-
Notifications
You must be signed in to change notification settings - Fork 41
/
table_voronoi.html
422 lines (380 loc) · 12.1 KB
/
table_voronoi.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
<html>
<head>
<title>
TABLE_VORONOI - Voronoi Diagram Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TABLE_VORONOI <br> Voronoi Diagram Data
</h1>
<hr>
<p>
<b>TABLE_VORONOI</b>
is a C++ program which
reads in a dataset
describing a 2D pointset, and prints out information defining
the Voronoi diagram of the pointset.
</p>
<p>
The information describing the 2D pointset is in the simple
<a href = "../../data/table/table.html">TABLE format</a>.
</p>
<p>
<b>TABLE_VORONOI</b> is based on the GEOMPACK library of
Barry Joe, which computes the Delaunay triangulation. The
main work that <b>TABLE_VORONOI</b> does is to analyze that
Delaunay information and work out the location of the Voronoi
vertices, and their specific arrangement around each of the
original data nodes.
</p>
<p>
<b>TABLE_VORONOI</b> is a work in progress; the output is
currently simply printed, which is not very useful except for
toy problems; printed output is of very little use for big problems.
To handle big, interesting problems, I have to think about how
to store this information in a useful and accessible data structure.
</p>
<p>
Moreover, I haven't thought enough about how to deal with the
inevitable "infinite" Voronoi cells.
</p>
<p>
The program begins with the pointset, of which a typical element
is a point <b>G</b>. Each <b>G</b> generates a Voronoi polygon (or
semi-infinite region, which we will persist in calling a polygon).
A typical vertex of the polygon is called <b>V</b>. For the semi-infinite
regions, we have a vertex at infinity, but it's really not helpful to
store a vertex (Inf,Inf), since we have lost information about the
direction from which we reach that infinite vertex. We will have to
treat these special regions with a little extra care.
</p>
<p>
We are interested in computing the following quantities:
<ul>
<li>
<b>G_DEGREE</b>, for generator <b>G</b>, the degree (number of
vertices) of the Voronoi polygon;
</li>
<li>
<b>G_START</b>, for generator <b>G</b>, the index of the first
Voronoi vertex in a traversal of the sides of the Voronoi polygon;
</li>
<li>
<b>G_FACE</b>, for all generators <b>G</b>, the sequence of Voronoi
vertices in a traversal of the sides of the Voronoi polygon.
A traversal of a semi-infinite polygon begins at an "infinite"
vertex, lists the finite vertices, and then ends with a
(different) infinite vertex. Infinite vertices are given
negative indexes.
</li>
<li>
<b>V_NUM</b>, the number of (finite) Voronoi vertices <b>V</b>;
</li>
<li>
<b>V_XY</b>, for each finite Voronoi vertex <b>V</b>,
the XY coordinates.
</li>
<li>
<b>I_NUM</b>, the number of Voronoi vertices at infinity;
</li>
<li>
<b>I_XY</b>, the "direction" associated with each Voronoi vertex
at infinity.
</li>
</ul>
</p>
<p>
So if we have to draw a semi-infinite region, we start at infinity.
We then need to draw a line from infinity to vertex #2. We do so
by drawing a line in the appropriate direction, stored in I_XY.
Having safely reached finite vertex #2, we can connect the finite
vertices, until it is time to draw another line to infinity, this
time in another direction, also stored in I_XY.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<dl>
<dt>
<b>table_voronoi</b> <i>file_name.xy</i>
</dt>
<dd>
reads the data in <i>file_name.xy</i>, computes and prints out
the Voronoi information.
</dd>
</dl>
</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>TABLE_VORONOI</b> is available in
<a href = "../../cpp_src/table_voronoi/table_voronoi.html">a C++ version</a> and
<a href = "../../f_src/table_voronoi/table_voronoi.html">a FORTRAN90 version</a> and
<a href = "../../m_src/table_voronoi/table_voronoi.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/geompack/geompack.html">
GEOMPACK</a>,
a C++ library which
computes the Delaunay triangulation
or Voronoi diagram.
</p>
<p>
<a href = "../../data/table/table.html">
TABLE</a>,
a file format which
is used for the input files.
</p>
<p>
<a href = "../../cpp_src/table_border/table_border.html">
TABLE_BORDER</a>,
a C++ program which
can read a TABLE file
and add zero entries corresponding to a single layer of
boundary data.
</p>
<p>
<a href = "../../cpp_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a C++ program which
reads a
file of 2d point coordinates and computes the Delaunay triangulation.
</p>
<p>
<a href = "../../cpp_src/table_io/table_io.html">
TABLE_IO</a>,
a C++ library which
can read or write
a TABLE file.
</p>
<p>
<a href = "../../cpp_src/table_latinize/table_latinize.html">
TABLE_LATINIZE</a>,
a C++ program which
can read a TABLE file
and write out a "latinized" version.
</p>
<p>
<a href = "../../cpp_src/table_quality/table_quality.html">
TABLE_QUALITY</a>,
a C++ program which
can read a TABLE file
and print out measures of the quality of dispersion of the points.
</p>
<p>
<a href = "../../cpp_src/table_unborder/table_unborder.html">
TABLE_UNBORDER</a>,
a C++ program which
can be used to remove the
border from a table file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, Number 3, pages 345-405, September 1991.
</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, pages 325-331, 1991.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "table_voronoi.cpp">table_voronoi.cpp</a>,
the source code.
</li>
<li>
<a href = "table_voronoi.sh">table_voronoi.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "diamond_02_00009.xy">diamond_02_00009.xy</a>,
a simple data file of 9 points.
</li>
<li>
<a href = "diamond_02_00009_output.txt">diamond_02_00009_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 TABLE_VORONOI.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is true if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DIAEDG</b> chooses a diagonal edge.
</li>
<li>
<b>DTABLE_DATA_READ</b> reads the data from a real TABLE file.
</li>
<li>
<b>DTABLE_HEADER_READ</b> reads the header from a real TABLE file.
</li>
<li>
<b>DTRIS2</b> constructs a Delaunay triangulation of 2D vertices.
</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>HANDLE_FILE</b> handles a single file.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two integers.
</li>
<li>
<b>I4_MIN</b> returns the smaller of two integers.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_SIGN</b> returns the sign of an integer.
</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 integer matrix, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an integer matrix, transposed.
</li>
<li>
<b>I4VEC_INDICATOR</b> sets an integer vector to the indicator vector.
</li>
<li>
<b>I4VEC_PRINT</b> prints an integer vector.
</li>
<li>
<b>LINE_EXP_NORMAL_2D</b> computes the unit normal vector to a line in 2D.
</li>
<li>
<b>LRLINE</b> determines where a point lies in relation to a directed line.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_INV</b> inverts a permutation "in place".
</li>
<li>
<b>R8_EPSILON</b> returns the round off unit for double precision arithmetic.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two real values.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two real values.
</li>
<li>
<b>R82VEC_PERMUTE</b> permutes an R2 vector in place.
</li>
<li>
<b>R82VEC_SORT_HEAP_INDEX_A</b> does an indexed heap ascending sort of an R2 vector.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints a real matrix, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of a real matrix, transposed.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</li>
<li>
<b>S_TO_R8</b> reads a real number from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads a real vector from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SWAPEC</b> swaps diagonal edges until all triangles are Delaunay.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> returns the current YMDHMS date as a string.
</li>
<li>
<b>TRI_AUGMENT</b> augments the triangle data using vertices at infinity.
</li>
<li>
<b>TRIANGLE_CIRCUMCENTER_2D</b> computes the circumcenter of a triangle in 2D.
</li>
<li>
<b>VBEDG</b> determines which boundary edges are visible to a point.
</li>
<li>
<b>VORONOI_DATA</b> returns data defining the Voronoi diagram.
</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 12 November 2006.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>