forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathsphere_grid.html
448 lines (403 loc) · 12.8 KB
/
sphere_grid.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
<html>
<head>
<title>
SPHERE_GRID - Grids on a Sphere
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPHERE_GRID <br> Grids on a Sphere
</h1>
<hr>
<p>
<b>SPHERE_GRID</b>
is a C++ library which
constructs a grid of points
on the surface of the unit sphere in 3D.
</p>
<p>
A grid on a sphere may mean a set of points, or a set of points and
lines that connect them, or a set of points, lines that connect them,
and the faces that are bounded by those lines.
</p>
<p>
A grid may be desired which simply organizes areas. In that case,
something like the latitude and longitude lines on a globe may be
sufficient, even though "evenly spaced" latitude and longitude
lines result in grid cells that are close to rectangular near
the equator, but become more asymmetric near the poles.
</p>
<p>
A grid may also be desired for sampling, that is, for choosing
a set of points that are well spread across the sphere. A simple
Monte Carlo approach can be used, although this means that the
data is only well spread out in the long view; there may be local
clusters and gaps.
</p>
<p>
Other grids are generated by drawing a spiral on the surface of the
sphere, and choosing points at regular spacings along that line, or
by projecting an icosahedron onto the surface of the sphere, which
divides the surface into 20 congruent spherical triangles, and then
dealing with the simpler issue of choosing points from the triangles.
</p>
<p>
The test program uses GNUPLOT to make images of some of the grids.
</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_GRID</b> is available in
<a href = "../../c_src/sphere_grid/sphere_grid.html">a C version</a> and
<a href = "../../cpp_src/sphere_grid/sphere_grid.html">a C++ version</a> and
<a href = "../../f77_src/sphere_grid/sphere_grid.html">a FORTRAN77 version</a> and
<a href = "../../f_src/sphere_grid/sphere_grid.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sphere_grid/sphere_grid.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/cube_grid/cube_grid.html">
CUBE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../cpp_src/disk_grid/disk_grid.html">
DISK_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a disk in 2D.
</p>
<p>
<a href = "../../cpp_src/geometry/geometry.html">
GEOMETRY</a>,
a C++ library which
performs geometric calculations in 2, 3 and N dimensional space.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
</p>
<p>
<a href = "../../cpp_src/hypercube_grid/hypercube_grid.html">
HYPERCUBE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a hypercube in M dimensions.
</p>
<p>
<a href = "../../cpp_src/line_grid/line_grid.html">
LINE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../cpp_src/polygon_grid/polygon_grid.html">
POLYGON_GRID</a>,
a C++ library which
generates a grid of points
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../cpp_src/pyramid_grid/pyramid_grid.html">
PYRAMID_GRID</a>,
a C++ library which
computes a grid of points
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../cpp_src/simplex_grid/simplex_grid.html">
SIMPLEX_GRID</a>,
a C++ library which
generates a grid of points
over the interior of a simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/sphere_fibonacci_grid/sphere_fibonacci_grid.html">
SPHERE_FIBONACCI_GRID</a>,
a C++ library which
uses a Fibonacci spiral to create a grid of points
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_llq_grid/sphere_llq_grid.html">
SPHERE_LLQ_GRID</a>,
a C++ library which
uses longitudes and latitudes to create grids of points,
lines, and quadrilaterals
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_llt_grid/sphere_llt_grid.html">
SPHERE_LLT_GRID</a>,
a C++ library which
uses longitudes and latitudes to create grids of points,
lines, and triangles
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/square_grid/square_grid.html">
SQUARE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a square in 2D.
</p>
<p>
<a href = "../../cpp_src/triangle_grid/triangle_grid.html">
TRIANGLE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/wedge_grid/wedge_grid.html">
WEDGE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edward Saff, Arno Kuijlaars,<br>
Distributing Many Points on a Sphere,<br>
The Mathematical Intelligencer,<br>
Volume 19, Number 1, 1997, pages 5-11.
</li>
<li>
Richard Swinbank, James Purser,<br>
Fibonacci grids: A novel approach to global modelling,<br>
Quarterly Journal of the Royal Meteorological Society,<br>
Volume 132, Number 619, July 2006 Part B, pages 1769-1793.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sphere_grid.cpp">sphere_grid.cpp</a>, the source code.
</li>
<li>
<a href = "sphere_grid.hpp">sphere_grid.hpp</a>, the include file.
</li>
<li>
<a href = "sphere_grid.sh">sphere_grid.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sphere_grid_prb.cpp">sphere_grid_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "sphere_grid_prb.sh">sphere_grid_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "sphere_grid_prb_output.txt">sphere_grid_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
To see the XYZ data files and images of the sphere grids created by this
example program, go to
<a href = "../../datasets/sphere_grid/sphere_grid.html">
the SPHERE_GRID dataset directory</a>.
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ARC_COSINE</b> computes the arc cosine function, with argument truncation.
</li>
<li>
<b>ARC_SINE</b> computes the arc sine function, with argument truncation.
</li>
<li>
<b>ATAN4</b> computes the inverse tangent of the ratio Y / X.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_POWER</b> returns the value of I^J.
</li>
<li>
<b>I4_TO_STRING</b> converts an I4 to a C++ string.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an I4MAT, transposed.
</li>
<li>
<b>I4VEC_COPY</b> copies an I4VEC.
</li>
<li>
<b>ICOS_SHAPE</b> describes a icosahedron.
</li>
<li>
<b>ICOS_NUM</b> gives "sizes" for an icosahedron.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_MODP</b> returns the nonnegative remainder of R8 division.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</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>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>R8VEC_COPY</b> copies an R8VEC.
</li>
<li>
<b>R8VEC_DIFF_NORM</b> returns the L2 norm of the difference of R8VEC's.
</li>
<li>
<b>R8VEC_DOT_PRODUCT</b> computes the dot product of a pair of R8VEC's.
</li>
<li>
<b>R8VEC_EQ</b> is true if every pair of entries in two R8VEC's is equal.
</li>
<li>
<b>R8VEC_NORM</b> returns the L2 norm of an R8VEC.
</li>
<li>
<b>R8VEC_POLARIZE</b> decomposes an R8VEC into normal and parallel components.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>SPHERE_CUBED_IJK_TO_XYZ:</b> cubed sphere IJK to XYZ coordinates.
</li>
<li>
<b>SPHERE_CUBED_LINE_NUM</b> counts lines on a cubed sphere grid.
</li>
<li>
<b>SPHERE_CUBED_LINES</b> computes the lines on a cubed sphere grid.
</li>
<li>
<b>SPHERE_CUBED_POINTS</b> computes the points on a cubed sphere grid.
</li>
<li>
<b>SPHERE_CUBED_POINTS_FACE:</b> points on one face of a cubed sphere grid.
</li>
<li>
<b>SPHERE_CUBED_POINT_NUM</b> counts the points on a cubed sphere grid.
</li>
<li>
<b>SPHERE_DISTANCE_XYZ</b> computes great circle distances on a sphere.
</li>
<li>
<b>SPHERE_FIBONACCI_POINTS</b> computes sphere points on a Fibonacci spiral.
</li>
<li>
<b>SPHERE_GRID_Q4:</b> rectangular grid on a sphere.
</li>
<li>
<b>SPHERE_GRID_T3</b> produces a triangle grid on a sphere.
</li>
<li>
<b>SPHERE_ICOS_EDGE_NUM</b> sizes an icosahedral grid on a sphere.
</li>
<li>
<b>SPHERE_ICOS_FACE_NUM</b> sizes an icosahedral grid on a sphere.
</li>
<li>
<b>SPHERE_ICOS_POINT_NUM</b> sizes an icosahedral grid on a sphere.
</li>
<li>
<b>SPHERE_ICOS1_POINTS</b> returns icosahedral grid points on a sphere.
</li>
<li>
<b>SPHERE_ICOS2_POINTS</b> returns icosahedral grid points on a sphere.
</li>
<li>
<b>SPHERE_LINE_PROJECT</b> projects a line onto an implicit sphere.
</li>
<li>
<b>SPHERE_LL_LINES</b> produces lines from a latitude/longitude grid.
</li>
<li>
<b>SPHERE_LL_LINE_NUM</b> counts lines for a latitude/longitude grid.
</li>
<li>
<b>SPHERE_LL_POINTS</b> produces points on a latitude/longitude grid.
</li>
<li>
<b>SPHERE_LL_POINT_NUM</b> counts points for a latitude/longitude grid.
</li>
<li>
<b>SPHERE_LLQ_LINES:</b> latitude/longitude quadrilateral grid lines.
</li>
<li>
<b>SPHERE_LLQ_LINE_NUM</b> counts lines for a latitude/longitude quadrilateral grid.
</li>
<li>
<b>SPHERE_SPIRALPOINTS</b> produces spiral points on an implicit sphere.
</li>
<li>
<b>SPHERE_UNIT_SAMPLE</b> picks a random point on the unit sphere.
</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 = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 21 October 2013.
</i>
<!-- John Burkardt -->
</body>
</html>