-
Notifications
You must be signed in to change notification settings - Fork 59
/
cvt_fixed.html
259 lines (230 loc) · 7.71 KB
/
cvt_fixed.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
<html>
<head>
<title>
CVT_FIXED - CVT with Some Generators Fixed
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CVT_FIXED <br> CVT with Some Generators Fixed
</h1>
<hr>
<p>
<b>CVT_FIXED</b>
is a FORTRAN90 library which
can be used to "update" a centroidal Voronoi tessellation (CVT).
</p>
<p>
<b>CVT_FIXED</b> attempts to compute a new CVT starting from
an existing one, updating some of the cell generators, but
leaving designated cell generators fixed.
The updated cell generators are replaced by the centroid of
their cells.
</p>
<p>
The user specifies which generators are to be fixed, and which
may be updated. Watching an animation of the evolution of the
system, the cells corresponding to fixed generators comprise obstacles,
and the free cells behave like soap bubbles that flow around
the obstacles, trying to balance pressures (cell volume).
</p>
<p>
A second feature has been added, a maximum influence distance.
This is the variable "cutoff_dist". When sampling the region,
if the nearest generator is further than this distance, we
don't assign the point at all.
</p>
<p>
The code includes the weight vector that was developed in the
<a href = "../cvt_size/cvt_size.html">CVT_SIZE</a> program.
Here, it is anticipated that the weight vector would be used
in situations where an initial set of generators has been
computed, and is to be augmented. The initial set of generators
is held fixed, and the new points are to be allowed to arrange
themselves. However, if we place the new points at random,
they will get trapped in local minima. By using the weight
vector, we can start out with the initial generators having
very little influence, and then gradually ramp their weights
up to equality with the new points.
</p>
<p>
We were interested in watching the behavior of the Voronoi
cells over "time". We set up a problem with 10 generators,
with weights 1, 2, 3, ..., 10. We started with random initial
locations for the generators, and carried out 100 iterations
of the CVT code. We saved a
<a href = "../../data/ppmb/ppmb.html">PPMB</a> file containing
an image of each step, used the
<a href = "http://www.ijg.org/">CJPEG</a>
program to convert these to
<a href = "../../data/jpg/jpg.html">JPEG files</a> with
consecutive file names, fed that into
<a href = "http://www.apple.com/quicktime/">QuickTime Pro</a>
to create an animation, and saved the result as an MPEG-4
file.
</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">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/ppmb/ppmb.html">
PPMB</a>,
a data format which
is used for the images of the CVT regions.
</p>
<p>
<a href = "../../f_src/pbmlib/pbmlib.html">
PBMLIB</a>,
a FORTRAN90 library which
is used to create the graphics files.
</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>
John Burkardt, Max Gunzburger, Janet Peterson and Rebecca Brannon,<br>
User Manual and Supporting Information for Library of Codes
for Centroidal Voronoi Placement and Associated Zeroth,
First, and Second Moment Determination,<br>
Sandia National Laboratories Technical Report SAND2002-0099,<br>
February 2002.
</li>
<li>
Qiang Du, Vance Faber, and Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
<li>
Lili Ju, Qiang Du, and Max Gunzburger,<br>
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,<br>
Parallel Computing,<br>
Volume 28, 2002, pages 1477-1500.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "cvt_fixed.f90">cvt_fixed.f90</a>, the source code.
</li>
<li>
<a href = "cvt_fixed.sh">cvt_fixed.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cvt_fixed_prb.f90">cvt_fixed_prb.f90</a>, a sample problem.
To run the various cases below, you have to make changes to
the text of this file.
</li>
<li>
<a href = "cvt_fixed_prb.sh">cvt_fixed_prb.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "cvt_fixed_prb_output.txt">cvt_fixed_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ANGLE_TO_RGB</b> returns a color on the perimeter of the color hexagon.
</li>
<li>
<b>CH_IS_DIGIT</b> returns .TRUE. if a character is a decimal digit.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>CVT_ITERATION</b> takes one step of the CVT iteration.
</li>
<li>
<b>DIGIT_INC</b> increments a decimal digit.
</li>
<li>
<b>DIGIT_TO_CH</b> returns the character representation of a decimal digit.
</li>
<li>
<b>FILE_NAME_INC</b> generates the next filename in a series.
</li>
<li>
<b>FIND_CLOSEST</b> finds the nearest R point to each S point.
</li>
<li>
<b>FIND_CLOSEST_SIZE</b> finds the Voronoi cell generator closest to a point X.
</li>
<li>
<b>GENERATOR_INIT</b> initializes the Voronoi cell generators.
</li>
<li>
<b>HEXCOL</b> returns a color on the perimeter of the color hexagon.
</li>
<li>
<b>I4_LOG_2</b> returns the integer part of the logarithm base 2 of |I|.
</li>
<li>
<b>I4_TO_ANGLE</b> maps integers to points on a circle.
</li>
<li>
<b>I4_TO_RGB</b> maps integers to RGB colors.
</li>
<li>
<b>R8VEC_DIST_L2</b> returns the L2 distance between a pair of vectors.
</li>
<li>
<b>RANDOM_INITIALIZE</b> initializes the FORTRAN 90 random number seed.
</li>
<li>
<b>REGION_PLOT_PPMB</b> makes a binary PPM plot of the CVT regions.
</li>
<li>
<b>REGION_SAMPLER</b> returns a sample point in the physical region.
</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 12 November 2006.
</i>
<!-- John Burkardt -->
</body>
</html>