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LZScene
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GLIsosurface.pas 
659 строк · 28.1 Кб
1
//
2
// This unit is part of the GLScene Engine https://github.com/glscene
3
//
4
{
5
  Polygonising a scalar field by construction of isosurfaces 
6


7
Algorithms
8
----------
9
Marching Cubes
10
 - Exploits a coarser Mesh then Marching Tetrahedra but produces less triangles
11
 - based on "Marching Cubes: A High Resolution 3D Surface
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   Construction Algorithm" by W.E.Lorensen and H.E.Cline
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 - patent free since 2005
14


15
Marching Tetrahedra
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 - Finer Mesh, better feature preservation
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 - based on "A new tetrahedral tesselation scheme for isosurface generation"
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   by S.L.Chan and E.O.Purisima
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 - patent free
20


21
Lookuptables
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 - by Paul Bourke (http://paulbourke.net/geometry/polygonise/)
23


24
Overall
25
 - Simple Data Structures to store Mesh. Vertices are calculated and stored twice
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   or even more often.
27


28
	 History :  
29
      05/08/12 - PW - Adapted to use with GLScene v.1.2 and later
30
	    12/06/04 - Wolf Blecher - Created, first implementation (Blechwolf@myrealbox.com)
31
	 
32
}
33


34
unit GLIsosurface;
35


36
interface
37


38
uses
39
  GLVectorGeometry;
40


41
{$I GLScene.inc}
42
  
43
type
44
  TSingle3DArray = array of array of array of Single;
45
  TVertexArray = array of TVertex;
46
  TIntegerArray = array of Integer;
47


48
// TIsoSurfaceExtractor
49
//
50
{ 3D Isosurface extractor class.
51
   This class allows to calculate and extract isosurfaces from scalar field
52
   voxel models using a given isovalue.
53
}
54
  TIsoSurfaceExtractor = class(TObject)
55
  private
56
    Data: TSingle3DArray;
57
    Dimensions: array ['x' .. 'z'] of Integer;
58


59
    function BuildIndex(var ADatavals: array of Single; Isovalue: Single): word;
60
    function Interpolate(V0, V1: TAffineVector;
61
      var Val0, Val1, Isovalue: Single): TVertex;
62


63
  public
64
    constructor Create(); overload;
65
    constructor Create(Xdim, Ydim, Zdim: Integer; var AData: TSingle3DArray); overload;
66
    destructor Destroy();
67


68
    procedure AssignData(Xdim, Ydim, Zdim: Integer;
69
      var AData: TSingle3DArray);
70


71
    procedure MarchingCubes(Isovalue: Single; out Vertices: TVertexArray;
72
      out Triangles: TIntegerArray);
73
    procedure MarchingTetrahedra(Isovalue: Single; out Vertices: TVertexArray;
74
      out Triangles: TIntegerArray);
75
  end;
76


77
//-------------------------------------------------------------------------
78
//-------------------------------------------------------------------------
79
//-------------------------------------------------------------------------
80
implementation
81
//-------------------------------------------------------------------------
82
//-------------------------------------------------------------------------
83
//-------------------------------------------------------------------------
84


85
const
86
 (*
87
     4----4------5
88
    /|          /|
89
   7 |         5 |
90
  /  |        /  |
91
 7-----6----6    |
92
 |   8       |   9
93
 |   |       |   |
94
 |   0----0--|---1
95
 11 /        10 /
96
 | 3         | 1
97
 |/          |/
98
 3-----2-----2
99
 *)
100
// Marching Cube TriTable
101
//
102
  MC_TRITABLE: array [0 .. 255, 0 .. 15] of Integer =
103
    ((-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
104
    (0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
105
    (0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
106
    (1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
107
    (1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
108
    (0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
109
    (9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
110
    (2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1),
111
    (3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
112
    (0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
113
    (1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
114
    (1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1),
115
    (3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
116
    (0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1),
117
    (3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1),
118
    (9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
119
    (4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
120
    (4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
121
    (0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
122
    (4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1),
123
    (1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
124
    (3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1),
125
    (9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1),
126
    (2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1),
127
    (8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
128
    (11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1),
129
    (9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1),
130
    (4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1),
131
    (3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1),
132
    (1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1),
133
    (4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1),
134
    (4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1),
135
    (9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
136
    (9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
137
    (0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
138
    (8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1),
139
    (1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
140
    (3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1),
141
    (5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1),
142
    (2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1),
143
    (9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
144
    (0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1),
145
    (0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1),
146
    (2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1),
147
    (10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1),
148
    (4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1),
149
    (5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1),
150
    (5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1),
151
    (9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
152
    (9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1),
153
    (0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1),
154
    (1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
155
    (9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1),
156
    (10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1),
157
    (8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1),
158
    (2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1),
159
    (7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1),
160
    (9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1),
161
    (2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1),
162
    (11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1),
163
    (9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1),
164
    (5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1),
165
    (11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1),
166
    (11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
167
    (10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
168
    (0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
169
    (9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
170
    (1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1),
171
    (1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
172
    (1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1),
173
    (9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1),
174
    (5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1),
175
    (2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
176
    (11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1),
177
    (0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1),
178
    (5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1),
179
    (6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1),
180
    (0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1),
181
    (3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1),
182
    (6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1),
183
    (5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
184
    (4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1),
185
    (1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1),
186
    (10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1),
187
    (6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1),
188
    (1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1),
189
    (8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1),
190
    (7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1),
191
    (3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1),
192
    (5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1),
193
    (0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1),
194
    (9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1),
195
    (8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1),
196
    (5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1),
197
    (0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1),
198
    (6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1),
199
    (10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
200
    (4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1),
201
    (10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1),
202
    (8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1),
203
    (1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1),
204
    (3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1),
205
    (0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
206
    (8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1),
207
    (10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1),
208
    (0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1),
209
    (3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1),
210
    (6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1),
211
    (9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1),
212
    (8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1),
213
    (3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1),
214
    (6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
215
    (7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1),
216
    (0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1),
217
    (10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1),
218
    (10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1),
219
    (1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1),
220
    (2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1),
221
    (7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1),
222
    (7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
223
    (2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1),
224
    (2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1),
225
    (1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1),
226
    (11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1),
227
    (8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1),
228
    (0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
229
    (7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1),
230
    (7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
231
    (7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
232
    (3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
233
    (0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
234
    (8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1),
235
    (10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
236
    (1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1),
237
    (2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1),
238
    (6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1),
239
    (7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
240
    (7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1),
241
    (2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1),
242
    (1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1),
243
    (10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1),
244
    (10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1),
245
    (0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1),
246
    (7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1),
247
    (6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
248
    (3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1),
249
    (8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1),
250
    (9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1),
251
    (6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1),
252
    (1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1),
253
    (4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1),
254
    (10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1),
255
    (8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1),
256
    (0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
257
    (1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1),
258
    (1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1),
259
    (8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1),
260
    (10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1),
261
    (4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1),
262
    (10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
263
    (4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
264
    (0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1),
265
    (5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1),
266
    (11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1),
267
    (9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1),
268
    (6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1),
269
    (7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1),
270
    (3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1),
271
    (7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1),
272
    (9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1),
273
    (3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1),
274
    (6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1),
275
    (9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1),
276
    (1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1),
277
    (4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1),
278
    (7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1),
279
    (6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1),
280
    (3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1),
281
    (0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1),
282
    (6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1),
283
    (1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1),
284
    (0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1),
285
    (11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1),
286
    (6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1),
287
    (5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1),
288
    (9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1),
289
    (1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1),
290
    (1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
291
    (1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1),
292
    (10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1),
293
    (0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
294
    (10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
295
    (11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
296
    (11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1),
297
    (5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1),
298
    (10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1),
299
    (11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1),
300
    (0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1),
301
    (9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1),
302
    (7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1),
303
    (2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1),
304
    (8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1),
305
    (9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1),
306
    (9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1),
307
    (1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
308
    (0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1),
309
    (9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1),
310
    (9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
311
    (5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1),
312
    (5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1),
313
    (0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1),
314
    (10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1),
315
    (2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1),
316
    (0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1),
317
    (0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1),
318
    (9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
319
    (2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1),
320
    (5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1),
321
    (3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1),
322
    (5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1),
323
    (8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1),
324
    (0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
325
    (8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1),
326
    (9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
327
    (4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1),
328
    (0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1),
329
    (1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1),
330
    (3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1),
331
    (4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1),
332
    (9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1),
333
    (11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1),
334
    (11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1),
335
    (2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1),
336
    (9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1),
337
    (3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1),
338
    (1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
339
    (4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1),
340
    (4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1),
341
    (4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
342
    (4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
343
    (9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
344
    (3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1),
345
    (0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1),
346
    (3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
347
    (1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1),
348
    (3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1),
349
    (0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
350
    (3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
351
    (2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1),
352
    (9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
353
    (2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1),
354
    (1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
355
    (1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
356
    (0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
357
    (0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1),
358
    (-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1));
359


360
// Marching Cube EdgeTable
361
//
362
  MC_EDGETABLE: array [0 .. 11, 0 .. 1] of Integer = ((0, 1), (1, 2), (2, 3),
363
    (3, 0), (4, 5), (5, 6), (6, 7), (7, 4), (0, 4), (1, 5), (2, 6), (3, 7));
364


365
(*
366
        + 0
367
         /|\
368
        / | \
369
       /  |  0
370
      3   |   \
371
     /    2    \
372
    /     |     \
373
   +----4--------+ 1
374
  3 \     |     /
375
     \    |    /
376
      5   |   1
377
       \  |  /
378
        \ | /
379
         \|/
380
        + 2
381
*)
382


383
// Marching Tetrahedra TriTable
384
//
385
  MT_TRITABLE: array [0 .. 15, 0 .. 6] of Integer =
386
    ((-1, -1, -1, -1, -1, -1, -1), (2, 3, 0, -1, -1, -1, -1),
387
    (4, 1, 0, -1, -1, -1, -1), (2, 4, 1, 3, 4, 2, -1),
388
    (5, 2, 1, -1, -1, -1, -1), (5, 3, 0, 1, 5, 0, -1), (5, 2, 0, 4, 5, 0, -1),
389
    (3, 4, 5, -1, -1, -1, -1), (5, 4, 3, -1, -1, -1, -1),
390
    (0, 5, 4, 0, 2, 5, -1), (0, 5, 1, 0, 3, 5, -1), (1, 2, 5, -1, -1, -1, -1),
391
    (2, 4, 3, 1, 4, 2, -1), (0, 1, 4, -1, -1, -1, -1),
392
    (0, 3, 2, -1, -1, -1, -1), (-1, -1, -1, -1, -1, -1, -1));
393


394
// Marching Tetrahedra EdgeTable
395
//
396
  MT_EDGETABLE: array [0 .. 5, 0 .. 1] of Integer = ((0, 1), (1, 2), (2, 0),
397
    (0, 3), (1, 3), (2, 3));
398


399
// Marching Tetrahedra CubeSplit
400
//
401
  MT_CUBESPLIT: array [0 .. 5, 0 .. 3] of Integer = ((0, 5, 1, 6), (0, 1, 2, 6),
402
    (0, 2, 3, 6), (0, 3, 7, 6), (0, 7, 4, 6), (0, 4, 5, 6));
403


404
{-------------------------------------------------------------------------
405
 Class IsoSurfaceExtractor
406
 Purpose: Extract an Isosurface from volume dataset for given Isovalue
407
 -------------------------------------------------------------------------}
408


409
// Build Index depending on whether the edges are outside or inside the surface
410
//
411
function TIsoSurfaceExtractor.BuildIndex(var ADatavals: array of Single;
412
  Isovalue: Single): word;
413
var
414
  i: Integer;
415
  val: word;
416
begin
417
  val := 1;
418
  Result := 0;
419
  for i := 1 to Length(ADatavals) do
420
  begin
421
    if ADatavals[i - 1] <= Isovalue then // Edge inside surface
422
      Result := Result + val;
423
    val := val * 2;
424
  end;
425
end;
426


427
// Compute intersection point of edge and surface by linear interpolation
428
//
429
function TIsoSurfaceExtractor.Interpolate(V0, V1: TAffineVector;
430
  var Val0, Val1, Isovalue: Single): TVertex;
431
var
432
  Diff: Single;
433
  i: Integer;
434
begin
435
  if Val0 <= Isovalue then
436
  begin
437
    Diff := Val0 / (Val0 + Val1);
438
    for i := 0 to 2 do
439
      Interpolate.V[i] := V0.V[i] + Diff * (V1.V[i] - V0.V[i]);
440
  end
441
  else
442
  begin
443
    Diff := Val1 / (Val0 + Val1);
444
    for i := 0 to 2 do
445
      Interpolate.V[i] := V1.V[i] + Diff * (V0.V[i] - V1.V[i]);
446
  end;
447
end;
448


449
// Launch Marching Tetrahedra
450
//
451
procedure TIsoSurfaceExtractor.MarchingTetrahedra(Isovalue: Single; out Vertices: TVertexArray;
452
  out Triangles: TIntegerArray);
453
var
454
  i, j, k: Integer;
455
  index: word;
456
  CubeVertices: array of TAffineVector;
457
  Tetrahedron: array [0 .. 3] of TAffineVector;
458
  DataTetra: array [0 .. 3] of Single;
459


460
  // Add Triangle to List
461
  procedure AppendTri();
462
  var
463
    edge: byte;
464
    Ver1, Ver2, Ver3: TVertex;
465
    VListlength: Integer;
466
    TListlength: Integer;
467
  begin
468
    edge := 0;
469
    while MT_TRITABLE[index, edge] <> -1 do
470
    begin
471
      Ver1 := Interpolate(Tetrahedron[MT_EDGETABLE[MT_TRITABLE[index, edge], 0]],
472
        Tetrahedron[MT_EDGETABLE[MT_TRITABLE[index, edge], 1]],
473
        DataTetra[MT_EDGETABLE[MT_TRITABLE[index, edge], 0]],
474
        DataTetra[MT_EDGETABLE[MT_TRITABLE[index, edge], 1]], Isovalue);
475
      Ver2 := Interpolate(Tetrahedron[MT_EDGETABLE[MT_TRITABLE[index, edge + 1], 0]
476
        ], Tetrahedron[MT_EDGETABLE[MT_TRITABLE[index, edge + 1], 1]],
477
        DataTetra[MT_EDGETABLE[MT_TRITABLE[index, edge + 1], 0]],
478
        DataTetra[MT_EDGETABLE[MT_TRITABLE[index, edge + 1], 1]], Isovalue);
479
      Ver3 := Interpolate(Tetrahedron[MT_EDGETABLE[MT_TRITABLE[index, edge + 2], 0]
480
        ], Tetrahedron[MT_EDGETABLE[MT_TRITABLE[index, edge + 2], 1]],
481
        DataTetra[MT_EDGETABLE[MT_TRITABLE[index, edge + 2], 0]],
482
        DataTetra[MT_EDGETABLE[MT_TRITABLE[index, edge + 2], 1]], Isovalue);
483
      VListlength := Length(Vertices) + 3;
484
      TListlength := Length(Triangles) + 3;
485
      SetLength(Vertices, VListlength);
486
      SetLength(Triangles, TListlength);
487
      Vertices[VListlength - 3] := Ver1;
488
      Vertices[VListlength - 2] := Ver2;
489
      Vertices[VListlength - 1] := Ver3;
490
      Triangles[TListlength - 3] := VListlength - 3;
491
      Triangles[TListlength - 2] := VListlength - 2;
492
      Triangles[TListlength - 1] := VListlength - 1;
493
      edge := edge + 3;
494
    end;
495
  end;
496


497
// Split Cube in 6 Tetrahedrons and process each tetrahedron
498
//
499
  procedure SplitCube();
500
  var
501
    i, j: Integer;
502
  begin
503
    for i := 0 to 5 do
504
    begin
505
      for j := 0 to 3 do
506
      begin
507
        Tetrahedron[j] := CubeVertices[MT_CUBESPLIT[i, j]];
508
        DataTetra[j] := Data[Trunc(Tetrahedron[j].V[0]), Trunc(Tetrahedron[j].V[1]),
509
          Trunc(Tetrahedron[j].V[2])];
510
      end;
511
      index := BuildIndex(DataTetra, Isovalue);
512
      AppendTri();
513
    end;
514
  end;
515


516
begin
517
(*
518
      1----2
519
     /|   /|
520
    0----3 |
521
    | 5--|-6
522
    |/   |/
523
    4----7
524
*)
525
  SetLength(CubeVertices, 8);
526
  for k := 0 to Dimensions['z'] - 2 do
527
  begin
528
    for j := 0 to Dimensions['y'] - 2 do
529
    begin
530
      for i := 0 to Dimensions['x'] - 2 do
531
      begin
532
        CubeVertices[0] := AffineVectorMake(i, j, k);
533
        CubeVertices[1] := AffineVectorMake(i, j, k + 1);
534
        CubeVertices[2] := AffineVectorMake(i + 1, j, k + 1);
535
        CubeVertices[3] := AffineVectorMake(i + 1, j, k);
536
        CubeVertices[4] := AffineVectorMake(i, j + 1, k);
537
        CubeVertices[5] := AffineVectorMake(i, j + 1, k + 1);
538
        CubeVertices[6] := AffineVectorMake(i + 1, j + 1, k + 1);
539
        CubeVertices[7] := AffineVectorMake(i + 1, j + 1, k);
540


541
        SplitCube();
542
      end; // for k
543
    end; // for j
544
  end; // for i
545
end; // ccMT
546


547
constructor TIsoSurfaceExtractor.Create;
548
begin
549
  inherited;
550
end;
551


552
constructor TIsoSurfaceExtractor.Create(Xdim, Ydim, Zdim: Integer;
553
  var AData: TSingle3DArray);
554
begin
555
  Create();
556
  AssignData(Xdim, Ydim, Zdim, AData);
557
end;
558


559
destructor TIsoSurfaceExtractor.Destroy;
560
begin
561
  inherited;
562
end;
563


564
procedure TIsoSurfaceExtractor.AssignData(Xdim, Ydim, Zdim: Integer;
565
  var AData: TSingle3DArray);
566
begin
567
  Dimensions['x'] := Xdim;
568
  Dimensions['y'] := Ydim;
569
  Dimensions['z'] := Zdim;
570


571
  Data := AData;
572
end;
573


574
// Launch Marching Cubes
575
//
576
procedure TIsoSurfaceExtractor.MarchingCubes(Isovalue: Single; out Vertices: TVertexArray;
577
  out Triangles: TIntegerArray);
578
var
579
  i, j, k: Integer;
580
  index: word;
581
  CubeVertices: array [0 .. 7] of TAffineVector;
582
  CubeData: array [0 .. 7] of Single;
583


584
  procedure AppendTri();
585
  var
586
    edge: byte;
587
    Ver1, Ver2, Ver3: TVertex;
588
    VListlength: Integer;
589
    TListlength: Integer;
590
  begin
591
    edge := 0;
592
    while MC_TRITABLE[index, edge] <> -1 do
593
    begin
594
      ver1 := Interpolate(CubeVertices[MC_EDGETABLE[MC_TRITABLE[index, edge], 0]],
595
        CubeVertices[MC_EDGETABLE[MC_TRITABLE[index, edge], 1]],
596
        CubeData[MC_EDGETABLE[MC_TRITABLE[index, edge], 0]],
597
        CubeData[MC_EDGETABLE[MC_TRITABLE[index, edge], 1]], Isovalue);
598
      ver2 := Interpolate(CubeVertices[MC_EDGETABLE[MC_TRITABLE[index, edge + 1], 0]],
599
        CubeVertices[MC_EDGETABLE[MC_TRITABLE[index, edge + 1], 1]],
600
        CubeData[MC_EDGETABLE[MC_TRITABLE[index, edge + 1], 0]],
601
        CubeData[MC_EDGETABLE[MC_TRITABLE[index, edge + 1], 1]], Isovalue);
602
      ver3 := Interpolate(CubeVertices[MC_EDGETABLE[MC_TRITABLE[index, edge + 2], 0]],
603
        CubeVertices[MC_EDGETABLE[MC_TRITABLE[index, edge + 2], 1]],
604
        CubeData[MC_EDGETABLE[MC_TRITABLE[index, edge + 2], 0]],
605
        CubeData[MC_EDGETABLE[MC_TRITABLE[index, edge + 2], 1]], Isovalue);
606
      VListlength := Length(Vertices) + 3;
607
      TListlength := Length(Triangles) + 3;
608
      SetLength(Vertices, VListlength);
609
      SetLength(Triangles, TListlength);
610
      Vertices[VListlength - 3] := Ver1;
611
      Vertices[VListlength - 2] := Ver2;
612
      Vertices[VListlength - 1] := Ver3;
613
      Triangles[TListlength - 3] := VListlength - 3;
614
      Triangles[TListlength - 2] := VListlength - 2;
615
      Triangles[TListlength - 1] := VListlength - 1;
616
      edge := edge + 3;
617
    end;
618
  end;
619


620
begin
621
(*
622
       7----6
623
      /|   /|
624
     3----2 |
625
    | 4--|-5
626
    |/   |/
627
    0----1
628
*)
629
  for i := 0 to Dimensions['x'] - 2 do
630
  begin
631
    for j := 1 to Dimensions['y'] - 1 do
632
    begin
633
      for k := 0 to Dimensions['z'] - 2 do
634
      begin
635
        CubeVertices[0] := AffineVectorMake(i, j, k);
636
        CubeVertices[1] := AffineVectorMake(i + 1, j, k);
637
        CubeVertices[2] := AffineVectorMake(i + 1, j - 1, k);
638
        CubeVertices[3] := AffineVectorMake(i, j - 1, k);
639
        CubeVertices[4] := AffineVectorMake(i, j, k + 1);
640
        CubeVertices[5] := AffineVectorMake(i + 1, j, k + 1);
641
        CubeVertices[6] := AffineVectorMake(i + 1, j - 1, k + 1);
642
        CubeVertices[7] := AffineVectorMake(i, j - 1, k + 1);
643
        CubeData[0] := Data[i, j, k];
644
        CubeData[1] := Data[i + 1, j, k];
645
        CubeData[2] := Data[i + 1, j - 1, k];
646
        CubeData[3] := Data[i, j - 1, k];
647
        CubeData[4] := Data[i, j, k + 1];
648
        CubeData[5] := Data[i + 1, j, k + 1];
649
        CubeData[6] := Data[i + 1, j - 1, k + 1];
650
        CubeData[7] := Data[i, j - 1, k + 1];
651


652
        index := BuildIndex(CubeData, Isovalue);
653
        AppendTri();
654
      end; // for k
655
    end; // for j
656
  end; // for i
657
end;
658


659
end.
660

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