-
Notifications
You must be signed in to change notification settings - Fork 56
/
sphere_delaunay.html
371 lines (334 loc) · 11.2 KB
/
sphere_delaunay.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
<html>
<head>
<title>
SPHERE_DELAUNAY - Delaunay Triangulation of Points on the Unit Sphere
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPHERE_DELAUNAY <br> Delaunay Triangulation of Points on the Unit Sphere
</h1>
<hr>
<p>
<b>SPHERE_DELAUNAY</b>
is a MATLAB library which
computes the Delaunay triangulation of points on the unit sphere.
</p>
<p>
According to Steven Fortune, it is possible to compute the Delaunay triangulation
of points on a sphere by computing their convex hull. If the sphere is the unit
sphere at the origin, the facet normals are the Voronoi vertices.
</p>
<p>
<b>SPHERE_DELAUNAY</b> uses this approach, by calling MATLAB's <b>convhulln</b>
function to generate the convex hull. The information defining the convex hull
is actually the desired triangulation of the points. Since this computation
is so easy, other parts of the program are designed to analyze the resulting
Delaunay triangulation and return other information, such as the areas of the
triangles and so on.
</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>SPHERE_DELAUNAY</b> is available in
<a href = "../../f_src/sphere_delaunay/sphere_delaunay.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sphere_delaunay/sphere_delaunay.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/geometry/geometry.html">
GEOMETRY</a>,
a MATLAB library which
computes various geometric quantities, including grids on spheres.
</p>
<p>
<a href = "../../m_src/sphere_cvt/sphere_cvt.html">
SPHERE_CVT</a>,
a MATLAB library which
creates a mesh of well-separated points on a unit sphere by applying the
Centroidal Voronoi Tessellation (CVT) iteration.
</p>
<p>
<a href = "../../f_src/sphere_design_rule/sphere_design_rule.html">
SPHERE_DESIGN_RULE</a>,
a FORTRAN90 library which
returns point sets on the surface of the unit sphere, known as "designs",
which can be useful for estimating integrals on the surface, among other uses.
</p>
<p>
<a href = "../../m_src/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a MATLAB library which
provides a number of ways of generating grids of points, or of
points and lines, or of points and lines and faces, over the unit sphere.
</p>
<p>
<a href = "../../m_src/sphere_voronoi/sphere_voronoi.html">
SPHERE_VORONOI</a>,
a MATLAB program which
computes the Voronoi diagram of points on a sphere.
</p>
<p>
<a href = "../../cpp_src/sphere_voronoi_display_opengl/sphere_voronoi_display_opengl.html">
SPHERE_VORONOI_DISPLAY_OPENGL</a>,
a C++ program which
displays a sphere and randomly selected generator points, and then
gradually colors in points in the sphere that are closest to each generator.
</p>
<p>
<a href = "../../m_src/sphere_xyz_display/sphere_xyz_display.html">
SPHERE_XYZ_DISPLAY</a>,
a MATLAB program which
reads XYZ information defining points in 3D,
and displays a unit sphere and the points in the MATLAB graphics window.
</p>
<p>
<a href = "../../m_src/sphere_xyzf_display/sphere_xyzf_display.html">
SPHERE_XYZF_DISPLAY</a>,
a MATLAB program which
reads XYZF information defining points and faces,
and displays a unit sphere, the points, and the faces,
in the MATLAB graphics window. This can be used, for instance, to
display Voronoi diagrams or Delaunay triangulations on the unit sphere.
</p>
<p>
<a href = "../../f_src/stripack/stripack.html">
STRIPACK</a>,
a FORTRAN90 library which
computes the Delaunay triangulation or Voronoi diagram of points on a unit sphere.
</p>
<p>
<a href = "../../f_src/stripack_delaunay/stripack_delaunay.html">
STRIPACK_DELAUNAY</a>,
a FORTRAN90 program which
reads an XYZ file of 3D points on
the unit sphere, computes the Delaunay triangulation, and writes it
to a file.
</p>
<p>
<a href = "../../f77_src/toms772/toms772.html">
TOMS772</a>,
a FORTRAN77 library which
is the original text of the STRIPACK program.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Jacob Goodman, Joseph ORourke, editors,<br>
Handbook of Discrete and Computational Geometry,<br>
Second Edition,<br>
CRC/Chapman and Hall, 2004,<br>
ISBN: 1-58488-301-4,<br>
LC: QA167.H36.
</li>
<li>
Robert Renka,<br>
Algorithm 772: <br>
STRIPACK:
Delaunay Triangulation and Voronoi Diagram on the Surface
of a Sphere,<br>
ACM Transactions on Mathematical Software,<br>
Volume 23, Number 3, September 1997, pages 416-434.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "arc_cosine.m">arc_cosine.m</a>,
computes the inverse cosine function;
</li>
<li>
<a href = "arc_sine.m">arc_sine.m</a>,
computes the inverse cosine function;
</li>
<li>
<a href = "atan4.m">atan4.m</a>,
computes the inverse tangent;
</li>
<li>
<a href = "i4col_compare.m">i4col_compare.m</a>,
compares two columns of an I4COL;
</li>
<li>
<a href = "i4col_sort_a.m">i4col_sort_a.m</a>,
ascending sorts the columns of an I4COL;
</li>
<li>
<a href = "i4col_swap.m">
i4col_swap.m</a>,
swaps two columns of an I4COL;
</li>
<li>
<a href = "i4mat_transpose_print.m">i4mat_transpose_print.m</a>,
prints an I4MAT, transposed;
</li>
<li>
<a href = "i4mat_transpose_print_some.m">
i4mat_transpose_print_some.m</a>,
prints some of an I4MAT, transposed;
</li>
<li>
<a href = "icos_shape.m">icos_shape.m</a>,
returns the shape of an icosahedron.
</li>
<li>
<a href = "icos_size.m">icos_size.m</a>,
returns size information for an icosahedron.
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>,
prints the transpose of an R8MAT;
</li>
<li>
<a href = "r8mat_transpose_print_some.m">
r8mat_transpose_print_some.m</a>,
prints some of the transpose of an R8MAT;
</li>
<li>
<a href = "r8mat_uniform_01.m">r8mat_uniform_01.m</a>,
returns a unit pseudorandom R8MAT;
</li>
<li>
<a href = "r8vec_normal_01.m">r8vec_normal_01.m</a>,
returns unit pseudonormal R8VEC.
</li>
<li>
<a href = "r8vec_polarize.m">r8vec_polarize.m</a>,
decomposes an R8VEC into normal and parallel components;
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>,
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "sort_heap_external.m">sort_heap_external.m</a>,
external sorts a list of values into ascending order;
</li>
<li>
<a href = "sphere_delaunay.m">
sphere_delaunay.m</a>,
returns the Delaunay triangulation of points on the unit sphere.
</li>
<li>
<a href = "sphere_grid_icos_size.m">
sphere_grid_icos_size.m</a>,
returns size information for an icosahedral grid on the sphere.
</li>
<li>
<a href = "sphere_gridpoints_icos2.m">
sphere_gridpoints_icos2.m</a>,
returnspoints of an icosahedral grid on the sphere.
</li>
<li>
<a href = "stri_angles_to_area.m">
stri_angles_to_area.m</a>,
computes the area of a spherical triangle;
</li>
<li>
<a href = "stri_sides_to_angles.m">
stri_sides_to_angles.m</a>,
computes the angles of a spherical triangle from its sides;
</li>
<li>
<a href = "stri_vertices_to_area.m">
stri_vertices_to_area.m</a>,
computes the area of a spherical triangle from its vertices;
</li>
<li>
<a href = "stri_vertices_to_sides.m">
stri_vertices_to_sides.m</a>,
computes the sides of a spherical triangle from its sides;
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a timestamp;
</li>
<li>
<a href = "triangulation_neighbor_triangles.m">
triangulation_neighhbor_triangles.m</a>,
determines triangle neighbors in a triangulation;
</li>
<li>
<a href = "uniform_on_sphere01_map.m">
uniform_on_sphere01_map.m</a>,
returns uniform random points on the unit sphere.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sphere_delaunay_test.m">sphere_delaunay_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "sphere_delaunay_test_output.txt">sphere_delaunay_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "sphere_delaunay_test01.m">sphere_delaunay_test01.m</a>,
test 1;
</li>
<li>
<a href = "sphere_delaunay_test02.m">sphere_delaunay_test02.m</a>,
test 2;
</li>
<li>
<a href = "sphere_delaunay_test03.m">sphere_delaunay_test03.m</a>,
test 3;
</li>
<li>
<a href = "test02_plot1.png">test02_plot1.png</a>,
a TRISURF plot of the Delaunay triangulation.
</li>
<li>
<a href = "test02_plot2.png">test02_plot2.png</a>,
a PATCH plot of the Delaunay triangulation.
</li>
<li>
<a href = "test03_plot1.png">test03_plot1.png</a>,
a TRISURF plot of the Delaunay triangulation.
</li>
<li>
<a href = "test03_plot2.png">test03_plot2.png</a>,
a PATCH plot of the Delaunay triangulation.
</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 22 May 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>