forked from johannesgerer/jburkardt-m
-
Notifications
You must be signed in to change notification settings - Fork 0
/
triangulation_boundary_nodes.html
374 lines (325 loc) · 10.9 KB
/
triangulation_boundary_nodes.html
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
<html>
<head>
<title>
TRIANGULATION_BOUNDARY_NODES - Boundary Nodes of a Triangulation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_BOUNDARY_NODES <br> Boundary Nodes of a Triangulation
</h1>
<hr>
<p>
<b>TRIANGULATION_BOUNDARY_NODES</b>
is a MATLAB program which
analyzes the triangulation
of a region, and identifies each boundary node with the label "1".
</p>
<p>
Either a 3-node or 6-node triangulation may be used.
</p>
<p>
Although this boundary information is useful, it would be more
useful to divide the boundary nodes up, if the boundary consists
of more than one connected segment. Moreover, it would also be
useful to report the sequence of nodes necessary to trace out
a connected segment of the boundary. I imagine I will come back
to work on those projects later!
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_boundary_nodes</b> ( <i>'prefix'</i> )
</blockquote>
where <i>prefix</i> is the common filename prefix:
<ul>
<li>
<i>prefix</i><b>_nodes.txt</b> contains the node coordinates,
</li>
<li>
<i>prefix</i><b>_elements.txt</b> contains the element definitions.
</li>
<li>
<i>prefix</i><b>_boundary_nodes.txt</b> will contain a 0 for each internal
node, and a 1 for each boundary node.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TRIANGULATION_BOUNDARY_NODES</b> is available in
<a href = "../../cpp_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">a C++ version</a> and
<a href = "../../f_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
triangulates a set of nodes whose coordinates are stored in a file.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
computes a triangulation of a geometric region.
</p>
<p>
<a href = "../../m_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a MATLAB library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_boundary_edges/triangulation_boundary_edges.html">
TRIANGULATION_BOUNDARY_EDGES</a>,
a MATLAB program which
reads data defining a triangulation, determines which edges
lie on the boundary, organizes them into connected components,
and writes this information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a MATLAB program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../m_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a MATLAB program which
measures the amount by which a triangulation fails the local Delaunay test;
</p>
<p>
<a href = "../../m_src/triangulation_display/triangulation_display.html">
TRIANGULATION_DISPLAY</a>,
a MATLAB program which
displays the nodes and elements of a triangulation on the MATLAB graphics screen;
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image using Open GL.
</p>
<p>
<a href = "../../m_src/triangulation_histogram/triangulation_histogram.html">
TRIANGULATION_HISTOGRAM</a>,
a MATLAB program which
computes histograms of data over a triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a MATLAB program which
reads data defining a 3-node triangulation and generates
midside nodes and writes out the corresponding 6-node triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a MATLAB program which
takes an existing triangulation and deletes triangles and
their corresponding nodes as requested by the user.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a data directory which
contains a description and
examples of order 3 triangulations.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a data directory which
contains a description and examples of order 6 triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a MATLAB program which
reads data defining a triangulation, makes sure that
every triangle has positive orientation, and if not, writes a
corrected triangle file.
</p>
<p>
<a href = "../../m_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a MATLAB program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../m_src/triangulation_q2l/triangulation_q2l.html">
TRIANGULATION_Q2L</a>,
a MATLAB program which
reads data defining a 6-node triangulation, and subdivides
each triangle into 4 3-node triangles, writing the resulting
triangulation to a file.
</p>
<p>
<a href = "../../m_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a MATLAB program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../m_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a MATLAB program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../m_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a MATLAB program which
reads data defining a triangulation, determines an ordering
of the nodes that will reduce the bandwidth of the adjacency
matrix, and writes the new triangulation information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a MATLAB program which
reads data defining a triangulation, replaces each triangle
by four congruent smaller ones, and writes the new triangulation
information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>,
a MATLAB program which
reads data defining a triangulation, determines the neighboring
triangles of each triangle, and writes that information to a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Marc deBerg, Marc Krevald, Mark Overmars,
Otfried Schwarzkopf,<br>
Computational Geometry,<br>
Springer, 2000,<br>
ISBN: 3-540-65620-0.
</li>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Second Edition,<br>
Cambridge, 1998,<br>
ISBN: 0521649765,<br>
LC: QA448.D38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangulation_boundary_nodes.m">triangulation_boundary_nodes.m</a>
is the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>ELBOW</b> is a curved region, looking like an elbow, that lies inside
the unit square. It is triangulated using order 3 triangles. There are
320 nodes and 568 triangles. There are 66 nodes on the boundary.
<ul>
<li>
<a href = "elbow_nodes.txt">elbow_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "elbow_nodes.png">elbow_nodes.png</a>,
a PNG image of the nodes.
</li>
<li>
<a href = "elbow_elements.txt">elbow_elements.txt</a>,
the triangles.
</li>
<li>
<a href = "elbow_output.txt">elbow_output.txt</a>,
the printed output from a run of the sample program.
</li>
<li>
<a href = "elbow_boundary_nodes.txt">
elbow_boundary_nodes.txt</a>,
the boundary node file.
</li>
<li>
<a href = "elbow_boundary_nodes.png">
elbow_boundary_nodes.png</a>,
a PNG image of the boundary nodes.
</li>
</ul>
</p>
<p>
<b>LAKE</b> is an irregular lake-shaped region with an "island".
It is triangulated using order 3 triangles.
<ul>
<li>
<a href = "lake_nodes.txt">lake_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "lake_nodes.png">lake_nodes.png</a>,
a PNG image of the nodes.
</li>
<li>
<a href = "lake_elements.txt">lake_elements.txt</a>,
the triangles.
</li>
<li>
<a href = "lake_output.txt">lake_output.txt</a>,
the printed output from a run of the sample program.
</li>
<li>
<a href = "lake_boundary_nodes.txt">
lake_boundary_nodes.txt</a>,
the boundary node file.
</li>
<li>
<a href = "lake_boundary_nodes.png">
lake_boundary_nodes.png</a>,
a PNG image of the boundary nodes.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 02 December 2010.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>