forked from xiaolongma/jburkardt-f
-
Notifications
You must be signed in to change notification settings - Fork 1
/
triangulation_q2l.html
458 lines (406 loc) · 13.5 KB
/
triangulation_q2l.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
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
<html>
<head>
<title>
TRIANGULATION_Q2L - 6-Node Triangulation to 3-Node Triangulation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_Q2L <br> 6-Node Triangulation to 3-Node Triangulation
</h1>
<hr>
<p>
<b>TRIANGULATION_Q2L</b>
is a FORTRAN90 program which
reads information
describing a triangulation of a set of points using 6-node
("quadratic") triangles, and creates a 3-node ("linear")
triangulation.
</p>
<p>
The same nodes are used, but each 6-node triangle is broken
up into four smaller 3-node triangles.
</p>
<p>
Thus, the program might be given the following 4 triangles:
<pre>
11-12-13-14-15
|\ |\ |
| \ | \ |
6 7 8 9 10
| \ | \ |
| \| \|
1--2--3--4--5
</pre>
</p>
<p>
It would make a new triangulation involving 16 triangles:
<pre>
11-12-13-14-15
|\ |\ |\ |\ |
| \| \| \| \|
6--7--8--9-10
|\ |\ |\ |\ |
| \| \| \| \|
1--2--3--4--5
</pre>
</p>
<p>
The input and output files use the simple
<a href = "../../data/table/table.html">TABLE format</a>;
comment lines begin with a "#" character. Otherwise, each line
of the file contains one set of information, either the coordinates
of a node (for a node file), or the indices of nodes that make up
a triangle, (for a triangle file).
</p>
<p>
The input file <i>prefix</i>_elements.txt</i> contains the triangle information
for the 6-node triangulation. Each line contains the indices of six
nodes that form a triangle, in counterclockwise order. The first three
indices are the vertices, in counterclockwise order. The fourth
index is the midside node between vertices 1 and 2, the fifth
the midside between vertices 2 and 3, and the sixth the midside
between vertices 3 and 1.
</p>
<p>
The output file <i>prefix</i>_q2l_elements.txt contains the triangle
information for the 3-node triangulation. The vertices for
each triangle are listed in counterclockwise order. There are
4 times as many triangles in this triangulation.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_q2l</b> <i>prefix</i>
</blockquote>
where <i>prefix</i> is the common filename prefix:
<ul>
<li>
<i>prefix</i>_nodes.txt contains the node coordinates (not needed by this program),
</li>
<li>
<i>prefix</i>_elements.txt contains the quadratic element definitions.
</li>
<li>
<i>prefix</i>_q2l_elements.txt will contain the linear element
definitions, based on the same set of nodes.
</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_Q2L</b> is available in
<a href = "../../cpp_src/triangulation_q2l/triangulation_q2l.html">a C++ version</a> and
<a href = "../../f_src/triangulation_q2l/triangulation_q2l.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_q2l/triangulation_q2l.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and 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 = "../../f_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a FORTRAN90 library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../f_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">
TRIANGULATION_BOUNDARY_NODES</a>,
a FORTRAN90 program which
reads data defining a triangulation, determines which nodes
lie on the boundary, and writes their coordinates to a file.
</p>
<p>
<a href = "../../f_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a FORTRAN90 program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../f_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a FORTRAN90 program which
measures the amount by which a triangulation fails the local Delaunay test;
</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 = "../../f_src/triangulation_histogram/triangulation_histogram.html">
TRIANGULATION_HISTOGRAM</a>,
a FORTRAN90 program which
computes histograms of data over a triangulation.
</p>
<p>
<a href = "../../f_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a FORTRAN90 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 = "../../f_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a FORTRAN90 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 = "../../f_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a FORTRAN90 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 = "../../f_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a FORTRAN90 program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../f_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a FORTRAN90 program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../f_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a FORTRAN90 program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../f_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a FORTRAN90 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 = "../../f_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a FORTRAN90 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 = "../../f_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>,
a FORTRAN90 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.
</li>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Cambridge University Press,<br>
Second Edition, 1998.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangulation_q2l.f90">triangulation_q2l.f90</a>,
the source code.
</li>
<li>
<a href = "triangulation_q2l.sh">triangulation_q2l.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>EXAMPLE</b> is a set of demonstration data.
<ul>
<li>
<a href = "example_nodes.txt">example_nodes.txt</a>,
the nodes.
</li>
<li>
<a href = "example_elements.txt">example_elements.txt</a>,
the triangles for the 6-node triangulation.
</li>
<li>
<a href = "example.png">example.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the 6-node triangulation, created by
<a href = "../triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>.
</li>
<li>
<a href = "example_q2l_elements.txt">example_q2l_elements.txt</a>,
the triangles for the 3-node triangulation.
</li>
<li>
<a href = "example_q2l.png">example_q2l.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the 3-node triangulation, created by
<a href = "../triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TRIANGULATION_Q2L.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_NAME_EXT_GET</b> determines the "extension" of a file name.
</li>
<li>
<b>FILE_NAME_EXT_SWAP</b> replaces the current "extension" of a file name.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_WRAP</b> forces an integer to lie between given limits by wrapping.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>ITABLE_DATA_READ</b> reads data from an integer table file.
</li>
<li>
<b>ITABLE_DATA_WRITE</b> writes data to an integer table file.
</li>
<li>
<b>ITABLE_HEADER_READ</b> reads the header from an integer table file.
</li>
<li>
<b>ITABLE_HEADER_WRITE</b> writes the header to an integer table file.
</li>
<li>
<b>ITABLE_WRITE</b> writes an integer table file.
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_INDEX_LAST</b> finds the LAST occurrence of a given substring.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an I4VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
<li>
<b>TRIANGULATION_ORDER6_TO_ORDER3</b> linearizes a quadratic triangulation.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 25 October 2006.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>