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<h1>Source code for matplotlib.tri.trirefine</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">Mesh refinement for triangular grids.</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="p">(</span><span class="n">absolute_import</span><span class="p">,</span> <span class="n">division</span><span class="p">,</span> <span class="n">print_function</span><span class="p">,</span>
<span class="n">unicode_literals</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">six</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.tri.triangulation</span> <span class="k">import</span> <span class="n">Triangulation</span>
<span class="kn">import</span> <span class="nn">matplotlib.tri.triinterpolate</span>
<div class="viewcode-block" id="TriRefiner"><a class="viewcode-back" href="../../../api/tri_api.html#matplotlib.tri.TriRefiner">[docs]</a><span class="k">class</span> <span class="nc">TriRefiner</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Abstract base class for classes implementing mesh refinement.</span>
<span class="sd"> A TriRefiner encapsulates a Triangulation object and provides tools for</span>
<span class="sd"> mesh refinement and interpolation.</span>
<span class="sd"> Derived classes must implements:</span>
<span class="sd"> - ``refine_triangulation(return_tri_index=False, **kwargs)`` , where</span>
<span class="sd"> the optional keyword arguments *kwargs* are defined in each</span>
<span class="sd"> TriRefiner concrete implementation, and which returns :</span>
<span class="sd"> - a refined triangulation</span>
<span class="sd"> - optionally (depending on *return_tri_index*), for each</span>
<span class="sd"> point of the refined triangulation: the index of</span>
<span class="sd"> the initial triangulation triangle to which it belongs.</span>
<span class="sd"> - ``refine_field(z, triinterpolator=None, **kwargs)`` , where:</span>
<span class="sd"> - *z* array of field values (to refine) defined at the base</span>
<span class="sd"> triangulation nodes</span>
<span class="sd"> - *triinterpolator* is a</span>
<span class="sd"> :class:`~matplotlib.tri.TriInterpolator` (optional)</span>
<span class="sd"> - the other optional keyword arguments *kwargs* are defined in</span>
<span class="sd"> each TriRefiner concrete implementation</span>
<span class="sd"> and which returns (as a tuple) a refined triangular mesh and the</span>
<span class="sd"> interpolated values of the field at the refined triangulation nodes.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">triangulation</span><span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">triangulation</span><span class="p">,</span> <span class="n">Triangulation</span><span class="p">):</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Expected a Triangulation object"</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_triangulation</span> <span class="o">=</span> <span class="n">triangulation</span></div>
<div class="viewcode-block" id="UniformTriRefiner"><a class="viewcode-back" href="../../../api/tri_api.html#matplotlib.tri.UniformTriRefiner">[docs]</a><span class="k">class</span> <span class="nc">UniformTriRefiner</span><span class="p">(</span><span class="n">TriRefiner</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Uniform mesh refinement by recursive subdivisions.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> triangulation : :class:`~matplotlib.tri.Triangulation`</span>
<span class="sd"> The encapsulated triangulation (to be refined)</span>
<span class="sd"> """</span>
<span class="c1"># See Also</span>
<span class="c1"># --------</span>
<span class="c1"># :class:`~matplotlib.tri.CubicTriInterpolator` and</span>
<span class="c1"># :class:`~matplotlib.tri.TriAnalyzer`.</span>
<span class="c1"># """</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">triangulation</span><span class="p">):</span>
<span class="n">TriRefiner</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">triangulation</span><span class="p">)</span>
<div class="viewcode-block" id="UniformTriRefiner.refine_triangulation"><a class="viewcode-back" href="../../../api/tri_api.html#matplotlib.tri.UniformTriRefiner.refine_triangulation">[docs]</a> <span class="k">def</span> <span class="nf">refine_triangulation</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">return_tri_index</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">subdiv</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Computes an uniformly refined triangulation *refi_triangulation* of</span>
<span class="sd"> the encapsulated :attr:`triangulation`.</span>
<span class="sd"> This function refines the encapsulated triangulation by splitting each</span>
<span class="sd"> father triangle into 4 child sub-triangles built on the edges midside</span>
<span class="sd"> nodes, recursively (level of recursion *subdiv*).</span>
<span class="sd"> In the end, each triangle is hence divided into ``4**subdiv``</span>
<span class="sd"> child triangles.</span>
<span class="sd"> The default value for *subdiv* is 3 resulting in 64 refined</span>
<span class="sd"> subtriangles for each triangle of the initial triangulation.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> return_tri_index : boolean, optional</span>
<span class="sd"> Boolean indicating whether an index table indicating the father</span>
<span class="sd"> triangle index of each point will be returned. Default value</span>
<span class="sd"> False.</span>
<span class="sd"> subdiv : integer, optional</span>
<span class="sd"> Recursion level for the subdivision. Defaults value 3.</span>
<span class="sd"> Each triangle will be divided into ``4**subdiv`` child triangles.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> refi_triangulation : :class:`~matplotlib.tri.Triangulation`</span>
<span class="sd"> The returned refined triangulation</span>
<span class="sd"> found_index : array-like of integers</span>
<span class="sd"> Index of the initial triangulation containing triangle, for each</span>
<span class="sd"> point of *refi_triangulation*.</span>
<span class="sd"> Returned only if *return_tri_index* is set to True.</span>
<span class="sd"> """</span>
<span class="n">refi_triangulation</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_triangulation</span>
<span class="n">ntri</span> <span class="o">=</span> <span class="n">refi_triangulation</span><span class="o">.</span><span class="n">triangles</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="c1"># Computes the triangulation ancestors numbers in the reference</span>
<span class="c1"># triangulation.</span>
<span class="n">ancestors</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">ntri</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">subdiv</span><span class="p">):</span>
<span class="n">refi_triangulation</span><span class="p">,</span> <span class="n">ancestors</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_refine_triangulation_once</span><span class="p">(</span>
<span class="n">refi_triangulation</span><span class="p">,</span> <span class="n">ancestors</span><span class="p">)</span>
<span class="n">refi_npts</span> <span class="o">=</span> <span class="n">refi_triangulation</span><span class="o">.</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">refi_triangles</span> <span class="o">=</span> <span class="n">refi_triangulation</span><span class="o">.</span><span class="n">triangles</span>
<span class="c1"># Now we compute found_index table if needed</span>
<span class="k">if</span> <span class="n">return_tri_index</span><span class="p">:</span>
<span class="c1"># We have to initialize found_index with -1 because some nodes</span>
<span class="c1"># may very well belong to no triangle at all, e.g., in case of</span>
<span class="c1"># Delaunay Triangulation with DuplicatePointWarning.</span>
<span class="n">found_index</span> <span class="o">=</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">refi_npts</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
<span class="n">tri_mask</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_triangulation</span><span class="o">.</span><span class="n">mask</span>
<span class="k">if</span> <span class="n">tri_mask</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">found_index</span><span class="p">[</span><span class="n">refi_triangles</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">ancestors</span><span class="p">,</span>
<span class="mi">3</span><span class="p">)</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">3</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># There is a subtlety here: we want to avoid whenever possible</span>
<span class="c1"># that refined points container is a masked triangle (which</span>
<span class="c1"># would result in artifacts in plots).</span>
<span class="c1"># So we impose the numbering from masked ancestors first,</span>
<span class="c1"># then overwrite it with unmasked ancestor numbers.</span>
<span class="n">ancestor_mask</span> <span class="o">=</span> <span class="n">tri_mask</span><span class="p">[</span><span class="n">ancestors</span><span class="p">]</span>
<span class="n">found_index</span><span class="p">[</span><span class="n">refi_triangles</span><span class="p">[</span><span class="n">ancestor_mask</span><span class="p">,</span> <span class="p">:]</span>
<span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">ancestors</span><span class="p">[</span><span class="n">ancestor_mask</span><span class="p">],</span>
<span class="mi">3</span><span class="p">)</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">3</span><span class="p">)</span>
<span class="n">found_index</span><span class="p">[</span><span class="n">refi_triangles</span><span class="p">[</span><span class="o">~</span><span class="n">ancestor_mask</span><span class="p">,</span> <span class="p">:]</span>
<span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">ancestors</span><span class="p">[</span><span class="o">~</span><span class="n">ancestor_mask</span><span class="p">],</span>
<span class="mi">3</span><span class="p">)</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">3</span><span class="p">)</span>
<span class="k">return</span> <span class="n">refi_triangulation</span><span class="p">,</span> <span class="n">found_index</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">refi_triangulation</span></div>
<div class="viewcode-block" id="UniformTriRefiner.refine_field"><a class="viewcode-back" href="../../../api/tri_api.html#matplotlib.tri.UniformTriRefiner.refine_field">[docs]</a> <span class="k">def</span> <span class="nf">refine_field</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">triinterpolator</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">subdiv</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Refines a field defined on the encapsulated triangulation.</span>
<span class="sd"> Returns *refi_tri* (refined triangulation), *refi_z* (interpolated</span>
<span class="sd"> values of the field at the node of the refined triangulation).</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> z : 1d-array-like of length ``n_points``</span>
<span class="sd"> Values of the field to refine, defined at the nodes of the</span>
<span class="sd"> encapsulated triangulation. (``n_points`` is the number of points</span>
<span class="sd"> in the initial triangulation)</span>
<span class="sd"> triinterpolator : :class:`~matplotlib.tri.TriInterpolator`, optional</span>
<span class="sd"> Interpolator used for field interpolation. If not specified,</span>
<span class="sd"> a :class:`~matplotlib.tri.CubicTriInterpolator` will</span>
<span class="sd"> be used.</span>
<span class="sd"> subdiv : integer, optional</span>
<span class="sd"> Recursion level for the subdivision. Defaults to 3.</span>
<span class="sd"> Each triangle will be divided into ``4**subdiv`` child triangles.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> refi_tri : :class:`~matplotlib.tri.Triangulation` object</span>
<span class="sd"> The returned refined triangulation</span>
<span class="sd"> refi_z : 1d array of length: *refi_tri* node count.</span>
<span class="sd"> The returned interpolated field (at *refi_tri* nodes)</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">triinterpolator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">interp</span> <span class="o">=</span> <span class="n">matplotlib</span><span class="o">.</span><span class="n">tri</span><span class="o">.</span><span class="n">CubicTriInterpolator</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_triangulation</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">triinterpolator</span><span class="p">,</span>
<span class="n">matplotlib</span><span class="o">.</span><span class="n">tri</span><span class="o">.</span><span class="n">TriInterpolator</span><span class="p">):</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Expected a TriInterpolator object"</span><span class="p">)</span>
<span class="n">interp</span> <span class="o">=</span> <span class="n">triinterpolator</span>
<span class="n">refi_tri</span><span class="p">,</span> <span class="n">found_index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">refine_triangulation</span><span class="p">(</span>
<span class="n">subdiv</span><span class="o">=</span><span class="n">subdiv</span><span class="p">,</span> <span class="n">return_tri_index</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">refi_z</span> <span class="o">=</span> <span class="n">interp</span><span class="o">.</span><span class="n">_interpolate_multikeys</span><span class="p">(</span>
<span class="n">refi_tri</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">refi_tri</span><span class="o">.</span><span class="n">y</span><span class="p">,</span> <span class="n">tri_index</span><span class="o">=</span><span class="n">found_index</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">return</span> <span class="n">refi_tri</span><span class="p">,</span> <span class="n">refi_z</span></div>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">_refine_triangulation_once</span><span class="p">(</span><span class="n">triangulation</span><span class="p">,</span> <span class="n">ancestors</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> This function refines a matplotlib.tri *triangulation* by splitting</span>
<span class="sd"> each triangle into 4 child-masked_triangles built on the edges midside</span>
<span class="sd"> nodes.</span>
<span class="sd"> The masked triangles, if present, are also split but their children</span>
<span class="sd"> returned masked.</span>
<span class="sd"> If *ancestors* is not provided, returns only a new triangulation:</span>
<span class="sd"> child_triangulation.</span>
<span class="sd"> If the array-like key table *ancestor* is given, it shall be of shape</span>
<span class="sd"> (ntri,) where ntri is the number of *triangulation* masked_triangles.</span>
<span class="sd"> In this case, the function returns</span>
<span class="sd"> (child_triangulation, child_ancestors)</span>
<span class="sd"> child_ancestors is defined so that the 4 child masked_triangles share</span>
<span class="sd"> the same index as their father: child_ancestors.shape = (4 * ntri,).</span>
<span class="sd"> """</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">triangulation</span><span class="o">.</span><span class="n">x</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">triangulation</span><span class="o">.</span><span class="n">y</span>
<span class="c1"># According to tri.triangulation doc:</span>
<span class="c1"># neighbors[i,j] is the triangle that is the neighbor</span>
<span class="c1"># to the edge from point index masked_triangles[i,j] to point</span>
<span class="c1"># index masked_triangles[i,(j+1)%3].</span>
<span class="n">neighbors</span> <span class="o">=</span> <span class="n">triangulation</span><span class="o">.</span><span class="n">neighbors</span>
<span class="n">triangles</span> <span class="o">=</span> <span class="n">triangulation</span><span class="o">.</span><span class="n">triangles</span>
<span class="n">npts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">shape</span><span class="p">(</span><span class="n">x</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">ntri</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">shape</span><span class="p">(</span><span class="n">triangles</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">if</span> <span class="n">ancestors</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">ancestors</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">ancestors</span><span class="p">)</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">shape</span><span class="p">(</span><span class="n">ancestors</span><span class="p">)</span> <span class="o">!=</span> <span class="p">(</span><span class="n">ntri</span><span class="p">,):</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
<span class="s2">"Incompatible shapes provide for triangulation"</span>
<span class="s2">".masked_triangles and ancestors: </span><span class="si">{0}</span><span class="s2"> and </span><span class="si">{1}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
<span class="n">np</span><span class="o">.</span><span class="n">shape</span><span class="p">(</span><span class="n">triangles</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">shape</span><span class="p">(</span><span class="n">ancestors</span><span class="p">)))</span>
<span class="c1"># Initiating tables refi_x and refi_y of the refined triangulation</span>
<span class="c1"># points</span>
<span class="c1"># hint: each apex is shared by 2 masked_triangles except the borders.</span>
<span class="n">borders</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">neighbors</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">added_pts</span> <span class="o">=</span> <span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">ntri</span> <span class="o">+</span> <span class="n">borders</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
<span class="n">refi_npts</span> <span class="o">=</span> <span class="n">npts</span> <span class="o">+</span> <span class="n">added_pts</span>
<span class="n">refi_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">refi_npts</span><span class="p">)</span>
<span class="n">refi_y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">refi_npts</span><span class="p">)</span>
<span class="c1"># First part of refi_x, refi_y is just the initial points</span>
<span class="n">refi_x</span><span class="p">[:</span><span class="n">npts</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span>
<span class="n">refi_y</span><span class="p">[:</span><span class="n">npts</span><span class="p">]</span> <span class="o">=</span> <span class="n">y</span>
<span class="c1"># Second part contains the edge midside nodes.</span>
<span class="c1"># Each edge belongs to 1 triangle (if border edge) or is shared by 2</span>
<span class="c1"># masked_triangles (interior edge).</span>
<span class="c1"># We first build 2 * ntri arrays of edge starting nodes (edge_elems,</span>
<span class="c1"># edge_apexes) ; we then extract only the masters to avoid overlaps.</span>
<span class="c1"># The so-called 'master' is the triangle with biggest index</span>
<span class="c1"># The 'slave' is the triangle with lower index</span>
<span class="c1"># (can be -1 if border edge)</span>
<span class="c1"># For slave and master we will identify the apex pointing to the edge</span>
<span class="c1"># start</span>
<span class="n">edge_elems</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ravel</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">ntri</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">ntri</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">ntri</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)]))</span>
<span class="n">edge_apexes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ravel</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">ntri</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">ntri</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">ntri</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span><span class="o">*</span><span class="mi">2</span><span class="p">]))</span>
<span class="n">edge_neighbors</span> <span class="o">=</span> <span class="n">neighbors</span><span class="p">[</span><span class="n">edge_elems</span><span class="p">,</span> <span class="n">edge_apexes</span><span class="p">]</span>
<span class="n">mask_masters</span> <span class="o">=</span> <span class="p">(</span><span class="n">edge_elems</span> <span class="o">></span> <span class="n">edge_neighbors</span><span class="p">)</span>
<span class="c1"># Identifying the "masters" and adding to refi_x, refi_y vec</span>
<span class="n">masters</span> <span class="o">=</span> <span class="n">edge_elems</span><span class="p">[</span><span class="n">mask_masters</span><span class="p">]</span>
<span class="n">apex_masters</span> <span class="o">=</span> <span class="n">edge_apexes</span><span class="p">[</span><span class="n">mask_masters</span><span class="p">]</span>
<span class="n">x_add</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">triangles</span><span class="p">[</span><span class="n">masters</span><span class="p">,</span> <span class="n">apex_masters</span><span class="p">]]</span> <span class="o">+</span>
<span class="n">x</span><span class="p">[</span><span class="n">triangles</span><span class="p">[</span><span class="n">masters</span><span class="p">,</span> <span class="p">(</span><span class="n">apex_masters</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="mi">3</span><span class="p">]])</span> <span class="o">*</span> <span class="mf">0.5</span>
<span class="n">y_add</span> <span class="o">=</span> <span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">triangles</span><span class="p">[</span><span class="n">masters</span><span class="p">,</span> <span class="n">apex_masters</span><span class="p">]]</span> <span class="o">+</span>
<span class="n">y</span><span class="p">[</span><span class="n">triangles</span><span class="p">[</span><span class="n">masters</span><span class="p">,</span> <span class="p">(</span><span class="n">apex_masters</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="mi">3</span><span class="p">]])</span> <span class="o">*</span> <span class="mf">0.5</span>
<span class="n">refi_x</span><span class="p">[</span><span class="n">npts</span><span class="p">:]</span> <span class="o">=</span> <span class="n">x_add</span>
<span class="n">refi_y</span><span class="p">[</span><span class="n">npts</span><span class="p">:]</span> <span class="o">=</span> <span class="n">y_add</span>
<span class="c1"># Building the new masked_triangles ; each old masked_triangles hosts</span>
<span class="c1"># 4 new masked_triangles</span>
<span class="c1"># there are 6 pts to identify per 'old' triangle, 3 new_pt_corner and</span>
<span class="c1"># 3 new_pt_midside</span>
<span class="n">new_pt_corner</span> <span class="o">=</span> <span class="n">triangles</span>
<span class="c1"># What is the index in refi_x, refi_y of point at middle of apex iapex</span>
<span class="c1"># of elem ielem ?</span>
<span class="c1"># If ielem is the apex master: simple count, given the way refi_x was</span>
<span class="c1"># built.</span>
<span class="c1"># If ielem is the apex slave: yet we do not know ; but we will soon</span>
<span class="c1"># using the neighbors table.</span>
<span class="n">new_pt_midside</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">([</span><span class="n">ntri</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
<span class="n">cum_sum</span> <span class="o">=</span> <span class="n">npts</span>
<span class="k">for</span> <span class="n">imid</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">):</span>
<span class="n">mask_st_loc</span> <span class="o">=</span> <span class="p">(</span><span class="n">imid</span> <span class="o">==</span> <span class="n">apex_masters</span><span class="p">)</span>
<span class="n">n_masters_loc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">mask_st_loc</span><span class="p">)</span>
<span class="n">elem_masters_loc</span> <span class="o">=</span> <span class="n">masters</span><span class="p">[</span><span class="n">mask_st_loc</span><span class="p">]</span>
<span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="n">imid</span><span class="p">][</span><span class="n">elem_masters_loc</span><span class="p">]</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_masters_loc</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span> <span class="o">+</span> <span class="n">cum_sum</span>
<span class="n">cum_sum</span> <span class="o">+=</span> <span class="n">n_masters_loc</span>
<span class="c1"># Now dealing with slave elems.</span>
<span class="c1"># for each slave element we identify the master and then the inode</span>
<span class="c1"># once slave_masters is identified, slave_masters_apex is such that:</span>
<span class="c1"># neighbors[slaves_masters, slave_masters_apex] == slaves</span>
<span class="n">mask_slaves</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logical_not</span><span class="p">(</span><span class="n">mask_masters</span><span class="p">)</span>
<span class="n">slaves</span> <span class="o">=</span> <span class="n">edge_elems</span><span class="p">[</span><span class="n">mask_slaves</span><span class="p">]</span>
<span class="n">slaves_masters</span> <span class="o">=</span> <span class="n">edge_neighbors</span><span class="p">[</span><span class="n">mask_slaves</span><span class="p">]</span>
<span class="n">diff_table</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">neighbors</span><span class="p">[</span><span class="n">slaves_masters</span><span class="p">,</span> <span class="p">:]</span> <span class="o">-</span>
<span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">slaves</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)))</span>
<span class="n">slave_masters_apex</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmin</span><span class="p">(</span><span class="n">diff_table</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">slaves_apex</span> <span class="o">=</span> <span class="n">edge_apexes</span><span class="p">[</span><span class="n">mask_slaves</span><span class="p">]</span>
<span class="n">new_pt_midside</span><span class="p">[</span><span class="n">slaves</span><span class="p">,</span> <span class="n">slaves_apex</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_pt_midside</span><span class="p">[</span>
<span class="n">slaves_masters</span><span class="p">,</span> <span class="n">slave_masters_apex</span><span class="p">]</span>
<span class="c1"># Builds the 4 child masked_triangles</span>
<span class="n">child_triangles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">([</span><span class="n">ntri</span><span class="o">*</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
<span class="n">child_triangles</span><span class="p">[</span><span class="mi">0</span><span class="p">::</span><span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span>
<span class="n">new_pt_corner</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span>
<span class="n">child_triangles</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span>
<span class="n">new_pt_corner</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span>
<span class="n">child_triangles</span><span class="p">[</span><span class="mi">2</span><span class="p">::</span><span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span>
<span class="n">new_pt_corner</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">],</span>
<span class="n">new_pt_midside</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="n">child_triangles</span><span class="p">[</span><span class="mi">3</span><span class="p">::</span><span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span>
<span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">new_pt_midside</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span>
<span class="n">child_triangulation</span> <span class="o">=</span> <span class="n">Triangulation</span><span class="p">(</span><span class="n">refi_x</span><span class="p">,</span> <span class="n">refi_y</span><span class="p">,</span> <span class="n">child_triangles</span><span class="p">)</span>
<span class="c1"># Builds the child mask</span>
<span class="k">if</span> <span class="n">triangulation</span><span class="o">.</span><span class="n">mask</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">child_triangulation</span><span class="o">.</span><span class="n">set_mask</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">triangulation</span><span class="o">.</span><span class="n">mask</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="k">if</span> <span class="n">ancestors</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">child_triangulation</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">child_triangulation</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">ancestors</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span></div>
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