forked from johannesgerer/jburkardt-f
-
Notifications
You must be signed in to change notification settings - Fork 1
/
tet_mesh_l2q.html
470 lines (420 loc) · 13.7 KB
/
tet_mesh_l2q.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
459
460
461
462
463
464
465
466
467
468
469
470
<html>
<head>
<title>
TET_MESH_L2Q - 10-Node Tet Mesh from 4-Node Tet Mesh
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TET_MESH_L2Q <br> 10-Node Tet Mesh <br> from <br> 4-Node Tet Mesh
</h1>
<hr>
<p>
<b>TET_MESH_L2Q</b>
is a FORTRAN90 program which
converts a 4-node
tetrahedral mesh ("tet mesh") into a 10-node tet mesh.
</p>
<p>
In particular, <b>TET_MESH_L2Q</b> reads information
describing a set of 3D points, and a 4 node ("linear")
tet mesh of those points. It creates a "quadratic" tet
mesh, which has the same number of tetrahedrons, but in
which each tetrahedron is defined by 10 nodes. In the process,
it adds just enough nodes, at the midsides of the edges of
the original mesh, to define the new mesh. The data defining
the new mesh is written out to files for further use.
</p>
<p>
The refinement of a single tetrahedron is easy. Every pair
of nodes generates a new node whose location is the average of
the locations of the original two nodes. The problem is that
many tetrahedrons may share the same edge. The new node needs
to be generated exactly once, and assigned a unique index, which
all the tetrahedrons will share. The tricky part of this calculation
is thus figuring out whether it is time to generate a new node, or
whether the node has already been generated, in which case the
appropriate index must be retrieved.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>tet_mesh_l2q</b> <i>prefix</i>
</blockquote>
where <i>prefix</i> is the common file prefix:
<ul>
<li>
<i>prefix</i><b>_nodes.txt</b>, the node coordinates;
</li>
<li>
<i>prefix</i><b>_elements.txt</b>, the linear element definitions.
</li>
<li>
<i>prefix</i><b>_l2q_nodes.txt</b>, the quadratic node coordinates;
</li>
<li>
<i>prefix</i><b>_l2q_elements.txt</b>, the quadratic element definitions,
created by the program.
</li>
</ul>
</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 tetrahedron, (for a tetrahedron file).
</p>
<p>
The input file <i>prefix_nodes.txt</i> contains the coordinate information
for the 4-node tet mesh. Each data line contains the X and
Y coordinates of a single node.
</p>
<p>
The input file <i>prefix_elements.txt</i> contains the tetrahedron information
for the 4-node tet mesh. Each data line contains the indices
of four nodes that form a tetrahedron.
</p>
<p>
The output file <i>prefix_l2q_nodes.txt</i> contains the coordinate information
for the 10-node tet mesh. The data lines begin with the node
information from <i>nodes.txt</i>, followed by the coordinates of
the new nodes.
</p>
<p>
The output file <i>prefix_l2q_elements.txt</i> contains the tetrahedron
information for the 10-node tet mesh. There are exactly
as many tetrahedrons as before, but now each tetrahedron uses 10 nodes.
Each line of the file contains the indices of 10 nodes that form the
tetrahedron, listed in a particular order. The first four
node indices are the same as for the linear tet mesh. The next six
node indices may be thought of as being obtained as averages of
pairs of the first four nodes. Symbolically, this may be thought of as:
<pre>
1 2 3 4 (1+2) (1+3) (1+4) (2+3) (2+4) (3+4)
</pre>
</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>TET_MESH_L2Q</b> is available in
<a href = "../../cpp_src/tet_mesh_l2q/tet_mesh_l2q.html">a C++ version</a> and
<a href = "../../f_src/tet_mesh_l2q/tet_mesh_l2q.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tet_mesh_l2q/tet_mesh_l2q.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../f_src/cvt_tet_mesh/cvt_tet_mesh.html">
CVT_TET_MESH</a>,
a FORTRAN90 library which
uses CVT methods to compute a tet mesh in a region.
</p>
<p>
<a href = "../../f_src/table_tet_mesh/table_tet_mesh.html">
TABLE_TET_MESH</a>,
a FORTRAN90 program which
can compute the tet mesh for a given set of points.
</p>
<p>
<a href = "../../f_src/test_tet_mesh/test_tet_mesh.html">
TEST_TET_MESH</a>,
a FORTRAN90 library which
defines a few test regions for the generation
of a tet mesh.
</p>
<p>
<a href = "../../f_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a FORTRAN90 library which
includes a variety of routines for working
with tetrahedral meshes.
</p>
<p>
<a href = "../../m_src/tet_mesh_display/tet_mesh_display.html">
TET_MESH_DISPLAY</a>,
a MATLAB program which
can read in the
node and tetra files defining a tet mesh and display a wireframe
image.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_display_opengl/tet_mesh_display_opengl.html">
TET_MESH_DISPLAY_OPENGL</a>,
a C++ program which
reads a tet mesh and displays the
nodes and edges using OpenGL.
</p>
<p>
<a href = "../../data/tet_mesh_order4/tet_mesh_order4.html">
TET_MESH_ORDER4</a>,
a directory which
contains a description and
examples of a tet mesh using order 4 elements.
</p>
<p>
<a href = "../../data/tet_mesh_order10/tet_mesh_order10.html">
TET_MESH_ORDER10</a>,
a directory which
contains a description and
examples of a tet mesh using order 10 elements.
</p>
<p>
<a href = "../../f_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a FORTRAN90 program which
takes a 10-node tet mesh and makes
a 4-node tet mesh.
</p>
<p>
<a href = "../../f_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a FORTRAN90 program which
takes a 4-node tet mesh and computes
the "quality" of the mesh.
</p>
<p>
<a href = "../../f_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a FORTRAN90 program which
takes a tet mesh and
relabels the nodes to reduce the bandwidth of the
corresponding adjacency matrix.
</p>
<p>
<a href = "../../f_src/tet_mesh_refine/tet_mesh_refine.html">
TET_MESH_REFINE</a>,
a FORTRAN90 program which
can refine a tet mesh.
</p>
<p>
<a href = "../../f_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a FORTRAN90 program which
computes the tetrahedral adjacency information.
</p>
<p>
<a href = "../../f_src/tet_mesh_volumes/tet_mesh_volumes.html">
TET_MESH_VOLUMES</a>,
a FORTRAN90 program which
computes the volume of each tetrahedron in a tet mesh;
</p>
<p>
<a href = "../../f_src/tetrahedron_properties/tetrahedron_properties.html">
TETRAHEDRON_PROPERTIES</a>,
a FORTRAN90 program which
computes properties of a given tetrahedron.
</p>
<p>
<a href = "../../datasets/tetrahedrons/tetrahedrons.html">
TETRAHEDRONS</a>,
a dataset directory which
contains examples of tetrahedrons;
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Herbert Edelsbrunner,<br>
Geometry and Topology for Mesh Generation,<br>
Cambridge, 2001,<br>
ISBN: 0-521-79309-2,<br>
LC: QA377.E36.
</li>
<li>
Barry Joe,<br>
GEOMPACK - a software package for the generation of meshes
using geometric algorithms,<br>
Advances in Engineering Software,<br>
Volume 13, Number 5, 1991, pages 325-331.
</li>
<li>
Anwei Liu, Barry Joe,<br>
Quality Local Refinement of Tetrahedral Meshes Based
on 8-Subtetrahedron Subdivision,<br>
Mathematics of Computation,<br>
Volume 65, Number 215, July 1996, pages 1183-1200.
</li>
<li>
Per-Olof Persson, Gilbert Strang,<br>
A Simple Mesh Generator in MATLAB,<br>
SIAM Review,<br>
Volume 46, Number 2, June 2004, pages 329-345.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "tet_mesh_l2q.f90">tet_mesh_l2q.f90</a>,
the source code.
</li>
<li>
<a href = "tet_mesh_l2q.sh">tet_mesh_l2q.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
You may copy data defining an initial 4-node tet mesh:
<ul>
<li>
<a href = "mesh_nodes.txt">mesh_nodes.txt</a>,
the nodes for the 4-node tet mesh.
</li>
<li>
<a href = "mesh_elements.txt">mesh_elements.txt</a>,
the elements for the 4-node tet mesh.
<li>
<a href = "mesh_l2q_nodes.txt">mesh_l2q_nodes.txt</a>,
the nodes for the 10-node tet mesh.
</li>
<li>
<a href = "mesh_l2q_elements.txt">mesh_l2q_elements.txt</a>,
the elements for the 10-node tet mesh.
</li>
<li>
<a href = "mesh_output.txt">mesh_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TET_MESH_L2Q.
</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_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_SWAP</b> swaps two I4's.
</li>
<li>
<b>I4COL_COMPARE</b> compares columns I and J of an I4COL.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts an I4COL.
</li>
<li>
<b>I4COL_SORT2_A</b> ascending sorts the elements of each column of an I4COL.
</li>
<li>
<b>I4COL_SORTED_UNIQUE_COUNT</b> counts unique elements in an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps columns I and J of an I4COL.
</li>
<li>
<b>I4I4_SORT_A</b> ascending sorts a pair of I4's.
</li>
<li>
<b>I4MAT_DATA_READ</b> reads data from an I4MAT file.
</li>
<li>
<b>I4MAT_HEADER_READ</b> reads the header from an I4MAT.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>I4MAT_WRITE</b> writes an I4MAT file.
</li>
<li>
<b>MESH_BASE_ONE</b> ensures that the element definition is one-based.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</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_TO_R8</b> reads an R8VEC from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TET_MESH_ORDER4_TO_ORDER10_COMPUTE</b> computes a quadratic tet mesh from a linear one.
</li>
<li>
<b>TET_MESH_ORDER4_TO_ORDER10_SIZE</b> sizes a quadratic tet mesh from a linear one.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 30 September 2009.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>