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<h1>Source code for matplotlib.bezier</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">A module providing some utility functions regarding Bezier path manipulation.</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">lru_cache</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="kn">import</span> <span class="nn">warnings</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">_api</span>
<span class="c1"># same algorithm as 3.8's math.comb</span>
<span class="nd">@np</span><span class="o">.</span><span class="n">vectorize</span>
<span class="nd">@lru_cache</span><span class="p">(</span><span class="n">maxsize</span><span class="o">=</span><span class="mi">128</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_comb</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
<span class="k">if</span> <span class="n">k</span> <span class="o">></span> <span class="n">n</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">0</span>
<span class="n">k</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">)</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">((</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span><span class="o">/</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
<div class="viewcode-block" id="NonIntersectingPathException"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.NonIntersectingPathException">[docs]</a><span class="k">class</span> <span class="nc">NonIntersectingPathException</span><span class="p">(</span><span class="ne">ValueError</span><span class="p">):</span>
<span class="k">pass</span></div>
<span class="c1"># some functions</span>
<div class="viewcode-block" id="get_intersection"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.get_intersection">[docs]</a><span class="k">def</span> <span class="nf">get_intersection</span><span class="p">(</span><span class="n">cx1</span><span class="p">,</span> <span class="n">cy1</span><span class="p">,</span> <span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span><span class="p">,</span>
<span class="n">cx2</span><span class="p">,</span> <span class="n">cy2</span><span class="p">,</span> <span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Return the intersection between the line through (*cx1*, *cy1*) at angle</span>
<span class="sd"> *t1* and the line through (*cx2*, *cy2*) at angle *t2*.</span>
<span class="sd"> """</span>
<span class="c1"># line1 => sin_t1 * (x - cx1) - cos_t1 * (y - cy1) = 0.</span>
<span class="c1"># line1 => sin_t1 * x + cos_t1 * y = sin_t1*cx1 - cos_t1*cy1</span>
<span class="n">line1_rhs</span> <span class="o">=</span> <span class="n">sin_t1</span> <span class="o">*</span> <span class="n">cx1</span> <span class="o">-</span> <span class="n">cos_t1</span> <span class="o">*</span> <span class="n">cy1</span>
<span class="n">line2_rhs</span> <span class="o">=</span> <span class="n">sin_t2</span> <span class="o">*</span> <span class="n">cx2</span> <span class="o">-</span> <span class="n">cos_t2</span> <span class="o">*</span> <span class="n">cy2</span>
<span class="c1"># rhs matrix</span>
<span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">sin_t1</span><span class="p">,</span> <span class="o">-</span><span class="n">cos_t1</span>
<span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">sin_t2</span><span class="p">,</span> <span class="o">-</span><span class="n">cos_t2</span>
<span class="n">ad_bc</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">d</span> <span class="o">-</span> <span class="n">b</span> <span class="o">*</span> <span class="n">c</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">ad_bc</span><span class="p">)</span> <span class="o"><</span> <span class="mf">1e-12</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Given lines do not intersect. Please verify that "</span>
<span class="s2">"the angles are not equal or differ by 180 degrees."</span><span class="p">)</span>
<span class="c1"># rhs_inverse</span>
<span class="n">a_</span><span class="p">,</span> <span class="n">b_</span> <span class="o">=</span> <span class="n">d</span><span class="p">,</span> <span class="o">-</span><span class="n">b</span>
<span class="n">c_</span><span class="p">,</span> <span class="n">d_</span> <span class="o">=</span> <span class="o">-</span><span class="n">c</span><span class="p">,</span> <span class="n">a</span>
<span class="n">a_</span><span class="p">,</span> <span class="n">b_</span><span class="p">,</span> <span class="n">c_</span><span class="p">,</span> <span class="n">d_</span> <span class="o">=</span> <span class="p">[</span><span class="n">k</span> <span class="o">/</span> <span class="n">ad_bc</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="p">[</span><span class="n">a_</span><span class="p">,</span> <span class="n">b_</span><span class="p">,</span> <span class="n">c_</span><span class="p">,</span> <span class="n">d_</span><span class="p">]]</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">a_</span> <span class="o">*</span> <span class="n">line1_rhs</span> <span class="o">+</span> <span class="n">b_</span> <span class="o">*</span> <span class="n">line2_rhs</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">c_</span> <span class="o">*</span> <span class="n">line1_rhs</span> <span class="o">+</span> <span class="n">d_</span> <span class="o">*</span> <span class="n">line2_rhs</span>
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
<div class="viewcode-block" id="get_normal_points"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.get_normal_points">[docs]</a><span class="k">def</span> <span class="nf">get_normal_points</span><span class="p">(</span><span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">,</span> <span class="n">cos_t</span><span class="p">,</span> <span class="n">sin_t</span><span class="p">,</span> <span class="n">length</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> For a line passing through (*cx*, *cy*) and having an angle *t*, return</span>
<span class="sd"> locations of the two points located along its perpendicular line at the</span>
<span class="sd"> distance of *length*.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">length</span> <span class="o">==</span> <span class="mf">0.</span><span class="p">:</span>
<span class="k">return</span> <span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">,</span> <span class="n">cx</span><span class="p">,</span> <span class="n">cy</span>
<span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span> <span class="o">=</span> <span class="n">sin_t</span><span class="p">,</span> <span class="o">-</span><span class="n">cos_t</span>
<span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span> <span class="o">=</span> <span class="o">-</span><span class="n">sin_t</span><span class="p">,</span> <span class="n">cos_t</span>
<span class="n">x1</span><span class="p">,</span> <span class="n">y1</span> <span class="o">=</span> <span class="n">length</span> <span class="o">*</span> <span class="n">cos_t1</span> <span class="o">+</span> <span class="n">cx</span><span class="p">,</span> <span class="n">length</span> <span class="o">*</span> <span class="n">sin_t1</span> <span class="o">+</span> <span class="n">cy</span>
<span class="n">x2</span><span class="p">,</span> <span class="n">y2</span> <span class="o">=</span> <span class="n">length</span> <span class="o">*</span> <span class="n">cos_t2</span> <span class="o">+</span> <span class="n">cx</span><span class="p">,</span> <span class="n">length</span> <span class="o">*</span> <span class="n">sin_t2</span> <span class="o">+</span> <span class="n">cy</span>
<span class="k">return</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></div>
<span class="c1"># BEZIER routines</span>
<span class="c1"># subdividing bezier curve</span>
<span class="c1"># http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/Bezier/bezier-sub.html</span>
<span class="k">def</span> <span class="nf">_de_casteljau1</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
<span class="n">next_beta</span> <span class="o">=</span> <span class="n">beta</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">t</span><span class="p">)</span> <span class="o">+</span> <span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">*</span> <span class="n">t</span>
<span class="k">return</span> <span class="n">next_beta</span>
<div class="viewcode-block" id="split_de_casteljau"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.split_de_casteljau">[docs]</a><span class="k">def</span> <span class="nf">split_de_casteljau</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Split a Bezier segment defined by its control points *beta* into two</span>
<span class="sd"> separate segments divided at *t* and return their control points.</span>
<span class="sd"> """</span>
<span class="n">beta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
<span class="n">beta_list</span> <span class="o">=</span> <span class="p">[</span><span class="n">beta</span><span class="p">]</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">beta</span> <span class="o">=</span> <span class="n">_de_casteljau1</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span>
<span class="n">beta_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">break</span>
<span class="n">left_beta</span> <span class="o">=</span> <span class="p">[</span><span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">beta</span> <span class="ow">in</span> <span class="n">beta_list</span><span class="p">]</span>
<span class="n">right_beta</span> <span class="o">=</span> <span class="p">[</span><span class="n">beta</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">beta</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">beta_list</span><span class="p">)]</span>
<span class="k">return</span> <span class="n">left_beta</span><span class="p">,</span> <span class="n">right_beta</span></div>
<div class="viewcode-block" id="find_bezier_t_intersecting_with_closedpath"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.find_bezier_t_intersecting_with_closedpath">[docs]</a><span class="k">def</span> <span class="nf">find_bezier_t_intersecting_with_closedpath</span><span class="p">(</span>
<span class="n">bezier_point_at_t</span><span class="p">,</span> <span class="n">inside_closedpath</span><span class="p">,</span> <span class="n">t0</span><span class="o">=</span><span class="mf">0.</span><span class="p">,</span> <span class="n">t1</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">tolerance</span><span class="o">=</span><span class="mf">0.01</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Find the intersection of the Bezier curve with a closed path.</span>
<span class="sd"> The intersection point *t* is approximated by two parameters *t0*, *t1*</span>
<span class="sd"> such that *t0* <= *t* <= *t1*.</span>
<span class="sd"> Search starts from *t0* and *t1* and uses a simple bisecting algorithm</span>
<span class="sd"> therefore one of the end points must be inside the path while the other</span>
<span class="sd"> doesn't. The search stops when the distance of the points parametrized by</span>
<span class="sd"> *t0* and *t1* gets smaller than the given *tolerance*.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> bezier_point_at_t : callable</span>
<span class="sd"> A function returning x, y coordinates of the Bezier at parameter *t*.</span>
<span class="sd"> It must have the signature::</span>
<span class="sd"> bezier_point_at_t(t: float) -> tuple[float, float]</span>
<span class="sd"> inside_closedpath : callable</span>
<span class="sd"> A function returning True if a given point (x, y) is inside the</span>
<span class="sd"> closed path. It must have the signature::</span>
<span class="sd"> inside_closedpath(point: tuple[float, float]) -> bool</span>
<span class="sd"> t0, t1 : float</span>
<span class="sd"> Start parameters for the search.</span>
<span class="sd"> tolerance : float</span>
<span class="sd"> Maximal allowed distance between the final points.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> t0, t1 : float</span>
<span class="sd"> The Bezier path parameters.</span>
<span class="sd"> """</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">bezier_point_at_t</span><span class="p">(</span><span class="n">t0</span><span class="p">)</span>
<span class="n">end</span> <span class="o">=</span> <span class="n">bezier_point_at_t</span><span class="p">(</span><span class="n">t1</span><span class="p">)</span>
<span class="n">start_inside</span> <span class="o">=</span> <span class="n">inside_closedpath</span><span class="p">(</span><span class="n">start</span><span class="p">)</span>
<span class="n">end_inside</span> <span class="o">=</span> <span class="n">inside_closedpath</span><span class="p">(</span><span class="n">end</span><span class="p">)</span>
<span class="k">if</span> <span class="n">start_inside</span> <span class="o">==</span> <span class="n">end_inside</span> <span class="ow">and</span> <span class="n">start</span> <span class="o">!=</span> <span class="n">end</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">NonIntersectingPathException</span><span class="p">(</span>
<span class="s2">"Both points are on the same side of the closed path"</span><span class="p">)</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="c1"># return if the distance is smaller than the tolerance</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">hypot</span><span class="p">(</span><span class="n">start</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">end</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">start</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">end</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o"><</span> <span class="n">tolerance</span><span class="p">:</span>
<span class="k">return</span> <span class="n">t0</span><span class="p">,</span> <span class="n">t1</span>
<span class="c1"># calculate the middle point</span>
<span class="n">middle_t</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">t0</span> <span class="o">+</span> <span class="n">t1</span><span class="p">)</span>
<span class="n">middle</span> <span class="o">=</span> <span class="n">bezier_point_at_t</span><span class="p">(</span><span class="n">middle_t</span><span class="p">)</span>
<span class="n">middle_inside</span> <span class="o">=</span> <span class="n">inside_closedpath</span><span class="p">(</span><span class="n">middle</span><span class="p">)</span>
<span class="k">if</span> <span class="n">start_inside</span> <span class="o">^</span> <span class="n">middle_inside</span><span class="p">:</span>
<span class="n">t1</span> <span class="o">=</span> <span class="n">middle_t</span>
<span class="n">end</span> <span class="o">=</span> <span class="n">middle</span>
<span class="n">end_inside</span> <span class="o">=</span> <span class="n">middle_inside</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">middle_t</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">middle</span>
<span class="n">start_inside</span> <span class="o">=</span> <span class="n">middle_inside</span></div>
<div class="viewcode-block" id="BezierSegment"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.BezierSegment">[docs]</a><span class="k">class</span> <span class="nc">BezierSegment</span><span class="p">:</span>
<span class="sd">"""</span>
<span class="sd"> A d-dimensional Bezier segment.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> control_points : (N, d) array</span>
<span class="sd"> Location of the *N* control points.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">control_points</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_cpoints</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">control_points</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_N</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_d</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_cpoints</span><span class="o">.</span><span class="n">shape</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_orders</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_N</span><span class="p">)</span>
<span class="n">coeff</span> <span class="o">=</span> <span class="p">[</span><span class="n">math</span><span class="o">.</span><span class="n">factorial</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_N</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="o">//</span> <span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">factorial</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">factorial</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_N</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">i</span><span class="p">))</span>
<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="bp">self</span><span class="o">.</span><span class="n">_N</span><span class="p">)]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_px</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_cpoints</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">coeff</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Evaluate the Bezier curve at point(s) t in [0, 1].</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> t : (k,) array-like</span>
<span class="sd"> Points at which to evaluate the curve.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (k, d) array</span>
<span class="sd"> Value of the curve for each point in *t*.</span>
<span class="sd"> """</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">t</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_orders</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_orders</span><span class="p">))</span> <span class="o">@</span> <span class="bp">self</span><span class="o">.</span><span class="n">_px</span>
<div class="viewcode-block" id="BezierSegment.point_at_t"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.BezierSegment.point_at_t">[docs]</a> <span class="k">def</span> <span class="nf">point_at_t</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Evaluate the curve at a single point, returning a tuple of *d* floats.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="bp">self</span><span class="p">(</span><span class="n">t</span><span class="p">))</span></div>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">control_points</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""The control points of the curve."""</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_cpoints</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">dimension</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""The dimension of the curve."""</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_d</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">degree</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Degree of the polynomial. One less the number of control points."""</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_N</span> <span class="o">-</span> <span class="mi">1</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">polynomial_coefficients</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> The polynomial coefficients of the Bezier curve.</span>
<span class="sd"> .. warning:: Follows opposite convention from `numpy.polyval`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (n+1, d) array</span>
<span class="sd"> Coefficients after expanding in polynomial basis, where :math:`n`</span>
<span class="sd"> is the degree of the bezier curve and :math:`d` its dimension.</span>
<span class="sd"> These are the numbers (:math:`C_j`) such that the curve can be</span>
<span class="sd"> written :math:`\sum_{j=0}^n C_j t^j`.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The coefficients are calculated as</span>
<span class="sd"> .. math::</span>
<span class="sd"> {n \choose j} \sum_{i=0}^j (-1)^{i+j} {j \choose i} P_i</span>
<span class="sd"> where :math:`P_i` are the control points of the curve.</span>
<span class="sd"> """</span>
<span class="n">n</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">degree</span>
<span class="c1"># matplotlib uses n <= 4. overflow plausible starting around n = 15.</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">></span> <span class="mi">10</span><span class="p">:</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Polynomial coefficients formula unstable for high "</span>
<span class="s2">"order Bezier curves!"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
<span class="n">P</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">control_points</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</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="kc">None</span><span class="p">]</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</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="kc">None</span><span class="p">,</span> <span class="p">:]</span> <span class="c1"># _comb is non-zero for i <= j</span>
<span class="n">prefactor</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">*</span> <span class="n">_comb</span><span class="p">(</span><span class="n">j</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span> <span class="c1"># j on axis 0, i on axis 1</span>
<span class="k">return</span> <span class="n">_comb</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span> <span class="o">*</span> <span class="n">prefactor</span> <span class="o">@</span> <span class="n">P</span> <span class="c1"># j on axis 0, self.dimension on 1</span>
<div class="viewcode-block" id="BezierSegment.axis_aligned_extrema"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.BezierSegment.axis_aligned_extrema">[docs]</a> <span class="k">def</span> <span class="nf">axis_aligned_extrema</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Return the dimension and location of the curve's interior extrema.</span>
<span class="sd"> The extrema are the points along the curve where one of its partial</span>
<span class="sd"> derivatives is zero.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> dims : array of int</span>
<span class="sd"> Index :math:`i` of the partial derivative which is zero at each</span>
<span class="sd"> interior extrema.</span>
<span class="sd"> dzeros : array of float</span>
<span class="sd"> Of same size as dims. The :math:`t` such that :math:`d/dx_i B(t) =</span>
<span class="sd"> 0`</span>
<span class="sd"> """</span>
<span class="n">n</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">degree</span>
<span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([]),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([])</span>
<span class="n">Cj</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">polynomial_coefficients</span>
<span class="n">dCj</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</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="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="n">Cj</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
<span class="n">dims</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">roots</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">pi</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">dCj</span><span class="o">.</span><span class="n">T</span><span class="p">):</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roots</span><span class="p">(</span><span class="n">pi</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">roots</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
<span class="n">dims</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">full_like</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">i</span><span class="p">))</span>
<span class="n">roots</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">roots</span><span class="p">)</span>
<span class="n">dims</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">dims</span><span class="p">)</span>
<span class="n">in_range</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">isreal</span><span class="p">(</span><span class="n">roots</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">roots</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">roots</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="n">dims</span><span class="p">[</span><span class="n">in_range</span><span class="p">],</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">roots</span><span class="p">)[</span><span class="n">in_range</span><span class="p">]</span></div></div>
<div class="viewcode-block" id="split_bezier_intersecting_with_closedpath"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.split_bezier_intersecting_with_closedpath">[docs]</a><span class="k">def</span> <span class="nf">split_bezier_intersecting_with_closedpath</span><span class="p">(</span>
<span class="n">bezier</span><span class="p">,</span> <span class="n">inside_closedpath</span><span class="p">,</span> <span class="n">tolerance</span><span class="o">=</span><span class="mf">0.01</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Split a Bezier curve into two at the intersection with a closed path.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> bezier : (N, 2) array-like</span>
<span class="sd"> Control points of the Bezier segment. See `.BezierSegment`.</span>
<span class="sd"> inside_closedpath : callable</span>
<span class="sd"> A function returning True if a given point (x, y) is inside the</span>
<span class="sd"> closed path. See also `.find_bezier_t_intersecting_with_closedpath`.</span>
<span class="sd"> tolerance : float</span>
<span class="sd"> The tolerance for the intersection. See also</span>
<span class="sd"> `.find_bezier_t_intersecting_with_closedpath`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> left, right</span>
<span class="sd"> Lists of control points for the two Bezier segments.</span>
<span class="sd"> """</span>
<span class="n">bz</span> <span class="o">=</span> <span class="n">BezierSegment</span><span class="p">(</span><span class="n">bezier</span><span class="p">)</span>
<span class="n">bezier_point_at_t</span> <span class="o">=</span> <span class="n">bz</span><span class="o">.</span><span class="n">point_at_t</span>
<span class="n">t0</span><span class="p">,</span> <span class="n">t1</span> <span class="o">=</span> <span class="n">find_bezier_t_intersecting_with_closedpath</span><span class="p">(</span>
<span class="n">bezier_point_at_t</span><span class="p">,</span> <span class="n">inside_closedpath</span><span class="p">,</span> <span class="n">tolerance</span><span class="o">=</span><span class="n">tolerance</span><span class="p">)</span>
<span class="n">_left</span><span class="p">,</span> <span class="n">_right</span> <span class="o">=</span> <span class="n">split_de_casteljau</span><span class="p">(</span><span class="n">bezier</span><span class="p">,</span> <span class="p">(</span><span class="n">t0</span> <span class="o">+</span> <span class="n">t1</span><span class="p">)</span> <span class="o">/</span> <span class="mf">2.</span><span class="p">)</span>
<span class="k">return</span> <span class="n">_left</span><span class="p">,</span> <span class="n">_right</span></div>
<span class="c1"># matplotlib specific</span>
<div class="viewcode-block" id="split_path_inout"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.split_path_inout">[docs]</a><span class="k">def</span> <span class="nf">split_path_inout</span><span class="p">(</span><span class="n">path</span><span class="p">,</span> <span class="n">inside</span><span class="p">,</span> <span class="n">tolerance</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">reorder_inout</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Divide a path into two segments at the point where ``inside(x, y)`` becomes</span>
<span class="sd"> False.</span>
<span class="sd"> """</span>
<span class="kn">from</span> <span class="nn">.path</span> <span class="kn">import</span> <span class="n">Path</span>
<span class="n">path_iter</span> <span class="o">=</span> <span class="n">path</span><span class="o">.</span><span class="n">iter_segments</span><span class="p">()</span>
<span class="n">ctl_points</span><span class="p">,</span> <span class="n">command</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">path_iter</span><span class="p">)</span>
<span class="n">begin_inside</span> <span class="o">=</span> <span class="n">inside</span><span class="p">(</span><span class="n">ctl_points</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:])</span> <span class="c1"># true if begin point is inside</span>
<span class="n">ctl_points_old</span> <span class="o">=</span> <span class="n">ctl_points</span>
<span class="n">iold</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">ctl_points</span><span class="p">,</span> <span class="n">command</span> <span class="ow">in</span> <span class="n">path_iter</span><span class="p">:</span>
<span class="n">iold</span> <span class="o">=</span> <span class="n">i</span>
<span class="n">i</span> <span class="o">+=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ctl_points</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
<span class="k">if</span> <span class="n">inside</span><span class="p">(</span><span class="n">ctl_points</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:])</span> <span class="o">!=</span> <span class="n">begin_inside</span><span class="p">:</span>
<span class="n">bezier_path</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">ctl_points_old</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:],</span> <span class="n">ctl_points</span><span class="p">])</span>
<span class="k">break</span>
<span class="n">ctl_points_old</span> <span class="o">=</span> <span class="n">ctl_points</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"The path does not intersect with the patch"</span><span class="p">)</span>
<span class="n">bp</span> <span class="o">=</span> <span class="n">bezier_path</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">left</span><span class="p">,</span> <span class="n">right</span> <span class="o">=</span> <span class="n">split_bezier_intersecting_with_closedpath</span><span class="p">(</span>
<span class="n">bp</span><span class="p">,</span> <span class="n">inside</span><span class="p">,</span> <span class="n">tolerance</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">left</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
<span class="n">codes_left</span> <span class="o">=</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">codes_right</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="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">left</span><span class="p">)</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
<span class="n">codes_left</span> <span class="o">=</span> <span class="p">[</span><span class="n">Path</span><span class="o">.</span><span class="n">CURVE3</span><span class="p">,</span> <span class="n">Path</span><span class="o">.</span><span class="n">CURVE3</span><span class="p">]</span>
<span class="n">codes_right</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">CURVE3</span><span class="p">,</span> <span class="n">Path</span><span class="o">.</span><span class="n">CURVE3</span><span class="p">]</span>
<span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">left</span><span class="p">)</span> <span class="o">==</span> <span class="mi">4</span><span class="p">:</span>
<span class="n">codes_left</span> <span class="o">=</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="n">codes_right</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="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">AssertionError</span><span class="p">(</span><span class="s2">"This should never be reached"</span><span class="p">)</span>
<span class="n">verts_left</span> <span class="o">=</span> <span class="n">left</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
<span class="n">verts_right</span> <span class="o">=</span> <span class="n">right</span><span class="p">[:]</span>
<span class="k">if</span> <span class="n">path</span><span class="o">.</span><span class="n">codes</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">path_in</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">path</span><span class="o">.</span><span class="n">vertices</span><span class="p">[:</span><span class="n">i</span><span class="p">],</span> <span class="n">verts_left</span><span class="p">]))</span>
<span class="n">path_out</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">verts_right</span><span class="p">,</span> <span class="n">path</span><span class="o">.</span><span class="n">vertices</span><span class="p">[</span><span class="n">i</span><span class="p">:]]))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">path_in</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">path</span><span class="o">.</span><span class="n">vertices</span><span class="p">[:</span><span class="n">iold</span><span class="p">],</span> <span class="n">verts_left</span><span class="p">]),</span>
<span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">path</span><span class="o">.</span><span class="n">codes</span><span class="p">[:</span><span class="n">iold</span><span class="p">],</span> <span class="n">codes_left</span><span class="p">]))</span>
<span class="n">path_out</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">verts_right</span><span class="p">,</span> <span class="n">path</span><span class="o">.</span><span class="n">vertices</span><span class="p">[</span><span class="n">i</span><span class="p">:]]),</span>
<span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">codes_right</span><span class="p">,</span> <span class="n">path</span><span class="o">.</span><span class="n">codes</span><span class="p">[</span><span class="n">i</span><span class="p">:]]))</span>
<span class="k">if</span> <span class="n">reorder_inout</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">begin_inside</span><span class="p">:</span>
<span class="n">path_in</span><span class="p">,</span> <span class="n">path_out</span> <span class="o">=</span> <span class="n">path_out</span><span class="p">,</span> <span class="n">path_in</span>
<span class="k">return</span> <span class="n">path_in</span><span class="p">,</span> <span class="n">path_out</span></div>
<div class="viewcode-block" id="inside_circle"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.inside_circle">[docs]</a><span class="k">def</span> <span class="nf">inside_circle</span><span class="p">(</span><span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Return a function that checks whether a point is in a circle with center</span>
<span class="sd"> (*cx*, *cy*) and radius *r*.</span>
<span class="sd"> The returned function has the signature::</span>
<span class="sd"> f(xy: tuple[float, float]) -> bool</span>
<span class="sd"> """</span>
<span class="n">r2</span> <span class="o">=</span> <span class="n">r</span> <span class="o">**</span> <span class="mi">2</span>
<span class="k">def</span> <span class="nf">_f</span><span class="p">(</span><span class="n">xy</span><span class="p">):</span>
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">xy</span>
<span class="k">return</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">cx</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="n">y</span> <span class="o">-</span> <span class="n">cy</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span> <span class="o"><</span> <span class="n">r2</span>
<span class="k">return</span> <span class="n">_f</span></div>
<span class="c1"># quadratic Bezier lines</span>
<div class="viewcode-block" id="get_cos_sin"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.get_cos_sin">[docs]</a><span class="k">def</span> <span class="nf">get_cos_sin</span><span class="p">(</span><span class="n">x0</span><span class="p">,</span> <span class="n">y0</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">dx</span><span class="p">,</span> <span class="n">dy</span> <span class="o">=</span> <span class="n">x1</span> <span class="o">-</span> <span class="n">x0</span><span class="p">,</span> <span class="n">y1</span> <span class="o">-</span> <span class="n">y0</span>
<span class="n">d</span> <span class="o">=</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> <span class="o">**</span> <span class="o">.</span><span class="mi">5</span>
<span class="c1"># Account for divide by zero</span>
<span class="k">if</span> <span class="n">d</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span>
<span class="k">return</span> <span class="n">dx</span> <span class="o">/</span> <span class="n">d</span><span class="p">,</span> <span class="n">dy</span> <span class="o">/</span> <span class="n">d</span></div>
<div class="viewcode-block" id="check_if_parallel"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.check_if_parallel">[docs]</a><span class="k">def</span> <span class="nf">check_if_parallel</span><span class="p">(</span><span class="n">dx1</span><span class="p">,</span> <span class="n">dy1</span><span class="p">,</span> <span class="n">dx2</span><span class="p">,</span> <span class="n">dy2</span><span class="p">,</span> <span class="n">tolerance</span><span class="o">=</span><span class="mf">1.e-5</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Check if two lines are parallel.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> dx1, dy1, dx2, dy2 : float</span>
<span class="sd"> The gradients *dy*/*dx* of the two lines.</span>
<span class="sd"> tolerance : float</span>
<span class="sd"> The angular tolerance in radians up to which the lines are considered</span>
<span class="sd"> parallel.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> is_parallel</span>
<span class="sd"> - 1 if two lines are parallel in same direction.</span>
<span class="sd"> - -1 if two lines are parallel in opposite direction.</span>
<span class="sd"> - False otherwise.</span>
<span class="sd"> """</span>
<span class="n">theta1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">dx1</span><span class="p">,</span> <span class="n">dy1</span><span class="p">)</span>
<span class="n">theta2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">dx2</span><span class="p">,</span> <span class="n">dy2</span><span class="p">)</span>
<span class="n">dtheta</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">theta1</span> <span class="o">-</span> <span class="n">theta2</span><span class="p">)</span>
<span class="k">if</span> <span class="n">dtheta</span> <span class="o"><</span> <span class="n">tolerance</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">1</span>
<span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">dtheta</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o"><</span> <span class="n">tolerance</span><span class="p">:</span>
<span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">False</span></div>
<div class="viewcode-block" id="get_parallels"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.get_parallels">[docs]</a><span class="k">def</span> <span class="nf">get_parallels</span><span class="p">(</span><span class="n">bezier2</span><span class="p">,</span> <span class="n">width</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Given the quadratic Bezier control points *bezier2*, returns</span>
<span class="sd"> control points of quadratic Bezier lines roughly parallel to given</span>
<span class="sd"> one separated by *width*.</span>
<span class="sd"> """</span>
<span class="c1"># The parallel Bezier lines are constructed by following ways.</span>
<span class="c1"># c1 and c2 are control points representing the begin and end of the</span>
<span class="c1"># Bezier line.</span>
<span class="c1"># cm is the middle point</span>
<span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span> <span class="o">=</span> <span class="n">bezier2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">cmx</span><span class="p">,</span> <span class="n">cmy</span> <span class="o">=</span> <span class="n">bezier2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">c2x</span><span class="p">,</span> <span class="n">c2y</span> <span class="o">=</span> <span class="n">bezier2</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<span class="n">parallel_test</span> <span class="o">=</span> <span class="n">check_if_parallel</span><span class="p">(</span><span class="n">c1x</span> <span class="o">-</span> <span class="n">cmx</span><span class="p">,</span> <span class="n">c1y</span> <span class="o">-</span> <span class="n">cmy</span><span class="p">,</span>
<span class="n">cmx</span> <span class="o">-</span> <span class="n">c2x</span><span class="p">,</span> <span class="n">cmy</span> <span class="o">-</span> <span class="n">c2y</span><span class="p">)</span>
<span class="k">if</span> <span class="n">parallel_test</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
<span class="n">_api</span><span class="o">.</span><span class="n">warn_external</span><span class="p">(</span>
<span class="s2">"Lines do not intersect. A straight line is used instead."</span><span class="p">)</span>
<span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span> <span class="o">=</span> <span class="n">get_cos_sin</span><span class="p">(</span><span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span><span class="p">,</span> <span class="n">c2x</span><span class="p">,</span> <span class="n">c2y</span><span class="p">)</span>
<span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span> <span class="o">=</span> <span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># t1 and t2 is the angle between c1 and cm, cm, c2. They are</span>
<span class="c1"># also a angle of the tangential line of the path at c1 and c2</span>
<span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span> <span class="o">=</span> <span class="n">get_cos_sin</span><span class="p">(</span><span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span><span class="p">,</span> <span class="n">cmx</span><span class="p">,</span> <span class="n">cmy</span><span class="p">)</span>
<span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span> <span class="o">=</span> <span class="n">get_cos_sin</span><span class="p">(</span><span class="n">cmx</span><span class="p">,</span> <span class="n">cmy</span><span class="p">,</span> <span class="n">c2x</span><span class="p">,</span> <span class="n">c2y</span><span class="p">)</span>
<span class="c1"># find c1_left, c1_right which are located along the lines</span>
<span class="c1"># through c1 and perpendicular to the tangential lines of the</span>
<span class="c1"># Bezier path at a distance of width. Same thing for c2_left and</span>
<span class="c1"># c2_right with respect to c2.</span>
<span class="n">c1x_left</span><span class="p">,</span> <span class="n">c1y_left</span><span class="p">,</span> <span class="n">c1x_right</span><span class="p">,</span> <span class="n">c1y_right</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">get_normal_points</span><span class="p">(</span><span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span><span class="p">,</span> <span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span><span class="p">,</span> <span class="n">width</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">c2x_left</span><span class="p">,</span> <span class="n">c2y_left</span><span class="p">,</span> <span class="n">c2x_right</span><span class="p">,</span> <span class="n">c2y_right</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">get_normal_points</span><span class="p">(</span><span class="n">c2x</span><span class="p">,</span> <span class="n">c2y</span><span class="p">,</span> <span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span><span class="p">,</span> <span class="n">width</span><span class="p">)</span>
<span class="p">)</span>
<span class="c1"># find cm_left which is the intersecting point of a line through</span>
<span class="c1"># c1_left with angle t1 and a line through c2_left with angle</span>
<span class="c1"># t2. Same with cm_right.</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">cmx_left</span><span class="p">,</span> <span class="n">cmy_left</span> <span class="o">=</span> <span class="n">get_intersection</span><span class="p">(</span><span class="n">c1x_left</span><span class="p">,</span> <span class="n">c1y_left</span><span class="p">,</span> <span class="n">cos_t1</span><span class="p">,</span>
<span class="n">sin_t1</span><span class="p">,</span> <span class="n">c2x_left</span><span class="p">,</span> <span class="n">c2y_left</span><span class="p">,</span>
<span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span><span class="p">)</span>
<span class="n">cmx_right</span><span class="p">,</span> <span class="n">cmy_right</span> <span class="o">=</span> <span class="n">get_intersection</span><span class="p">(</span><span class="n">c1x_right</span><span class="p">,</span> <span class="n">c1y_right</span><span class="p">,</span> <span class="n">cos_t1</span><span class="p">,</span>
<span class="n">sin_t1</span><span class="p">,</span> <span class="n">c2x_right</span><span class="p">,</span> <span class="n">c2y_right</span><span class="p">,</span>
<span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">ValueError</span><span class="p">:</span>
<span class="c1"># Special case straight lines, i.e., angle between two lines is</span>
<span class="c1"># less than the threshold used by get_intersection (we don't use</span>
<span class="c1"># check_if_parallel as the threshold is not the same).</span>
<span class="n">cmx_left</span><span class="p">,</span> <span class="n">cmy_left</span> <span class="o">=</span> <span class="p">(</span>
<span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">c1x_left</span> <span class="o">+</span> <span class="n">c2x_left</span><span class="p">),</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">c1y_left</span> <span class="o">+</span> <span class="n">c2y_left</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">cmx_right</span><span class="p">,</span> <span class="n">cmy_right</span> <span class="o">=</span> <span class="p">(</span>
<span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">c1x_right</span> <span class="o">+</span> <span class="n">c2x_right</span><span class="p">),</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">c1y_right</span> <span class="o">+</span> <span class="n">c2y_right</span><span class="p">)</span>
<span class="p">)</span>
<span class="c1"># the parallel Bezier lines are created with control points of</span>
<span class="c1"># [c1_left, cm_left, c2_left] and [c1_right, cm_right, c2_right]</span>
<span class="n">path_left</span> <span class="o">=</span> <span class="p">[(</span><span class="n">c1x_left</span><span class="p">,</span> <span class="n">c1y_left</span><span class="p">),</span>
<span class="p">(</span><span class="n">cmx_left</span><span class="p">,</span> <span class="n">cmy_left</span><span class="p">),</span>
<span class="p">(</span><span class="n">c2x_left</span><span class="p">,</span> <span class="n">c2y_left</span><span class="p">)]</span>
<span class="n">path_right</span> <span class="o">=</span> <span class="p">[(</span><span class="n">c1x_right</span><span class="p">,</span> <span class="n">c1y_right</span><span class="p">),</span>
<span class="p">(</span><span class="n">cmx_right</span><span class="p">,</span> <span class="n">cmy_right</span><span class="p">),</span>
<span class="p">(</span><span class="n">c2x_right</span><span class="p">,</span> <span class="n">c2y_right</span><span class="p">)]</span>
<span class="k">return</span> <span class="n">path_left</span><span class="p">,</span> <span class="n">path_right</span></div>
<div class="viewcode-block" id="find_control_points"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.find_control_points">[docs]</a><span class="k">def</span> <span class="nf">find_control_points</span><span class="p">(</span><span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span><span class="p">,</span> <span class="n">mmx</span><span class="p">,</span> <span class="n">mmy</span><span class="p">,</span> <span class="n">c2x</span><span class="p">,</span> <span class="n">c2y</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Find control points of the Bezier curve passing through (*c1x*, *c1y*),</span>
<span class="sd"> (*mmx*, *mmy*), and (*c2x*, *c2y*), at parametric values 0, 0.5, and 1.</span>
<span class="sd"> """</span>
<span class="n">cmx</span> <span class="o">=</span> <span class="o">.</span><span class="mi">5</span> <span class="o">*</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">mmx</span> <span class="o">-</span> <span class="p">(</span><span class="n">c1x</span> <span class="o">+</span> <span class="n">c2x</span><span class="p">))</span>
<span class="n">cmy</span> <span class="o">=</span> <span class="o">.</span><span class="mi">5</span> <span class="o">*</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">mmy</span> <span class="o">-</span> <span class="p">(</span><span class="n">c1y</span> <span class="o">+</span> <span class="n">c2y</span><span class="p">))</span>
<span class="k">return</span> <span class="p">[(</span><span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span><span class="p">),</span> <span class="p">(</span><span class="n">cmx</span><span class="p">,</span> <span class="n">cmy</span><span class="p">),</span> <span class="p">(</span><span class="n">c2x</span><span class="p">,</span> <span class="n">c2y</span><span class="p">)]</span></div>
<div class="viewcode-block" id="make_wedged_bezier2"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.make_wedged_bezier2">[docs]</a><span class="k">def</span> <span class="nf">make_wedged_bezier2</span><span class="p">(</span><span class="n">bezier2</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span> <span class="n">w1</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">wm</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">w2</span><span class="o">=</span><span class="mf">0.</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Being similar to get_parallels, returns control points of two quadratic</span>
<span class="sd"> Bezier lines having a width roughly parallel to given one separated by</span>
<span class="sd"> *width*.</span>
<span class="sd"> """</span>
<span class="c1"># c1, cm, c2</span>
<span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span> <span class="o">=</span> <span class="n">bezier2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">cmx</span><span class="p">,</span> <span class="n">cmy</span> <span class="o">=</span> <span class="n">bezier2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">c3x</span><span class="p">,</span> <span class="n">c3y</span> <span class="o">=</span> <span class="n">bezier2</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<span class="c1"># t1 and t2 is the angle between c1 and cm, cm, c3.</span>
<span class="c1"># They are also a angle of the tangential line of the path at c1 and c3</span>
<span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span> <span class="o">=</span> <span class="n">get_cos_sin</span><span class="p">(</span><span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span><span class="p">,</span> <span class="n">cmx</span><span class="p">,</span> <span class="n">cmy</span><span class="p">)</span>
<span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span> <span class="o">=</span> <span class="n">get_cos_sin</span><span class="p">(</span><span class="n">cmx</span><span class="p">,</span> <span class="n">cmy</span><span class="p">,</span> <span class="n">c3x</span><span class="p">,</span> <span class="n">c3y</span><span class="p">)</span>
<span class="c1"># find c1_left, c1_right which are located along the lines</span>
<span class="c1"># through c1 and perpendicular to the tangential lines of the</span>
<span class="c1"># Bezier path at a distance of width. Same thing for c3_left and</span>
<span class="c1"># c3_right with respect to c3.</span>
<span class="n">c1x_left</span><span class="p">,</span> <span class="n">c1y_left</span><span class="p">,</span> <span class="n">c1x_right</span><span class="p">,</span> <span class="n">c1y_right</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">get_normal_points</span><span class="p">(</span><span class="n">c1x</span><span class="p">,</span> <span class="n">c1y</span><span class="p">,</span> <span class="n">cos_t1</span><span class="p">,</span> <span class="n">sin_t1</span><span class="p">,</span> <span class="n">width</span> <span class="o">*</span> <span class="n">w1</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">c3x_left</span><span class="p">,</span> <span class="n">c3y_left</span><span class="p">,</span> <span class="n">c3x_right</span><span class="p">,</span> <span class="n">c3y_right</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">get_normal_points</span><span class="p">(</span><span class="n">c3x</span><span class="p">,</span> <span class="n">c3y</span><span class="p">,</span> <span class="n">cos_t2</span><span class="p">,</span> <span class="n">sin_t2</span><span class="p">,</span> <span class="n">width</span> <span class="o">*</span> <span class="n">w2</span><span class="p">)</span>
<span class="p">)</span>
<span class="c1"># find c12, c23 and c123 which are middle points of c1-cm, cm-c3 and</span>
<span class="c1"># c12-c23</span>
<span class="n">c12x</span><span class="p">,</span> <span class="n">c12y</span> <span class="o">=</span> <span class="p">(</span><span class="n">c1x</span> <span class="o">+</span> <span class="n">cmx</span><span class="p">)</span> <span class="o">*</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="p">(</span><span class="n">c1y</span> <span class="o">+</span> <span class="n">cmy</span><span class="p">)</span> <span class="o">*</span> <span class="o">.</span><span class="mi">5</span>
<span class="n">c23x</span><span class="p">,</span> <span class="n">c23y</span> <span class="o">=</span> <span class="p">(</span><span class="n">cmx</span> <span class="o">+</span> <span class="n">c3x</span><span class="p">)</span> <span class="o">*</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="p">(</span><span class="n">cmy</span> <span class="o">+</span> <span class="n">c3y</span><span class="p">)</span> <span class="o">*</span> <span class="o">.</span><span class="mi">5</span>
<span class="n">c123x</span><span class="p">,</span> <span class="n">c123y</span> <span class="o">=</span> <span class="p">(</span><span class="n">c12x</span> <span class="o">+</span> <span class="n">c23x</span><span class="p">)</span> <span class="o">*</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="p">(</span><span class="n">c12y</span> <span class="o">+</span> <span class="n">c23y</span><span class="p">)</span> <span class="o">*</span> <span class="o">.</span><span class="mi">5</span>
<span class="c1"># tangential angle of c123 (angle between c12 and c23)</span>
<span class="n">cos_t123</span><span class="p">,</span> <span class="n">sin_t123</span> <span class="o">=</span> <span class="n">get_cos_sin</span><span class="p">(</span><span class="n">c12x</span><span class="p">,</span> <span class="n">c12y</span><span class="p">,</span> <span class="n">c23x</span><span class="p">,</span> <span class="n">c23y</span><span class="p">)</span>
<span class="n">c123x_left</span><span class="p">,</span> <span class="n">c123y_left</span><span class="p">,</span> <span class="n">c123x_right</span><span class="p">,</span> <span class="n">c123y_right</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">get_normal_points</span><span class="p">(</span><span class="n">c123x</span><span class="p">,</span> <span class="n">c123y</span><span class="p">,</span> <span class="n">cos_t123</span><span class="p">,</span> <span class="n">sin_t123</span><span class="p">,</span> <span class="n">width</span> <span class="o">*</span> <span class="n">wm</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">path_left</span> <span class="o">=</span> <span class="n">find_control_points</span><span class="p">(</span><span class="n">c1x_left</span><span class="p">,</span> <span class="n">c1y_left</span><span class="p">,</span>
<span class="n">c123x_left</span><span class="p">,</span> <span class="n">c123y_left</span><span class="p">,</span>
<span class="n">c3x_left</span><span class="p">,</span> <span class="n">c3y_left</span><span class="p">)</span>
<span class="n">path_right</span> <span class="o">=</span> <span class="n">find_control_points</span><span class="p">(</span><span class="n">c1x_right</span><span class="p">,</span> <span class="n">c1y_right</span><span class="p">,</span>
<span class="n">c123x_right</span><span class="p">,</span> <span class="n">c123y_right</span><span class="p">,</span>
<span class="n">c3x_right</span><span class="p">,</span> <span class="n">c3y_right</span><span class="p">)</span>
<span class="k">return</span> <span class="n">path_left</span><span class="p">,</span> <span class="n">path_right</span></div>
<div class="viewcode-block" id="make_path_regular"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.make_path_regular">[docs]</a><span class="nd">@_api</span><span class="o">.</span><span class="n">deprecated</span><span class="p">(</span>
<span class="s2">"3.3"</span><span class="p">,</span> <span class="n">alternative</span><span class="o">=</span><span class="s2">"Path.cleaned() and remove the final STOP if needed"</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">make_path_regular</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> If the ``codes`` attribute of `.Path` *p* is None, return a copy of *p*</span>
<span class="sd"> with ``codes`` set to (MOVETO, LINETO, LINETO, ..., LINETO); otherwise</span>
<span class="sd"> return *p* itself.</span>
<span class="sd"> """</span>
<span class="kn">from</span> <span class="nn">.path</span> <span class="kn">import</span> <span class="n">Path</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">codes</span>
<span class="k">if</span> <span class="n">c</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">vertices</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">dtype</span><span class="o">=</span><span class="n">Path</span><span class="o">.</span><span class="n">code_type</span><span class="p">)</span>
<span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">Path</span><span class="o">.</span><span class="n">MOVETO</span>
<span class="k">return</span> <span class="n">Path</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">vertices</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">p</span></div>
<div class="viewcode-block" id="concatenate_paths"><a class="viewcode-back" href="../../api/bezier_api.html#matplotlib.bezier.concatenate_paths">[docs]</a><span class="nd">@_api</span><span class="o">.</span><span class="n">deprecated</span><span class="p">(</span><span class="s2">"3.3"</span><span class="p">,</span> <span class="n">alternative</span><span class="o">=</span><span class="s2">"Path.make_compound_path()"</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">concatenate_paths</span><span class="p">(</span><span class="n">paths</span><span class="p">):</span>
<span class="sd">"""Concatenate a list of paths into a single path."""</span>
<span class="kn">from</span> <span class="nn">.path</span> <span class="kn">import</span> <span class="n">Path</span>
<span class="k">return</span> <span class="n">Path</span><span class="o">.</span><span class="n">make_compound_path</span><span class="p">(</span><span class="o">*</span><span class="n">paths</span><span class="p">)</span></div>
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