition">¶</a></dt>
<dd><p>Cleans up the path according to the parameters returning a new
Path instance.</p>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last">See <a class="reference internal" href="#matplotlib.path.Path.iter_segments" title="matplotlib.path.Path.iter_segments"><tt class="xref py py-meth docutils literal"><span class="pre">iter_segments()</span></tt></a> for details of the keyword arguments.</p>
</div>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><strong>Path instance with cleaned up vertices and codes.</strong> :</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.clip_to_bbox">
<tt class="descname">clip_to_bbox</tt><span class="sig-paren">(</span><em>bbox</em>, <em>inside=True</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.clip_to_bbox" title="Permalink to this definition">¶</a></dt>
<dd><p>Clip the path to the given bounding box.</p>
<p>The path must be made up of one or more closed polygons. This
algorithm will not behave correctly for unclosed paths.</p>
<p>If <em>inside</em> is <tt class="xref py py-obj docutils literal"><span class="pre">True</span></tt>, clip to the inside of the box, otherwise
to the outside of the box.</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.code_type">
<tt class="descname">code_type</tt><a class="headerlink" href="#matplotlib.path.Path.code_type" title="Permalink to this definition">¶</a></dt>
<dd><p>alias of <tt class="xref py py-class docutils literal"><span class="pre">uint8</span></tt></p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.codes">
<tt class="descname">codes</tt><a class="headerlink" href="#matplotlib.path.Path.codes" title="Permalink to this definition">¶</a></dt>
<dd><p>The list of codes in the <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a> as a 1-D numpy array. Each
code is one of <a class="reference internal" href="#matplotlib.path.Path.STOP" title="matplotlib.path.Path.STOP"><tt class="xref py py-obj docutils literal"><span class="pre">STOP</span></tt></a>, <a class="reference internal" href="#matplotlib.path.Path.MOVETO" title="matplotlib.path.Path.MOVETO"><tt class="xref py py-obj docutils literal"><span class="pre">MOVETO</span></tt></a>, <a class="reference internal" href="#matplotlib.path.Path.LINETO" title="matplotlib.path.Path.LINETO"><tt class="xref py py-obj docutils literal"><span class="pre">LINETO</span></tt></a>, <a class="reference internal" href="#matplotlib.path.Path.CURVE3" title="matplotlib.path.Path.CURVE3"><tt class="xref py py-obj docutils literal"><span class="pre">CURVE3</span></tt></a>, <a class="reference internal" href="#matplotlib.path.Path.CURVE4" title="matplotlib.path.Path.CURVE4"><tt class="xref py py-obj docutils literal"><span class="pre">CURVE4</span></tt></a>
or <a class="reference internal" href="#matplotlib.path.Path.CLOSEPOLY" title="matplotlib.path.Path.CLOSEPOLY"><tt class="xref py py-obj docutils literal"><span class="pre">CLOSEPOLY</span></tt></a>. For codes that correspond to more than one
vertex (<a class="reference internal" href="#matplotlib.path.Path.CURVE3" title="matplotlib.path.Path.CURVE3"><tt class="xref py py-obj docutils literal"><span class="pre">CURVE3</span></tt></a> and <a class="reference internal" href="#matplotlib.path.Path.CURVE4" title="matplotlib.path.Path.CURVE4"><tt class="xref py py-obj docutils literal"><span class="pre">CURVE4</span></tt></a>), that code will be repeated so
that the length of <tt class="xref py py-obj docutils literal"><span class="pre">self.vertices</span></tt> and <tt class="xref py py-obj docutils literal"><span class="pre">self.codes</span></tt> is always
the same.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.contains_path">
<tt class="descname">contains_path</tt><span class="sig-paren">(</span><em>path</em>, <em>transform=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.contains_path" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <em>True</em> if this path completely contains the given path.</p>
<p>If <em>transform</em> is not <em>None</em>, the path will be transformed
before performing the test.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.contains_point">
<tt class="descname">contains_point</tt><span class="sig-paren">(</span><em>point</em>, <em>transform=None</em>, <em>radius=0.0</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.contains_point" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <em>True</em> if the path contains the given point.</p>
<p>If <em>transform</em> is not <em>None</em>, the path will be transformed
before performing the test.</p>
<p><em>radius</em> allows the path to be made slightly larger or
smaller.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.contains_points">
<tt class="descname">contains_points</tt><span class="sig-paren">(</span><em>points</em>, <em>transform=None</em>, <em>radius=0.0</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.contains_points" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a bool array which is <em>True</em> if the path contains the
corresponding point.</p>
<p>If <em>transform</em> is not <em>None</em>, the path will be transformed
before performing the test.</p>
<p><em>radius</em> allows the path to be made slightly larger or
smaller.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.copy">
<tt class="descname">copy</tt><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.copy" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a shallow copy of the <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a>, which will share the
vertices and codes with the source <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a>.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.deepcopy">
<tt class="descname">deepcopy</tt><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.deepcopy" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a deepcopy of the <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a>. The <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a> will not be
readonly, even if the source <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a> is.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.get_extents">
<tt class="descname">get_extents</tt><span class="sig-paren">(</span><em>transform=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.get_extents" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the extents (<em>xmin</em>, <em>ymin</em>, <em>xmax</em>, <em>ymax</em>) of the
path.</p>
<p>Unlike computing the extents on the <em>vertices</em> alone, this
algorithm will take into account the curves and deal with
control points appropriately.</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.has_nonfinite">
<tt class="descname">has_nonfinite</tt><a class="headerlink" href="#matplotlib.path.Path.has_nonfinite" title="Permalink to this definition">¶</a></dt>
<dd><p><tt class="xref py py-obj docutils literal"><span class="pre">True</span></tt> if the vertices array has nonfinite values.</p>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.hatch">
<em class="property">classmethod </em><tt class="descname">hatch</tt><span class="sig-paren">(</span><em>hatchpattern</em>, <em>density=6</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.hatch" title="Permalink to this definition">¶</a></dt>
<dd><p>Given a hatch specifier, <em>hatchpattern</em>, generates a Path that
can be used in a repeated hatching pattern. <em>density</em> is the
number of lines per unit square.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.interpolated">
<tt class="descname">interpolated</tt><span class="sig-paren">(</span><em>steps</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.interpolated" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a new path resampled to length N x steps. Does not
currently handle interpolating curves.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.intersects_bbox">
<tt class="descname">intersects_bbox</tt><span class="sig-paren">(</span><em>bbox</em>, <em>filled=True</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.intersects_bbox" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <em>True</em> if this path intersects a given
<a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.Bbox" title="matplotlib.transforms.Bbox"><tt class="xref py py-class docutils literal"><span class="pre">Bbox</span></tt></a>.</p>
<p><em>filled</em>, when True, treats the path as if it was filled.
That is, if one path completely encloses the other,
<a class="reference internal" href="#matplotlib.path.Path.intersects_path" title="matplotlib.path.Path.intersects_path"><tt class="xref py py-meth docutils literal"><span class="pre">intersects_path()</span></tt></a> will return True.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.intersects_path">
<tt class="descname">intersects_path</tt><span class="sig-paren">(</span><em>other</em>, <em>filled=True</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.intersects_path" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <em>True</em> if this path intersects another given path.</p>
<p><em>filled</em>, when True, treats the paths as if they were filled.
That is, if one path completely encloses the other,
<a class="reference internal" href="#matplotlib.path.Path.intersects_path" title="matplotlib.path.Path.intersects_path"><tt class="xref py py-meth docutils literal"><span class="pre">intersects_path()</span></tt></a> will return True.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.iter_segments">
<tt class="descname">iter_segments</tt><span class="sig-paren">(</span><em>transform=None</em>, <em>remove_nans=True</em>, <em>clip=None</em>, <em>snap=False</em>, <em>stroke_width=1.0</em>, <em>simplify=None</em>, <em>curves=True</em>, <em>sketch=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.iter_segments" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterates over all of the curve segments in the path. Each
iteration returns a 2-tuple (<em>vertices</em>, <em>code</em>), where
<em>vertices</em> is a sequence of 1 - 3 coordinate pairs, and <em>code</em> is
one of the <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> codes.</p>
<p>Additionally, this method can provide a number of standard
cleanups and conversions to the path.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>transform</strong> : None or <a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.Transform" title="matplotlib.transforms.Transform"><tt class="xref py py-class docutils literal"><span class="pre">Transform</span></tt></a> instance</p>
<blockquote>
<div><p>If not None, the given affine transformation will
be applied to the path.</p>
</div></blockquote>
<p><strong>remove_nans</strong> : {False, True}, optional</p>
<blockquote>
<div><p>If True, will remove all NaNs from the path and
insert MOVETO commands to skip over them.</p>
</div></blockquote>
<p><strong>clip</strong> : None or sequence, optional</p>
<blockquote>
<div><p>If not None, must be a four-tuple (x1, y1, x2, y2)
defining a rectangle in which to clip the path.</p>
</div></blockquote>
<p><strong>snap</strong> : None or bool, optional</p>
<blockquote>
<div><p>If None, auto-snap to pixels, to reduce
fuzziness of rectilinear lines. If True, force snapping, and
if False, don’t snap.</p>
</div></blockquote>
<p><strong>stroke_width</strong> : float, optional</p>
<blockquote>
<div><dl class="docutils">
<dt>The width of the stroke being drawn. Needed</dt>
<dd><p class="first last">as a hint for the snapping algorithm.</p>
</dd>
</dl>
</div></blockquote>
<p><strong>simplify</strong> : None or bool, optional</p>
<blockquote>
<div><dl class="docutils">
<dt>If True, perform simplification, to remove</dt>
<dd><p class="first last">vertices that do not affect the appearance of the path. If
False, perform no simplification. If None, use the
should_simplify member variable.</p>
</dd>
</dl>
</div></blockquote>
<p><strong>curves</strong> : {True, False}, optional</p>
<blockquote>
<div><p>If True, curve segments will be returned as curve
segments. If False, all curves will be converted to line
segments.</p>
</div></blockquote>
<p><strong>sketch</strong> : None or sequence, optional</p>
<blockquote class="last">
<div><p>If not None, must be a 3-tuple of the form
(scale, length, randomness), representing the sketch
parameters.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.make_compound_path">
<em class="property">classmethod </em><tt class="descname">make_compound_path</tt><span class="sig-paren">(</span><em>*args</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.make_compound_path" title="Permalink to this definition">¶</a></dt>
<dd><p>Make a compound path from a list of Path objects.</p>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.make_compound_path_from_polys">
<em class="property">classmethod </em><tt class="descname">make_compound_path_from_polys</tt><span class="sig-paren">(</span><em>XY</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.make_compound_path_from_polys" title="Permalink to this definition">¶</a></dt>
<dd><p>Make a compound path object to draw a number
of polygons with equal numbers of sides XY is a (numpolys x
numsides x 2) numpy array of vertices. Return object is a
<a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a></p>
<p>(<a class="reference external" href="../mpl_examples/api/histogram_path_demo.py">Source code</a>, <a class="reference external" href="../mpl_examples/api/histogram_path_demo.png">png</a>, <a class="reference external" href="../mpl_examples/api/histogram_path_demo.hires.png">hires.png</a>, <a class="reference external" href="../mpl_examples/api/histogram_path_demo.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/histogram_path_demo.png" src="../_images/histogram_path_demo.png" />
</div>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.readonly">
<tt class="descname">readonly</tt><a class="headerlink" href="#matplotlib.path.Path.readonly" title="Permalink to this definition">¶</a></dt>
<dd><p><tt class="xref py py-obj docutils literal"><span class="pre">True</span></tt> if the <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a> is read-only.</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.should_simplify">
<tt class="descname">should_simplify</tt><a class="headerlink" href="#matplotlib.path.Path.should_simplify" title="Permalink to this definition">¶</a></dt>
<dd><p><tt class="xref py py-obj docutils literal"><span class="pre">True</span></tt> if the vertices array should be simplified.</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.simplify_threshold">
<tt class="descname">simplify_threshold</tt><a class="headerlink" href="#matplotlib.path.Path.simplify_threshold" title="Permalink to this definition">¶</a></dt>
<dd><p>The fraction of a pixel difference below which vertices will
be simplified out.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.to_polygons">
<tt class="descname">to_polygons</tt><span class="sig-paren">(</span><em>transform=None</em>, <em>width=0</em>, <em>height=0</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.to_polygons" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert this path to a list of polygons. Each polygon is an
Nx2 array of vertices. In other words, each polygon has no
<tt class="docutils literal"><span class="pre">MOVETO</span></tt> instructions or curves. This is useful for
displaying in backends that do not support compound paths or
Bezier curves, such as GDK.</p>
<p>If <em>width</em> and <em>height</em> are both non-zero then the lines will
be simplified so that vertices outside of (0, 0), (width,
height) will be clipped.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.path.Path.transformed">
<tt class="descname">transformed</tt><span class="sig-paren">(</span><em>transform</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.transformed" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a transformed copy of the path.</p>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.TransformedPath" title="matplotlib.transforms.TransformedPath"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.transforms.TransformedPath</span></tt></a></dt>
<dd>A specialized path class that will cache the
transformed result and automatically update when the
transform changes.</dd>
</dl>
</div>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.unit_circle">
<em class="property">classmethod </em><tt class="descname">unit_circle</tt><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.unit_circle" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the readonly <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> of the unit circle.</p>
<p>For most cases, <a class="reference internal" href="#matplotlib.path.Path.circle" title="matplotlib.path.Path.circle"><tt class="xref py py-func docutils literal"><span class="pre">Path.circle()</span></tt></a> will be what you want.</p>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.unit_circle_righthalf">
<em class="property">classmethod </em><tt class="descname">unit_circle_righthalf</tt><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.unit_circle_righthalf" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> of the right half
of a unit circle. The circle is approximated using cubic Bezier
curves. This uses 4 splines around the circle using the approach
presented here:</p>
<blockquote>
<div>Lancaster, Don. <a class="reference external" href="http://www.tinaja.com/glib/ellipse4.pdf">Approximating a Circle or an Ellipse Using Four
Bezier Cubic Splines</a>.</div></blockquote>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.unit_rectangle">
<em class="property">classmethod </em><tt class="descname">unit_rectangle</tt><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.unit_rectangle" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> instance of the unit rectangle
from (0, 0) to (1, 1).</p>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.unit_regular_asterisk">
<em class="property">classmethod </em><tt class="descname">unit_regular_asterisk</tt><span class="sig-paren">(</span><em>numVertices</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.unit_regular_asterisk" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> for a unit regular
asterisk with the given numVertices and radius of 1.0,
centered at (0, 0).</p>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.unit_regular_polygon">
<em class="property">classmethod </em><tt class="descname">unit_regular_polygon</tt><span class="sig-paren">(</span><em>numVertices</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.unit_regular_polygon" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> instance for a unit regular
polygon with the given <em>numVertices</em> and radius of 1.0,
centered at (0, 0).</p>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.unit_regular_star">
<em class="property">classmethod </em><tt class="descname">unit_regular_star</tt><span class="sig-paren">(</span><em>numVertices</em>, <em>innerCircle=0.5</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.unit_regular_star" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> for a unit regular star
with the given numVertices and radius of 1.0, centered at (0,
0).</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.path.Path.vertices">
<tt class="descname">vertices</tt><a class="headerlink" href="#matplotlib.path.Path.vertices" title="Permalink to this definition">¶</a></dt>
<dd><p>The list of vertices in the <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-obj docutils literal"><span class="pre">Path</span></tt></a> as an Nx2 numpy array.</p>
</dd></dl>
<dl class="classmethod">
<dt id="matplotlib.path.Path.wedge">
<em class="property">classmethod </em><tt class="descname">wedge</tt><span class="sig-paren">(</span><em>theta1</em>, <em>theta2</em>, <em>n=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.Path.wedge" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a wedge of the unit circle from angle
<em>theta1</em> to angle <em>theta2</em> (in degrees).</p>
<p>If <em>n</em> is provided, it is the number of spline segments to make.
If <em>n</em> is not provided, the number of spline segments is
determined based on the delta between <em>theta1</em> and <em>theta2</em>.</p>
</dd></dl>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.cleanup_path">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">cleanup_path</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.cleanup_path" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The cleanup_path function was deprecated in version 1.3. Use path.Path.cleaned instead.</p>
</div>
<p>cleanup_path(path, trans, remove_nans, clip, snap, simplify, curves, sketch_params)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.clip_path_to_rect">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">clip_path_to_rect</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.clip_path_to_rect" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The clip_path_to_rect function was deprecated in version 1.3. Use path.Path.clip_to_bbox instead.</p>
</div>
<p>clip_path_to_rect(path, bbox, inside)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.convert_path_to_polygons">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">convert_path_to_polygons</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.convert_path_to_polygons" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The convert_path_to_polygons function was deprecated in version 1.3. Use path.Path.to_polygons instead.</p>
</div>
<p>convert_path_to_polygons(path, trans, width, height)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.get_path_collection_extents">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">get_path_collection_extents</tt><span class="sig-paren">(</span><em>master_transform</em>, <em>paths</em>, <em>transforms</em>, <em>offsets</em>, <em>offset_transform</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.get_path_collection_extents" title="Permalink to this definition">¶</a></dt>
<dd><p>Given a sequence of <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> objects,
<a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.Transform" title="matplotlib.transforms.Transform"><tt class="xref py py-class docutils literal"><span class="pre">Transform</span></tt></a> objects and offsets, as
found in a <a class="reference internal" href="collections_api.html#matplotlib.collections.PathCollection" title="matplotlib.collections.PathCollection"><tt class="xref py py-class docutils literal"><span class="pre">PathCollection</span></tt></a>,
returns the bounding box that encapsulates all of them.</p>
<p><em>master_transform</em> is a global transformation to apply to all paths</p>
<p><em>paths</em> is a sequence of <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> instances.</p>
<p><em>transforms</em> is a sequence of
<a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.Affine2D" title="matplotlib.transforms.Affine2D"><tt class="xref py py-class docutils literal"><span class="pre">Affine2D</span></tt></a> instances.</p>
<p><em>offsets</em> is a sequence of (x, y) offsets (or an Nx2 array)</p>
<p><em>offset_transform</em> is a <a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.Affine2D" title="matplotlib.transforms.Affine2D"><tt class="xref py py-class docutils literal"><span class="pre">Affine2D</span></tt></a>
to apply to the offsets before applying the offset to the path.</p>
<p>The way that <em>paths</em>, <em>transforms</em> and <em>offsets</em> are combined
follows the same method as for collections. Each is iterated over
independently, so if you have 3 paths, 2 transforms and 1 offset,
their combinations are as follows:</p>
<blockquote>
<div>(A, A, A), (B, B, A), (C, A, A)</div></blockquote>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.get_path_extents">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">get_path_extents</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.get_path_extents" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The get_path_extents function was deprecated in version 1.3. Use path.Path.get_extents instead.</p>
</div>
<p>get_path_extents(path, trans)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.get_paths_extents">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">get_paths_extents</tt><span class="sig-paren">(</span><em>paths</em>, <em>transforms=[]</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.get_paths_extents" title="Permalink to this definition">¶</a></dt>
<dd><p>Given a sequence of <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> objects and optional
<a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.Transform" title="matplotlib.transforms.Transform"><tt class="xref py py-class docutils literal"><span class="pre">Transform</span></tt></a> objects, returns the
bounding box that encapsulates all of them.</p>
<p><em>paths</em> is a sequence of <a class="reference internal" href="#matplotlib.path.Path" title="matplotlib.path.Path"><tt class="xref py py-class docutils literal"><span class="pre">Path</span></tt></a> instances.</p>
<p><em>transforms</em> is an optional sequence of
<a class="reference internal" href="../devel/transformations.html#matplotlib.transforms.Affine2D" title="matplotlib.transforms.Affine2D"><tt class="xref py py-class docutils literal"><span class="pre">Affine2D</span></tt></a> instances to apply to
each path.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.path_in_path">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">path_in_path</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.path_in_path" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The path_in_path function was deprecated in version 1.3. Use path.Path.contains_path instead.</p>
</div>
<p>path_in_path(a, atrans, b, btrans)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.path_intersects_path">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">path_intersects_path</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.path_intersects_path" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The path_intersects_path function was deprecated in version 1.3. Use path.Path.intersects_path instead.</p>
</div>
<p>path_intersects_path(p1, p2)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.point_in_path">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">point_in_path</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.point_in_path" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The point_in_path function was deprecated in version 1.3. Use path.Path.contains_point instead.</p>
</div>
<p>point_in_path(x, y, path, trans)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.point_in_path_collection">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">point_in_path_collection</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.point_in_path_collection" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The point_in_path_collection function was deprecated in version 1.3. Use collection.Collection.contains instead.</p>
</div>
<p>point_in_path_collection(x, y, r, trans, paths, transforms, offsets, offsetTrans, filled)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.path.points_in_path">
<tt class="descclassname">matplotlib.path.</tt><tt class="descname">points_in_path</tt><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.path.points_in_path" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 1.3: </span>The points_in_path function was deprecated in version 1.3. Use path.Path.contains_points instead.</p>
</div>
<p>points_in_path(points, path, trans)</p>
</dd></dl>
</div>
</div>
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Last updated on Sep 02, 2014.
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