Basic Image AlgorithmS Library  2.8.0
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MarchingCubes.cpp
1 /*
2 This file is part of the BIAS library (Basic ImageAlgorithmS).
3 
4 Copyright (C) 2003-2009 (see file CONTACT for details)
5  Multimediale Systeme der Informationsverarbeitung
6  Institut fuer Informatik
7  Christian-Albrechts-Universitaet Kiel
8 
9 
10 BIAS is free software; you can redistribute it and/or modify
11 it under the terms of the GNU Lesser General Public License as published by
12 the Free Software Foundation; either version 2.1 of the License, or
13 (at your option) any later version.
14 
15 BIAS is distributed in the hope that it will be useful,
16 but WITHOUT ANY WARRANTY; without even the implied warranty of
17 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 GNU Lesser General Public License for more details.
19 
20 You should have received a copy of the GNU Lesser General Public License
21 along with BIAS; if not, write to the Free Software
22 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23 */
24 
25 /*
26  * MarchingCubes.cpp
27  *
28  * Created on: Apr 1, 2010
29  * Author: ischiller
30  */
31 
32 
33 #include "MarchingCubes.hh"
34 #include <math.h>
35 #include <stdlib.h>
36 using namespace BIAS;
37 
38 namespace BIAS {
39 
40 int edgeTable[256]={
41 0x0 , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
42 0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
43 0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
44 0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
45 0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
46 0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
47 0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
48 0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
49 0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
50 0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
51 0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
52 0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
53 0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
54 0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
55 0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
56 0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
57 0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
58 0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
59 0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
60 0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
61 0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
62 0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
63 0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
64 0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
65 0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
66 0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
67 0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
68 0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
69 0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
70 0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
71 0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
72 0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0 };
73 
74 
75 int triTable[256][16] =
76 {{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
77 {0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
78 {0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
79 {1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
80 {1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
81 {0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
82 {9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
83 {2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1},
84 {3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
85 {0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
86 {1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
87 {1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1},
88 {3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
89 {0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
90 {3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1},
91 {9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
92 {4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
93 {4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
94 {0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
95 {4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1},
96 {1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
97 {3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1},
98 {9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
99 {2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1},
100 {8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
101 {11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1},
102 {9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
103 {4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1},
104 {3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1},
105 {1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1},
106 {4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1},
107 {4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
108 {9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
109 {9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
110 {0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
111 {8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1},
112 {1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
113 {3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
114 {5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1},
115 {2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1},
116 {9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
117 {0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
118 {0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
119 {2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1},
120 {10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1},
121 {4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1},
122 {5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1},
123 {5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1},
124 {9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
125 {9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1},
126 {0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1},
127 {1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
128 {9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1},
129 {10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1},
130 {8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1},
131 {2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
132 {7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1},
133 {9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1},
134 {2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1},
135 {11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1},
136 {9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1},
137 {5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1},
138 {11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1},
139 {11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
140 {10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
141 {0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
142 {9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
143 {1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
144 {1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
145 {1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1},
146 {9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1},
147 {5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1},
148 {2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
149 {11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
150 {0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
151 {5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1},
152 {6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1},
153 {0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1},
154 {3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1},
155 {6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1},
156 {5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
157 {4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1},
158 {1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
159 {10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1},
160 {6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1},
161 {1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1},
162 {8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1},
163 {7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1},
164 {3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
165 {5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1},
166 {0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1},
167 {9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1},
168 {8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1},
169 {5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1},
170 {0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1},
171 {6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1},
172 {10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
173 {4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1},
174 {10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1},
175 {8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1},
176 {1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1},
177 {3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1},
178 {0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
179 {8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1},
180 {10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1},
181 {0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1},
182 {3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1},
183 {6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1},
184 {9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1},
185 {8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1},
186 {3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1},
187 {6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
188 {7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1},
189 {0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1},
190 {10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1},
191 {10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1},
192 {1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1},
193 {2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1},
194 {7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1},
195 {7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
196 {2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1},
197 {2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1},
198 {1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1},
199 {11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1},
200 {8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1},
201 {0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
202 {7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1},
203 {7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
204 {7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
205 {3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
206 {0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
207 {8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
208 {10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
209 {1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
210 {2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
211 {6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1},
212 {7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
213 {7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1},
214 {2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1},
215 {1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1},
216 {10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1},
217 {10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1},
218 {0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1},
219 {7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1},
220 {6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
221 {3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1},
222 {8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1},
223 {9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1},
224 {6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1},
225 {1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1},
226 {4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1},
227 {10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1},
228 {8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1},
229 {0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
230 {1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1},
231 {1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
232 {8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1},
233 {10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1},
234 {4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1},
235 {10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
236 {4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
237 {0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
238 {5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
239 {11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1},
240 {9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
241 {6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1},
242 {7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1},
243 {3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1},
244 {7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
245 {9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1},
246 {3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1},
247 {6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1},
248 {9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1},
249 {1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1},
250 {4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1},
251 {7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1},
252 {6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1},
253 {3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1},
254 {0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1},
255 {6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1},
256 {1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1},
257 {0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1},
258 {11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1},
259 {6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1},
260 {5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1},
261 {9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1},
262 {1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1},
263 {1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
264 {1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1},
265 {10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1},
266 {0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
267 {10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
268 {11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
269 {11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1},
270 {5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
271 {10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1},
272 {11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1},
273 {0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1},
274 {9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1},
275 {7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1},
276 {2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1},
277 {8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1},
278 {9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1},
279 {9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1},
280 {1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
281 {0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1},
282 {9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
283 {9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
284 {5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1},
285 {5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1},
286 {0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1},
287 {10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1},
288 {2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1},
289 {0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1},
290 {0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1},
291 {9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
292 {2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1},
293 {5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1},
294 {3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1},
295 {5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1},
296 {8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
297 {0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
298 {8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1},
299 {9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
300 {4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
301 {0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1},
302 {1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1},
303 {3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1},
304 {4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1},
305 {9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1},
306 {11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1},
307 {11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1},
308 {2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1},
309 {9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1},
310 {3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1},
311 {1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
312 {4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1},
313 {4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1},
314 {4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
315 {4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
316 {9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
317 {3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1},
318 {0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
319 {3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
320 {1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1},
321 {3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1},
322 {0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
323 {3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
324 {2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1},
325 {9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
326 {2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1},
327 {1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
328 {1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
329 {0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
330 {0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
331 {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}};
332 
333 bool MarchingCubesTriangle::
334 IsDifferent(MarchingCubesTriangle& mct){
335  double dist=0;
336  bool ret=true;
337  dist += p[0].Dist(mct.p[0]);
338  dist += p[1].Dist(mct.p[1]);
339  dist += p[2].Dist(mct.p[2]);
340  if(dist>1e-12) ret = false;
341 
342  dist =0;
343  dist += p[0].Dist(mct.p[1]);
344  dist += p[1].Dist(mct.p[2]);
345  dist += p[2].Dist(mct.p[0]);
346  if(dist>1e-12) ret = false;
347 
348  dist =0;
349  dist += p[0].Dist(mct.p[2]);
350  dist += p[1].Dist(mct.p[0]);
351  dist += p[2].Dist(mct.p[1]);
352  if(dist>1e-12) ret = false;
353 
354  return ret;
355 }
356 ////////////////////////////////////////////////////////
357 MarchingCubes::MarchingCubes() {
358 }
359 
360 MarchingCubes::~MarchingCubes() {
361 
362 }
363 
364 int MarchingCubes::
365 PolygoniseCube(MarchingCubesGridCell grid,double isolevel,
366  MarchingCubesTriangle *triangles)
367 {
368  int i=0,ntriang=0;
369  int cubeindex=0;
370  BIAS::Vector3<double> vertlist[12];
371 
372  /* Determine the index into the edge table which
373  tells us which vertices are inside of the surface */
374  if (grid.val[0] < isolevel) cubeindex |= 1;
375  if (grid.val[1] < isolevel) cubeindex |= 2;
376  if (grid.val[2] < isolevel) cubeindex |= 4;
377  if (grid.val[3] < isolevel) cubeindex |= 8;
378  if (grid.val[4] < isolevel) cubeindex |= 16;
379  if (grid.val[5] < isolevel) cubeindex |= 32;
380  if (grid.val[6] < isolevel) cubeindex |= 64;
381  if (grid.val[7] < isolevel) cubeindex |= 128;
382 
383  /* Cube is entirely in/out of the surface */
384  if (edgeTable[cubeindex] == 0)
385  return(0);
386 
387  /* Find the vertices where the surface intersects the cube */
388  if (edgeTable[cubeindex] & 1)
389  vertlist[0] =
390  InterpolateVertex_(isolevel,grid.p[0],grid.p[1],grid.val[0],grid.val[1]);
391  if (edgeTable[cubeindex] & 2)
392  vertlist[1] =
393  InterpolateVertex_(isolevel,grid.p[1],grid.p[2],grid.val[1],grid.val[2]);
394  if (edgeTable[cubeindex] & 4)
395  vertlist[2] =
396  InterpolateVertex_(isolevel,grid.p[2],grid.p[3],grid.val[2],grid.val[3]);
397  if (edgeTable[cubeindex] & 8)
398  vertlist[3] =
399  InterpolateVertex_(isolevel,grid.p[3],grid.p[0],grid.val[3],grid.val[0]);
400  if (edgeTable[cubeindex] & 16)
401  vertlist[4] =
402  InterpolateVertex_(isolevel,grid.p[4],grid.p[5],grid.val[4],grid.val[5]);
403  if (edgeTable[cubeindex] & 32)
404  vertlist[5] =
405  InterpolateVertex_(isolevel,grid.p[5],grid.p[6],grid.val[5],grid.val[6]);
406  if (edgeTable[cubeindex] & 64)
407  vertlist[6] =
408  InterpolateVertex_(isolevel,grid.p[6],grid.p[7],grid.val[6],grid.val[7]);
409  if (edgeTable[cubeindex] & 128)
410  vertlist[7] =
411  InterpolateVertex_(isolevel,grid.p[7],grid.p[4],grid.val[7],grid.val[4]);
412  if (edgeTable[cubeindex] & 256)
413  vertlist[8] =
414  InterpolateVertex_(isolevel,grid.p[0],grid.p[4],grid.val[0],grid.val[4]);
415  if (edgeTable[cubeindex] & 512)
416  vertlist[9] =
417  InterpolateVertex_(isolevel,grid.p[1],grid.p[5],grid.val[1],grid.val[5]);
418  if (edgeTable[cubeindex] & 1024)
419  vertlist[10] =
420  InterpolateVertex_(isolevel,grid.p[2],grid.p[6],grid.val[2],grid.val[6]);
421  if (edgeTable[cubeindex] & 2048)
422  vertlist[11] =
423  InterpolateVertex_(isolevel,grid.p[3],grid.p[7],grid.val[3],grid.val[7]);
424 
425  /* Create the triangle */
426  ntriang = 0;
427  for (i=0;triTable[cubeindex][i]!=-1;i+=3) {
428  triangles[ntriang].p[0] = vertlist[triTable[cubeindex][i ]];
429  triangles[ntriang].p[1] = vertlist[triTable[cubeindex][i+1]];
430  triangles[ntriang].p[2] = vertlist[triTable[cubeindex][i+2]];
431  ntriang++;
432  }
433 
434  return(ntriang);
435 }
436 
437 /*
438  Linearly interpolate the position where an isosurface cuts
439  an edge between two vertices, each with their own scalar value
440 */
441 BIAS::Vector3<double> MarchingCubes::
442 InterpolateVertex_(double isolevel,BIAS::Vector3<double> p1,
443  BIAS::Vector3<double> p2,double valp1,double valp2)
444 {
445  double mu;
446  BIAS::Vector3<double> p;
447 
448  if (abs(isolevel-valp1) < 0.00001)
449  return(p1);
450  if (abs(isolevel-valp2) < 0.00001)
451  return(p2);
452  if (abs(valp1-valp2) < 0.00001)
453  return(p1);
454  mu = (isolevel - valp1) / (valp2 - valp1);
455  p[0] = p1[0] + mu * (p2[0] - p1[0]);
456  p[1] = p1[1] + mu * (p2[1] - p1[1]);
457  p[2] = p1[2] + mu * (p2[2] - p1[2]);
458 
459  return(p);
460 }
461 }
BIAS::edgeTable
int edgeTable[256]
Definition: MarchingCubes.cpp:40
BIAS::MarchingCubes::PolygoniseCube
int PolygoniseCube(MarchingCubesGridCell grid, double isolevel, MarchingCubesTriangle *triangles)
Given a grid cell and an isolevel, calculate the triangular facets required to represent the isosurfa...
Definition: MarchingCubes.cpp:365
BIAS::MarchingCubesTriangle::p
BIAS::Vector3< double > p[3]
Definition: MarchingCubes.hh:37
BIAS::MarchingCubesGridCell::p
BIAS::Vector3< double > p[8]
Definition: MarchingCubes.hh:41
BIAS::MarchingCubesTriangle::IsDifferent
bool IsDifferent(MarchingCubesTriangle &mct)
Definition: MarchingCubes.cpp:334
BIAS::triTable
int triTable[256][16]
Definition: MarchingCubes.cpp:75
BIAS::MarchingCubes::InterpolateVertex_
BIAS::Vector3< double > InterpolateVertex_(double isolevel, BIAS::Vector3< double > p1, BIAS::Vector3< double > p2, double valp1, double valp2)
Definition: MarchingCubes.cpp:442
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