-
Notifications
You must be signed in to change notification settings - Fork 60
Expand file tree
/
Copy pathtri_api.html
More file actions
949 lines (895 loc) · 51.9 KB
/
tri_api.html
File metadata and controls
949 lines (895 loc) · 51.9 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>triangular grids — Matplotlib 2.0.2 documentation</title>
<link rel="stylesheet" href="../_static/mpl.css"
type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css"
type="text/css" />
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: '../',
VERSION: '2.0.2',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt'
};
</script>
<script type="text/javascript" src="../_static/jquery.js"></script>
<script type="text/javascript" src="../_static/underscore.js"></script>
<script type="text/javascript" src="../_static/doctools.js"></script>
<link rel="search" type="application/opensearchdescription+xml"
title="Search within Matplotlib 2.0.2 documentation"
href="../_static/opensearch.xml"/>
<link rel="shortcut icon" href="../_static/favicon.ico"/>
<link rel="index" title="Index" href="../genindex.html"
/>
<link rel="search" title="Search" href="../search.html"
/>
<link rel="top" title="Matplotlib 2.0.2 documentation" href="../index.html" />
<link rel="up" title="The Matplotlib API" href="index.html" />
<link rel="next" title="type1font" href="type1font.html" />
<link rel="prev" title="Working with transformations" href="transformations.html" />
<link rel="canonical" href="https://matplotlib.org/stable/api/tri_api.html" />
</head>
<body>
<div id="unreleased-message"> You are reading an old version of the documentation (v2.0.2). For the latest version see <a href="https://matplotlib.org/stable/api/tri_api.html">https://matplotlib.org/stable/api/tri_api.html</a></div>
<!-- The "Fork me on github" ribbon -->
<img style="float: right; margin-bottom: -40px; top: 0; right: 0; border: 0;" src="https://s3.amazonaws.com/github/ribbons/forkme_right_orange_ff7600.png" usemap="#ribbonmap"/>
<map name="ribbonmap">
<area shape="poly" coords="15,0,148,-1,148,135" href="https://github.com/matplotlib/matplotlib" title="Fork me on GitHub" />
</map>
<div style="background-color: white; text-align: left; padding: 10px 10px 15px 15px">
<a href="../index.html"><img src="../_static/logo2.svg" width="540px" border="0" alt="matplotlib"/></a>
</div>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li class="right" >
<a href="type1font.html" title="type1font"
accesskey="N">next</a> |</li>
<li class="right" >
<a href="transformations.html" title="Working with transformations"
accesskey="P">previous</a> |</li>
<li><a href="../index.html">home</a>| </li>
<li><a href="../examples/index.html">examples</a>| </li>
<li><a href="../gallery.html">gallery</a>| </li>
<li><a href="pyplot_summary.html">pyplot</a>| </li>
<li><a href="../contents.html">docs</a> »</li>
<li><a href="index.html" accesskey="U">The Matplotlib API</a> »</li>
</ul>
</div>
<div class="sphinxsidebar">
<div class="sphinxsidebarwrapper">
<a href="http://depsy.org/package/python/matplotlib">
<img src="../_static/depsy_badge.svg">
</a>
<br/>
Travis-CI: <a href="https://travis-ci.org/matplotlib/matplotlib">
<img src="https://travis-ci.org/matplotlib/matplotlib.svg?branch=master"/>
</a>
<br/>
<h3><a href="../contents.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">triangular grids</a><ul>
<li><a class="reference internal" href="#module-matplotlib.tri"><code class="docutils literal"><span class="pre">matplotlib.tri</span></code></a></li>
</ul>
</li>
</ul>
<div class="relations">
<h3>Related Topics</h3>
<ul>
<li><a href="../contents.html">Documentation overview</a><ul>
<li><a href="index.html">The Matplotlib API</a><ul>
<li>Previous: <a href="transformations.html" title="previous chapter">Working with transformations</a></li>
<li>Next: <a href="type1font.html" title="next chapter">type1font</a></li>
</ul></li>
</ul></li>
</ul>
</div>
<div role="note" aria-label="source link">
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="../_sources/api/tri_api.rst.txt"
rel="nofollow">Show Source</a></li>
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3>Quick search</h3>
<form class="search" action="../search.html" method="get">
<div><input type="text" name="q" /></div>
<div><input type="submit" value="Go" /></div>
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body">
<div class="section" id="triangular-grids">
<h1>triangular grids<a class="headerlink" href="#triangular-grids" title="Permalink to this headline">¶</a></h1>
<div class="section" id="module-matplotlib.tri">
<span id="matplotlib-tri"></span><h2><a class="reference internal" href="#module-matplotlib.tri" title="matplotlib.tri"><code class="xref py py-mod docutils literal"><span class="pre">matplotlib.tri</span></code></a><a class="headerlink" href="#module-matplotlib.tri" title="Permalink to this headline">¶</a></h2>
<p>Unstructured triangular grid functions.</p>
<dl class="class">
<dt id="matplotlib.tri.Triangulation">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">Triangulation</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>triangles=None</em>, <em>mask=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.Triangulation" title="Permalink to this definition">¶</a></dt>
<dd><p>An unstructured triangular grid consisting of npoints points and
ntri triangles. The triangles can either be specified by the user
or automatically generated using a Delaunay triangulation.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>x, y</strong> : array_like of shape (npoints)</p>
<blockquote>
<div><p>Coordinates of grid points.</p>
</div></blockquote>
<p><strong>triangles</strong> : integer array_like of shape (ntri, 3), optional</p>
<blockquote>
<div><p>For each triangle, the indices of the three points that make
up the triangle, ordered in an anticlockwise manner. If not
specified, the Delaunay triangulation is calculated.</p>
</div></blockquote>
<p><strong>mask</strong> : boolean array_like of shape (ntri), optional</p>
<blockquote class="last">
<div><p>Which triangles are masked out.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>For a Triangulation to be valid it must not have duplicate points,
triangles formed from colinear points, or overlapping triangles.</p>
<p class="rubric">Attributes</p>
<table border="1" class="docutils">
<colgroup>
<col width="9%" />
<col width="91%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#matplotlib.tri.Triangulation.edges" title="matplotlib.tri.Triangulation.edges"><code class="xref py py-obj docutils literal"><span class="pre">edges</span></code></a></td>
<td> </td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#matplotlib.tri.Triangulation.neighbors" title="matplotlib.tri.Triangulation.neighbors"><code class="xref py py-obj docutils literal"><span class="pre">neighbors</span></code></a></td>
<td> </td>
</tr>
<tr class="row-odd"><td>is_delaunay</td>
<td>(bool) Whether the Triangulation is a calculated Delaunay triangulation (where <code class="xref py py-obj docutils literal"><span class="pre">triangles</span></code> was not specified) or not.</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="matplotlib.tri.Triangulation.calculate_plane_coefficients">
<code class="descname">calculate_plane_coefficients</code><span class="sig-paren">(</span><em>z</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.Triangulation.calculate_plane_coefficients" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculate plane equation coefficients for all unmasked triangles from
the point (x,y) coordinates and specified z-array of shape (npoints).
Returned array has shape (npoints,3) and allows z-value at (x,y)
position in triangle tri to be calculated using
z = array[tri,0]*x + array[tri,1]*y + array[tri,2].</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.tri.Triangulation.edges">
<code class="descname">edges</code><a class="headerlink" href="#matplotlib.tri.Triangulation.edges" title="Permalink to this definition">¶</a></dt>
<dd><p>Return integer array of shape (nedges,2) containing all edges of
non-masked triangles.</p>
<p>Each edge is the start point index and end point index. Each
edge (start,end and end,start) appears only once.</p>
</dd></dl>
<dl class="staticmethod">
<dt id="matplotlib.tri.Triangulation.get_from_args_and_kwargs">
<em class="property">static </em><code class="descname">get_from_args_and_kwargs</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.Triangulation.get_from_args_and_kwargs" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a Triangulation object from the args and kwargs, and
the remaining args and kwargs with the consumed values removed.</p>
<p>There are two alternatives: either the first argument is a
Triangulation object, in which case it is returned, or the args
and kwargs are sufficient to create a new Triangulation to
return. In the latter case, see Triangulation.__init__ for
the possible args and kwargs.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.tri.Triangulation.get_masked_triangles">
<code class="descname">get_masked_triangles</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.Triangulation.get_masked_triangles" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an array of triangles that are not masked.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.tri.Triangulation.get_trifinder">
<code class="descname">get_trifinder</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.Triangulation.get_trifinder" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the default <a class="reference internal" href="#matplotlib.tri.TriFinder" title="matplotlib.tri.TriFinder"><code class="xref py py-class docutils literal"><span class="pre">matplotlib.tri.TriFinder</span></code></a> of this
triangulation, creating it if necessary. This allows the same
TriFinder object to be easily shared.</p>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.tri.Triangulation.neighbors">
<code class="descname">neighbors</code><a class="headerlink" href="#matplotlib.tri.Triangulation.neighbors" title="Permalink to this definition">¶</a></dt>
<dd><p>Return integer array of shape (ntri,3) containing neighbor
triangles.</p>
<p>For each triangle, the indices of the three triangles that
share the same edges, or -1 if there is no such neighboring
triangle. neighbors[i,j] is the triangle that is the neighbor
to the edge from point index triangles[i,j] to point index
triangles[i,(j+1)%3].</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.tri.Triangulation.set_mask">
<code class="descname">set_mask</code><span class="sig-paren">(</span><em>mask</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.Triangulation.set_mask" title="Permalink to this definition">¶</a></dt>
<dd><p>Set or clear the mask array. This is either None, or a boolean
array of shape (ntri).</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.TriFinder">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">TriFinder</code><span class="sig-paren">(</span><em>triangulation</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TriFinder" title="Permalink to this definition">¶</a></dt>
<dd><p>Abstract base class for classes used to find the triangles of a
Triangulation in which (x,y) points lie.</p>
<p>Rather than instantiate an object of a class derived from TriFinder, it is
usually better to use the function
<a class="reference internal" href="#matplotlib.tri.Triangulation.get_trifinder" title="matplotlib.tri.Triangulation.get_trifinder"><code class="xref py py-func docutils literal"><span class="pre">matplotlib.tri.Triangulation.get_trifinder()</span></code></a>.</p>
<p>Derived classes implement __call__(x,y) where x,y are array_like point
coordinates of the same shape.</p>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.TrapezoidMapTriFinder">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">TrapezoidMapTriFinder</code><span class="sig-paren">(</span><em>triangulation</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TrapezoidMapTriFinder" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">matplotlib.tri.trifinder.TriFinder</span></code></p>
<p><a class="reference internal" href="#matplotlib.tri.TriFinder" title="matplotlib.tri.TriFinder"><code class="xref py py-class docutils literal"><span class="pre">TriFinder</span></code></a> class implemented using the trapezoid
map algorithm from the book “Computational Geometry, Algorithms and
Applications”, second edition, by M. de Berg, M. van Kreveld, M. Overmars
and O. Schwarzkopf.</p>
<p>The triangulation must be valid, i.e. it must not have duplicate points,
triangles formed from colinear points, or overlapping triangles. The
algorithm has some tolerance to triangles formed from colinear points, but
this should not be relied upon.</p>
<dl class="method">
<dt id="matplotlib.tri.TrapezoidMapTriFinder.__call__">
<code class="descname">__call__</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TrapezoidMapTriFinder.__call__" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an array containing the indices of the triangles in which the
specified x,y points lie, or -1 for points that do not lie within a
triangle.</p>
<p><em>x</em>, <em>y</em> are array_like x and y coordinates of the same shape and any
number of dimensions.</p>
<p>Returns integer array with the same shape and <em>x</em> and <em>y</em>.</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.TriInterpolator">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">TriInterpolator</code><span class="sig-paren">(</span><em>triangulation</em>, <em>z</em>, <em>trifinder=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TriInterpolator" title="Permalink to this definition">¶</a></dt>
<dd><p>Abstract base class for classes used to perform interpolation on
triangular grids.</p>
<p>Derived classes implement the following methods:</p>
<blockquote>
<div><ul class="simple">
<li><code class="docutils literal"><span class="pre">__call__(x,</span> <span class="pre">y)</span></code> ,
where x, y are array_like point coordinates of the same shape, and
that returns a masked array of the same shape containing the
interpolated z-values.</li>
<li><code class="docutils literal"><span class="pre">gradient(x,</span> <span class="pre">y)</span></code> ,
where x, y are array_like point coordinates of the same
shape, and that returns a list of 2 masked arrays of the same shape
containing the 2 derivatives of the interpolator (derivatives of
interpolated z values with respect to x and y).</li>
</ul>
</div></blockquote>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.LinearTriInterpolator">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">LinearTriInterpolator</code><span class="sig-paren">(</span><em>triangulation</em>, <em>z</em>, <em>trifinder=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.LinearTriInterpolator" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">matplotlib.tri.triinterpolate.TriInterpolator</span></code></p>
<p>A LinearTriInterpolator performs linear interpolation on a triangular grid.</p>
<p>Each triangle is represented by a plane so that an interpolated value at
point (x,y) lies on the plane of the triangle containing (x,y).
Interpolated values are therefore continuous across the triangulation, but
their first derivatives are discontinuous at edges between triangles.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>triangulation</strong> : <a class="reference internal" href="#matplotlib.tri.Triangulation" title="matplotlib.tri.Triangulation"><code class="xref py py-class docutils literal"><span class="pre">Triangulation</span></code></a> object</p>
<blockquote>
<div><p>The triangulation to interpolate over.</p>
</div></blockquote>
<p><strong>z</strong> : array_like of shape (npoints,)</p>
<blockquote>
<div><p>Array of values, defined at grid points, to interpolate between.</p>
</div></blockquote>
<p><strong>trifinder</strong> : <a class="reference internal" href="#matplotlib.tri.TriFinder" title="matplotlib.tri.TriFinder"><code class="xref py py-class docutils literal"><span class="pre">TriFinder</span></code></a> object, optional</p>
<blockquote class="last">
<div><p>If this is not specified, the Triangulation’s default TriFinder will
be used by calling
<a class="reference internal" href="#matplotlib.tri.Triangulation.get_trifinder" title="matplotlib.tri.Triangulation.get_trifinder"><code class="xref py py-func docutils literal"><span class="pre">matplotlib.tri.Triangulation.get_trifinder()</span></code></a>.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Methods</p>
<table border="1" class="docutils">
<colgroup>
<col width="26%" />
<col width="74%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#matplotlib.tri.LinearTriInterpolator.__call__" title="matplotlib.tri.LinearTriInterpolator.__call__"><code class="xref py py-obj docutils literal"><span class="pre">__call__</span></code></a> (x, y)</td>
<td>( Returns interpolated values at x,y points)</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#matplotlib.tri.LinearTriInterpolator.gradient" title="matplotlib.tri.LinearTriInterpolator.gradient"><code class="xref py py-obj docutils literal"><span class="pre">gradient</span></code></a> (x, y)</td>
<td>(Returns interpolated derivatives at x,y points)</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="matplotlib.tri.LinearTriInterpolator.__call__">
<code class="descname">__call__</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.LinearTriInterpolator.__call__" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a masked array containing interpolated values at the specified
x,y points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>x, y</strong> : array-like</p>
<blockquote>
<div><p>x and y coordinates of the same shape and any number of
dimensions.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>z</strong> : np.ma.array</p>
<blockquote class="last">
<div><p>Masked array of the same shape as <em>x</em> and <em>y</em> ; values
corresponding to (<em>x</em>, <em>y</em>) points outside of the triangulation
are masked out.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="matplotlib.tri.LinearTriInterpolator.gradient">
<code class="descname">gradient</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.LinearTriInterpolator.gradient" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a list of 2 masked arrays containing interpolated derivatives
at the specified x,y points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>x, y</strong> : array-like</p>
<blockquote>
<div><p>x and y coordinates of the same shape and any number of
dimensions.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>dzdx, dzdy</strong> : np.ma.array</p>
<blockquote class="last">
<div><p>2 masked arrays of the same shape as <em>x</em> and <em>y</em> ; values
corresponding to (x,y) points outside of the triangulation
are masked out.
The first returned array contains the values of
<img src="../_images/mathmpl/math-c05929fd30.png" style="position: relative; bottom: -10px"/> and the second those of
<img src="../_images/mathmpl/math-99abe4d704.png" style="position: relative; bottom: -13px"/>.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.CubicTriInterpolator">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">CubicTriInterpolator</code><span class="sig-paren">(</span><em>triangulation</em>, <em>z</em>, <em>kind='min_E'</em>, <em>trifinder=None</em>, <em>dz=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.CubicTriInterpolator" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">matplotlib.tri.triinterpolate.TriInterpolator</span></code></p>
<p>A CubicTriInterpolator performs cubic interpolation on triangular grids.</p>
<p>In one-dimension - on a segment - a cubic interpolating function is
defined by the values of the function and its derivative at both ends.
This is almost the same in 2-d inside a triangle, except that the values
of the function and its 2 derivatives have to be defined at each triangle
node.</p>
<p>The CubicTriInterpolator takes the value of the function at each node -
provided by the user - and internally computes the value of the
derivatives, resulting in a smooth interpolation.
(As a special feature, the user can also impose the value of the
derivatives at each node, but this is not supposed to be the common
usage.)</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>triangulation</strong> : <a class="reference internal" href="#matplotlib.tri.Triangulation" title="matplotlib.tri.Triangulation"><code class="xref py py-class docutils literal"><span class="pre">Triangulation</span></code></a> object</p>
<blockquote>
<div><p>The triangulation to interpolate over.</p>
</div></blockquote>
<p><strong>z</strong> : array_like of shape (npoints,)</p>
<blockquote>
<div><p>Array of values, defined at grid points, to interpolate between.</p>
</div></blockquote>
<p><strong>kind</strong> : {‘min_E’, ‘geom’, ‘user’}, optional</p>
<blockquote>
<div><p>Choice of the smoothing algorithm, in order to compute
the interpolant derivatives (defaults to ‘min_E’):</p>
<blockquote>
<div><ul class="simple">
<li>if ‘min_E’: (default) The derivatives at each node is computed
to minimize a bending energy.</li>
<li>if ‘geom’: The derivatives at each node is computed as a
weighted average of relevant triangle normals. To be used for
speed optimization (large grids).</li>
<li>if ‘user’: The user provides the argument <code class="xref py py-obj docutils literal"><span class="pre">dz</span></code>, no computation
is hence needed.</li>
</ul>
</div></blockquote>
</div></blockquote>
<p><strong>trifinder</strong> : <a class="reference internal" href="#matplotlib.tri.TriFinder" title="matplotlib.tri.TriFinder"><code class="xref py py-class docutils literal"><span class="pre">TriFinder</span></code></a> object, optional</p>
<blockquote>
<div><p>If not specified, the Triangulation’s default TriFinder will
be used by calling
<a class="reference internal" href="#matplotlib.tri.Triangulation.get_trifinder" title="matplotlib.tri.Triangulation.get_trifinder"><code class="xref py py-func docutils literal"><span class="pre">matplotlib.tri.Triangulation.get_trifinder()</span></code></a>.</p>
</div></blockquote>
<p><strong>dz</strong> : tuple of array_likes (dzdx, dzdy), optional</p>
<blockquote class="last">
<div><p>Used only if <em>kind</em> =’user’. In this case <em>dz</em> must be provided as
(dzdx, dzdy) where dzdx, dzdy are arrays of the same shape as <em>z</em> and
are the interpolant first derivatives at the <em>triangulation</em> points.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>This note is a bit technical and details the way a
<a class="reference internal" href="#matplotlib.tri.CubicTriInterpolator" title="matplotlib.tri.CubicTriInterpolator"><code class="xref py py-class docutils literal"><span class="pre">CubicTriInterpolator</span></code></a> computes a cubic
interpolation.</p>
<p>The interpolation is based on a Clough-Tocher subdivision scheme of
the <em>triangulation</em> mesh (to make it clearer, each triangle of the
grid will be divided in 3 child-triangles, and on each child triangle
the interpolated function is a cubic polynomial of the 2 coordinates).
This technique originates from FEM (Finite Element Method) analysis;
the element used is a reduced Hsieh-Clough-Tocher (HCT)
element. Its shape functions are described in <a class="reference internal" href="#r1" id="id1">[R1]</a>.
The assembled function is guaranteed to be C1-smooth, i.e. it is
continuous and its first derivatives are also continuous (this
is easy to show inside the triangles but is also true when crossing the
edges).</p>
<p>In the default case (<em>kind</em> =’min_E’), the interpolant minimizes a
curvature energy on the functional space generated by the HCT element
shape functions - with imposed values but arbitrary derivatives at each
node. The minimized functional is the integral of the so-called total
curvature (implementation based on an algorithm from <a class="reference internal" href="#r2" id="id2">[R2]</a> - PCG sparse
solver):</p>
<blockquote>
<div><img src="../_images/mathmpl/math-4d96f7ca18.png" class="center" /></div></blockquote>
<p>If the case <em>kind</em> =’geom’ is chosen by the user, a simple geometric
approximation is used (weighted average of the triangle normal
vectors), which could improve speed on very large grids.</p>
<p class="rubric">References</p>
<table class="docutils citation" frame="void" id="r1" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[R1]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id3">2</a>)</em> Michel Bernadou, Kamal Hassan, “Basis functions for general
Hsieh-Clough-Tocher triangles, complete or reduced.”,
International Journal for Numerical Methods in Engineering,
17(5):784 - 789. 2.01.</td></tr>
</tbody>
</table>
<table class="docutils citation" frame="void" id="r2" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[R2]</td><td><em>(<a class="fn-backref" href="#id2">1</a>, <a class="fn-backref" href="#id4">2</a>)</em> C.T. Kelley, “Iterative Methods for Optimization”.</td></tr>
</tbody>
</table>
<p class="rubric">Methods</p>
<table border="1" class="docutils">
<colgroup>
<col width="26%" />
<col width="74%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#matplotlib.tri.CubicTriInterpolator.__call__" title="matplotlib.tri.CubicTriInterpolator.__call__"><code class="xref py py-obj docutils literal"><span class="pre">__call__</span></code></a> (x, y)</td>
<td>( Returns interpolated values at x,y points)</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#matplotlib.tri.CubicTriInterpolator.gradient" title="matplotlib.tri.CubicTriInterpolator.gradient"><code class="xref py py-obj docutils literal"><span class="pre">gradient</span></code></a> (x, y)</td>
<td>(Returns interpolated derivatives at x,y points)</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="matplotlib.tri.CubicTriInterpolator.__call__">
<code class="descname">__call__</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.CubicTriInterpolator.__call__" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a masked array containing interpolated values at the specified
x,y points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>x, y</strong> : array-like</p>
<blockquote>
<div><p>x and y coordinates of the same shape and any number of
dimensions.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>z</strong> : np.ma.array</p>
<blockquote class="last">
<div><p>Masked array of the same shape as <em>x</em> and <em>y</em> ; values
corresponding to (<em>x</em>, <em>y</em>) points outside of the triangulation
are masked out.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="matplotlib.tri.CubicTriInterpolator.gradient">
<code class="descname">gradient</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.CubicTriInterpolator.gradient" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a list of 2 masked arrays containing interpolated derivatives
at the specified x,y points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>x, y</strong> : array-like</p>
<blockquote>
<div><p>x and y coordinates of the same shape and any number of
dimensions.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>dzdx, dzdy</strong> : np.ma.array</p>
<blockquote class="last">
<div><p>2 masked arrays of the same shape as <em>x</em> and <em>y</em> ; values
corresponding to (x,y) points outside of the triangulation
are masked out.
The first returned array contains the values of
<img src="../_images/mathmpl/math-c05929fd30.png" style="position: relative; bottom: -10px"/> and the second those of
<img src="../_images/mathmpl/math-99abe4d704.png" style="position: relative; bottom: -13px"/>.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<p>An example of effective application is shown below (plot of the
direction of the vector field derivated from a known potential field):</p>
<p>(<a class="reference external" href="../mpl_examples/pylab_examples/trigradient_demo.py">Source code</a>, <a class="reference external" href="../mpl_examples/pylab_examples/trigradient_demo.png">png</a>, <a class="reference external" href="../mpl_examples/pylab_examples/trigradient_demo.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/trigradient_demo1.png" src="../_images/trigradient_demo1.png" />
</div>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.TriRefiner">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">TriRefiner</code><span class="sig-paren">(</span><em>triangulation</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TriRefiner" title="Permalink to this definition">¶</a></dt>
<dd><p>Abstract base class for classes implementing mesh refinement.</p>
<p>A TriRefiner encapsulates a Triangulation object and provides tools for
mesh refinement and interpolation.</p>
<p>Derived classes must implements:</p>
<blockquote>
<div><ul>
<li><p class="first"><code class="docutils literal"><span class="pre">refine_triangulation(return_tri_index=False,</span> <span class="pre">**kwargs)</span></code> , where
the optional keyword arguments <em>kwargs</em> are defined in each
TriRefiner concrete implementation, and which returns :</p>
<blockquote>
<div><ul class="simple">
<li>a refined triangulation</li>
<li>optionally (depending on <em>return_tri_index</em>), for each
point of the refined triangulation: the index of
the initial triangulation triangle to which it belongs.</li>
</ul>
</div></blockquote>
</li>
<li><p class="first"><code class="docutils literal"><span class="pre">refine_field(z,</span> <span class="pre">triinterpolator=None,</span> <span class="pre">**kwargs)</span></code> , where:</p>
<blockquote>
<div><ul class="simple">
<li><em>z</em> array of field values (to refine) defined at the base
triangulation nodes</li>
<li><em>triinterpolator</em> is a
<a class="reference internal" href="#matplotlib.tri.TriInterpolator" title="matplotlib.tri.TriInterpolator"><code class="xref py py-class docutils literal"><span class="pre">TriInterpolator</span></code></a> (optional)</li>
<li>the other optional keyword arguments <em>kwargs</em> are defined in
each TriRefiner concrete implementation</li>
</ul>
</div></blockquote>
<p>and which returns (as a tuple) a refined triangular mesh and the
interpolated values of the field at the refined triangulation nodes.</p>
</li>
</ul>
</div></blockquote>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.UniformTriRefiner">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">UniformTriRefiner</code><span class="sig-paren">(</span><em>triangulation</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.UniformTriRefiner" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">matplotlib.tri.trirefine.TriRefiner</span></code></p>
<p>Uniform mesh refinement by recursive subdivisions.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>triangulation</strong> : <a class="reference internal" href="#matplotlib.tri.Triangulation" title="matplotlib.tri.Triangulation"><code class="xref py py-class docutils literal"><span class="pre">Triangulation</span></code></a></p>
<blockquote class="last">
<div><p>The encapsulated triangulation (to be refined)</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="matplotlib.tri.UniformTriRefiner.refine_field">
<code class="descname">refine_field</code><span class="sig-paren">(</span><em>z</em>, <em>triinterpolator=None</em>, <em>subdiv=3</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.UniformTriRefiner.refine_field" title="Permalink to this definition">¶</a></dt>
<dd><p>Refines a field defined on the encapsulated triangulation.</p>
<p>Returns <em>refi_tri</em> (refined triangulation), <em>refi_z</em> (interpolated
values of the field at the node of the refined triangulation).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>z</strong> : 1d-array-like of length <code class="docutils literal"><span class="pre">n_points</span></code></p>
<blockquote>
<div><p>Values of the field to refine, defined at the nodes of the
encapsulated triangulation. (<code class="docutils literal"><span class="pre">n_points</span></code> is the number of points
in the initial triangulation)</p>
</div></blockquote>
<p><strong>triinterpolator</strong> : <a class="reference internal" href="#matplotlib.tri.TriInterpolator" title="matplotlib.tri.TriInterpolator"><code class="xref py py-class docutils literal"><span class="pre">TriInterpolator</span></code></a>, optional</p>
<blockquote>
<div><p>Interpolator used for field interpolation. If not specified,
a <a class="reference internal" href="#matplotlib.tri.CubicTriInterpolator" title="matplotlib.tri.CubicTriInterpolator"><code class="xref py py-class docutils literal"><span class="pre">CubicTriInterpolator</span></code></a> will
be used.</p>
</div></blockquote>
<p><strong>subdiv</strong> : integer, optional</p>
<blockquote>
<div><p>Recursion level for the subdivision. Defaults to 3.
Each triangle will be divided into <code class="docutils literal"><span class="pre">4**subdiv</span></code> child triangles.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>refi_tri</strong> : <a class="reference internal" href="#matplotlib.tri.Triangulation" title="matplotlib.tri.Triangulation"><code class="xref py py-class docutils literal"><span class="pre">Triangulation</span></code></a> object</p>
<blockquote>
<div><p>The returned refined triangulation</p>
</div></blockquote>
<p><strong>refi_z</strong> : 1d array of length: <em>refi_tri</em> node count.</p>
<blockquote class="last">
<div><p>The returned interpolated field (at <em>refi_tri</em> nodes)</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<p>The main application of this method is to plot high-quality
iso-contours on a coarse triangular grid (e.g., triangulation built
from relatively sparse test data):</p>
<p>(<a class="reference external" href="../mpl_examples/pylab_examples/tricontour_smooth_user.py">Source code</a>, <a class="reference external" href="../mpl_examples/pylab_examples/tricontour_smooth_user.png">png</a>, <a class="reference external" href="../mpl_examples/pylab_examples/tricontour_smooth_user.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/tricontour_smooth_user1.png" src="../_images/tricontour_smooth_user1.png" />
</div>
</dd></dl>
<dl class="method">
<dt id="matplotlib.tri.UniformTriRefiner.refine_triangulation">
<code class="descname">refine_triangulation</code><span class="sig-paren">(</span><em>return_tri_index=False</em>, <em>subdiv=3</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.UniformTriRefiner.refine_triangulation" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes an uniformly refined triangulation <em>refi_triangulation</em> of
the encapsulated <code class="xref py py-attr docutils literal"><span class="pre">triangulation</span></code>.</p>
<p>This function refines the encapsulated triangulation by splitting each
father triangle into 4 child sub-triangles built on the edges midside
nodes, recursively (level of recursion <em>subdiv</em>).
In the end, each triangle is hence divided into <code class="docutils literal"><span class="pre">4**subdiv</span></code>
child triangles.
The default value for <em>subdiv</em> is 3 resulting in 64 refined
subtriangles for each triangle of the initial triangulation.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>return_tri_index</strong> : boolean, optional</p>
<blockquote>
<div><p>Boolean indicating whether an index table indicating the father
triangle index of each point will be returned. Default value
False.</p>
</div></blockquote>
<p><strong>subdiv</strong> : integer, optional</p>
<blockquote>
<div><p>Recursion level for the subdivision. Defaults value 3.
Each triangle will be divided into <code class="docutils literal"><span class="pre">4**subdiv</span></code> child triangles.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>refi_triangulation</strong> : <a class="reference internal" href="#matplotlib.tri.Triangulation" title="matplotlib.tri.Triangulation"><code class="xref py py-class docutils literal"><span class="pre">Triangulation</span></code></a></p>
<blockquote>
<div><p>The returned refined triangulation</p>
</div></blockquote>
<p><strong>found_index</strong> : array-like of integers</p>
<blockquote class="last">
<div><p>Index of the initial triangulation containing triangle, for each
point of <em>refi_triangulation</em>.
Returned only if <em>return_tri_index</em> is set to True.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.tri.TriAnalyzer">
<em class="property">class </em><code class="descclassname">matplotlib.tri.</code><code class="descname">TriAnalyzer</code><span class="sig-paren">(</span><em>triangulation</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TriAnalyzer" title="Permalink to this definition">¶</a></dt>
<dd><p>Define basic tools for triangular mesh analysis and improvement.</p>
<p>A TriAnalizer encapsulates a <a class="reference internal" href="#matplotlib.tri.Triangulation" title="matplotlib.tri.Triangulation"><code class="xref py py-class docutils literal"><span class="pre">Triangulation</span></code></a>
object and provides basic tools for mesh analysis and mesh improvement.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>triangulation</strong> : <a class="reference internal" href="#matplotlib.tri.Triangulation" title="matplotlib.tri.Triangulation"><code class="xref py py-class docutils literal"><span class="pre">Triangulation</span></code></a> object</p>
<blockquote class="last">
<div><p>The encapsulated triangulation to analyze.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Attributes</p>
<table border="1" class="docutils">
<colgroup>
<col width="60%" />
<col width="40%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#matplotlib.tri.TriAnalyzer.scale_factors" title="matplotlib.tri.TriAnalyzer.scale_factors"><code class="xref py py-obj docutils literal"><span class="pre">scale_factors</span></code></a></td>
<td> </td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="matplotlib.tri.TriAnalyzer.circle_ratios">
<code class="descname">circle_ratios</code><span class="sig-paren">(</span><em>rescale=True</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TriAnalyzer.circle_ratios" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a measure of the triangulation triangles flatness.</p>
<p>The ratio of the incircle radius over the circumcircle radius is a
widely used indicator of a triangle flatness.
It is always <code class="docutils literal"><span class="pre"><=</span> <span class="pre">0.5</span></code> and <code class="docutils literal"><span class="pre">==</span> <span class="pre">0.5</span></code> only for equilateral
triangles. Circle ratios below 0.01 denote very flat triangles.</p>
<p>To avoid unduly low values due to a difference of scale between the 2
axis, the triangular mesh can first be rescaled to fit inside a unit
square with <a class="reference internal" href="#matplotlib.tri.TriAnalyzer.scale_factors" title="matplotlib.tri.TriAnalyzer.scale_factors"><code class="xref py py-attr docutils literal"><span class="pre">scale_factors</span></code></a> (Only if <em>rescale</em> is True, which is
its default value).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>rescale</strong> : boolean, optional</p>
<blockquote>
<div><p>If True, a rescaling will be internally performed (based on
<a class="reference internal" href="#matplotlib.tri.TriAnalyzer.scale_factors" title="matplotlib.tri.TriAnalyzer.scale_factors"><code class="xref py py-attr docutils literal"><span class="pre">scale_factors</span></code></a>, so that the (unmasked) triangles fit
exactly inside a unit square mesh. Default is True.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>circle_ratios</strong> : masked array</p>
<blockquote class="last">
<div><p>Ratio of the incircle radius over the
circumcircle radius, for each ‘rescaled’ triangle of the
encapsulated triangulation.
Values corresponding to masked triangles are masked out.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="matplotlib.tri.TriAnalyzer.get_flat_tri_mask">
<code class="descname">get_flat_tri_mask</code><span class="sig-paren">(</span><em>min_circle_ratio=0.01</em>, <em>rescale=True</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.tri.TriAnalyzer.get_flat_tri_mask" title="Permalink to this definition">¶</a></dt>
<dd><p>Eliminates excessively flat border triangles from the triangulation.</p>
<p>Returns a mask <em>new_mask</em> which allows to clean the encapsulated
triangulation from its border-located flat triangles
(according to their <a class="reference internal" href="#matplotlib.tri.TriAnalyzer.circle_ratios" title="matplotlib.tri.TriAnalyzer.circle_ratios"><code class="xref py py-meth docutils literal"><span class="pre">circle_ratios()</span></code></a>).
This mask is meant to be subsequently applied to the triangulation
using <a class="reference internal" href="#matplotlib.tri.Triangulation.set_mask" title="matplotlib.tri.Triangulation.set_mask"><code class="xref py py-func docutils literal"><span class="pre">matplotlib.tri.Triangulation.set_mask()</span></code></a> .
<em>new_mask</em> is an extension of the initial triangulation mask
in the sense that an initially masked triangle will remain masked.</p>
<p>The <em>new_mask</em> array is computed recursively ; at each step flat
triangles are removed only if they share a side with the current
mesh border. Thus no new holes in the triangulated domain will be
created.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>min_circle_ratio</strong> : float, optional</p>
<blockquote>
<div><p>Border triangles with incircle/circumcircle radii ratio r/R will
be removed if r/R < <em>min_circle_ratio</em>. Default value: 0.01</p>
</div></blockquote>
<p><strong>rescale</strong> : boolean, optional</p>
<blockquote>
<div><p>If True, a rescaling will first be internally performed (based on
<a class="reference internal" href="#matplotlib.tri.TriAnalyzer.scale_factors" title="matplotlib.tri.TriAnalyzer.scale_factors"><code class="xref py py-attr docutils literal"><span class="pre">scale_factors</span></code></a> ), so that the (unmasked) triangles fit
exactly inside a unit square mesh. This rescaling accounts for the
difference of scale which might exist between the 2 axis. Default
(and recommended) value is True.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>new_mask</strong> : array-like of booleans</p>
<blockquote class="last">
<div><p>Mask to apply to encapsulated triangulation.
All the initially masked triangles remain masked in the
<em>new_mask</em>.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The rationale behind this function is that a Delaunay
triangulation - of an unstructured set of points - sometimes contains
almost flat triangles at its border, leading to artifacts in plots
(especially for high-resolution contouring).
Masked with computed <em>new_mask</em>, the encapsulated
triangulation would contain no more unmasked border triangles
with a circle ratio below <em>min_circle_ratio</em>, thus improving the
mesh quality for subsequent plots or interpolation.</p>
<p class="rubric">Examples</p>
<p>Please refer to the following illustrating example:</p>
<p>(<a class="reference external" href="../mpl_examples/pylab_examples/tricontour_smooth_delaunay.py">Source code</a>, <a class="reference external" href="../mpl_examples/pylab_examples/tricontour_smooth_delaunay.png">png</a>, <a class="reference external" href="../mpl_examples/pylab_examples/tricontour_smooth_delaunay.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/tricontour_smooth_delaunay1.png" src="../_images/tricontour_smooth_delaunay1.png" />
</div>
</dd></dl>
<dl class="attribute">
<dt id="matplotlib.tri.TriAnalyzer.scale_factors">
<code class="descname">scale_factors</code><a class="headerlink" href="#matplotlib.tri.TriAnalyzer.scale_factors" title="Permalink to this definition">¶</a></dt>
<dd><p>Factors to rescale the triangulation into a unit square.</p>
<p>Returns <em>k</em>, tuple of 2 scale factors.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>k</strong> : tuple of 2 floats (kx, ky)</p>
<blockquote class="last">
<div><p>Tuple of floats that would rescale the triangulation :
<code class="docutils literal"><span class="pre">[triangulation.x</span> <span class="pre">*</span> <span class="pre">kx,</span> <span class="pre">triangulation.y</span> <span class="pre">*</span> <span class="pre">ky]</span></code>
fits exactly inside a unit square.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
</div>
</div>
</div>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="footer">
© Copyright 2002 - 2012 John Hunter, Darren Dale, Eric Firing, Michael Droettboom and the Matplotlib development team; 2012 - 2016 The Matplotlib development team.
Last updated on May 10, 2017.
Created using <a
href="http://sphinx-doc.org/">Sphinx</a> 1.5.5.
</div>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-55954603-1', 'auto');
ga('send', 'pageview');
</script>
</body>
<footer>
</footer>
</html>