forked from johannesgerer/jburkardt-f
-
Notifications
You must be signed in to change notification settings - Fork 1
/
triangulation_quality.html
317 lines (281 loc) · 8.66 KB
/
triangulation_quality.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
<html>
<head>
<title>
TRIANGULATION_QUALITY - Triangulation Quality Measures
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_QUALITY <br>
Triangulation Quality Measures
</h1>
<hr>
<p>
<b>TRIANGULATION_QUALITY</b>
is a FORTRAN90 program which
computes and prints quality measures for a given triangulation of a set of points in 2D.
</p>
<p>
The triangulation is defined by a <i>node file</i> containing
the coordinates of nodes, and a <i>triangle file</i> containing
sets of 3 or 6 node indices.
</p>
<p>
The quality measures computed include:
<ul>
<li>
<b>Alpha</b>, the minimum angle divided by the maximum possible
minimum angle.
</li>
<li>
<b>Area</b>, the ratio of the minimum area to the maximum area;
</li>
<li>
<b>Q</b>, the triangle shape uniformity measure, twice the
radius of the inscribed circle divided by the radius of the
circumscribed circle;
</li>
</ul>
</p>
<p>
Each quality measure is defined as the minimum of its value
over all the triangles; the maximum and best possible value is
1, and the minimum and worst possible value is 0.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_quality</b> <i>prefix</i>
</blockquote>
where <i>prefix</i> is the common prefix for the node and element files
<ul>
<li>
<i>prefix</i><b>_nodes.txt</b>, the node coordinates;
</li>
<li>
<i>prefix</i><b>_elements.txt</b>, the element definitions.
</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_QUALITY</b> is available in
<a href = "../../cpp_src/triangulation_quality/triangulation_quality.html">a C++ version</a> and
<a href = "../../f_src/triangulation_quality/triangulation_quality.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_quality/triangulation_quality.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/distmesh/distmesh.html">
DISTMESH</a>,
a MATLAB library which
carries out triangular or tetrahedral mesh generation,
by Per-Olof Persson and Gilbert Strang.
</p>
<p>
<a href = "../../m_src/mesh2d/mesh2d.html">
MESH2D</a>,
a MATLAB library which
can automatically create a triangular mesh for a given polygonal region,
by Darren Engwirda.
</p>
<p>
<a href = "../../f_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a FORTRAN90 program which
computes quality measures of a tetrahedral mesh.
</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 = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a 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>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangulation_quality.f90">triangulation_quality.f90</a>,
the source code.
</li>
<li>
<a href = "triangulation_quality.sh">triangulation_quality.sh</a>,
commands to compile, link and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>ELL3</b> is a set of nodes in an L-shaped region, which have
been arranged into an order 3 triangulation.
<ul>
<li>
<a href = "../../data/triangulation_order3/ell3_nodes.txt">ell3_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "../../data/triangulation_order3/ell3_elements.txt">ell3_elements.txt</a>,
the element file.
</li>
<li>
<a href = "ell3_quality.txt">ell3_quality.txt</a>,
the report from the program.
</li>
</ul>
</p>
<p>
<b>HEX_HOLES6</b> is a set of nodes in an square region, with
two hexagonal holes, which have
been arranged into an order 6 triangulation.
<ul>
<li>
<a href = "../../data/triangulation_order6/hex_holes6_nodes.txt">hex_holes6_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "../../data/triangulation_order6/hex_holes6_elements.txt">
hex_holes6_elements.txt</a>,
the element file.
</li>
<li>
<a href = "hex_holes6_quality.txt">hex_holes6_quality.txt</a>,
the report from the program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TRIANGULATION_QUALITY.
</li>
<li>
<b>ALPHA_MEASURE</b> determines the triangulated pointset quality measure ALPHA.
</li>
<li>
<b>ARC_COSINE</b> computes the arc cosine function, with argument truncation.
</li>
<li>
<b>AREA_MEASURE</b> determines the area ratio quality measure.
</li>
<li>
<b>BANDWIDTH</b> determines the bandwidth associated with the finite element mesh.
</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>DTABLE_DATA_READ</b> reads data from a double precision table file.
</li>
<li>
<b>DTABLE_HEADER_READ</b> reads the header from a double precision table file.
</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>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_HEADER_READ</b> reads the header from an integer table file.
</li>
<li>
<b>Q_MEASURE</b> determines the triangulated pointset quality measure Q.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</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 R8 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>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 21 June 2009.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>