1 |
greg |
2.1 |
#ifndef lint |
2 |
greg |
2.6 |
static const char RCSid[] = "$Id: bsdfinterp.c,v 2.5 2012/11/08 00:31:17 greg Exp $"; |
3 |
greg |
2.1 |
#endif |
4 |
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/* |
5 |
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* Interpolate BSDF data from radial basis functions in advection mesh. |
6 |
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* |
7 |
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* G. Ward |
8 |
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*/ |
9 |
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10 |
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#define _USE_MATH_DEFINES |
11 |
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#include <stdio.h> |
12 |
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#include <stdlib.h> |
13 |
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#include <string.h> |
14 |
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#include <math.h> |
15 |
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#include "bsdfrep.h" |
16 |
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17 |
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/* Insert vertex in ordered list */ |
18 |
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static void |
19 |
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insert_vert(RBFNODE **vlist, RBFNODE *v) |
20 |
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{ |
21 |
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int i, j; |
22 |
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23 |
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for (i = 0; vlist[i] != NULL; i++) { |
24 |
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if (v == vlist[i]) |
25 |
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return; |
26 |
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if (v->ord < vlist[i]->ord) |
27 |
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break; |
28 |
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} |
29 |
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for (j = i; vlist[j] != NULL; j++) |
30 |
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; |
31 |
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while (j > i) { |
32 |
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vlist[j] = vlist[j-1]; |
33 |
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--j; |
34 |
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} |
35 |
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vlist[i] = v; |
36 |
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} |
37 |
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38 |
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/* Sort triangle edges in standard order */ |
39 |
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static int |
40 |
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order_triangle(MIGRATION *miga[3]) |
41 |
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{ |
42 |
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RBFNODE *vert[7]; |
43 |
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MIGRATION *ord[3]; |
44 |
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int i; |
45 |
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/* order vertices, first */ |
46 |
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memset(vert, 0, sizeof(vert)); |
47 |
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for (i = 3; i--; ) { |
48 |
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if (miga[i] == NULL) |
49 |
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return(0); |
50 |
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insert_vert(vert, miga[i]->rbfv[0]); |
51 |
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insert_vert(vert, miga[i]->rbfv[1]); |
52 |
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} |
53 |
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/* should be just 3 vertices */ |
54 |
greg |
2.4 |
if ((vert[2] == NULL) | (vert[3] != NULL)) |
55 |
greg |
2.1 |
return(0); |
56 |
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/* identify edge 0 */ |
57 |
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for (i = 3; i--; ) |
58 |
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if (miga[i]->rbfv[0] == vert[0] && |
59 |
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miga[i]->rbfv[1] == vert[1]) { |
60 |
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ord[0] = miga[i]; |
61 |
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break; |
62 |
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} |
63 |
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if (i < 0) |
64 |
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return(0); |
65 |
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/* identify edge 1 */ |
66 |
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for (i = 3; i--; ) |
67 |
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if (miga[i]->rbfv[0] == vert[1] && |
68 |
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miga[i]->rbfv[1] == vert[2]) { |
69 |
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ord[1] = miga[i]; |
70 |
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break; |
71 |
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} |
72 |
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if (i < 0) |
73 |
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return(0); |
74 |
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/* identify edge 2 */ |
75 |
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for (i = 3; i--; ) |
76 |
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if (miga[i]->rbfv[0] == vert[0] && |
77 |
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miga[i]->rbfv[1] == vert[2]) { |
78 |
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ord[2] = miga[i]; |
79 |
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break; |
80 |
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} |
81 |
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if (i < 0) |
82 |
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return(0); |
83 |
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/* reassign order */ |
84 |
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miga[0] = ord[0]; miga[1] = ord[1]; miga[2] = ord[2]; |
85 |
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return(1); |
86 |
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} |
87 |
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88 |
greg |
2.4 |
/* Determine if we are close enough to an edge */ |
89 |
greg |
2.3 |
static int |
90 |
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on_edge(const MIGRATION *ej, const FVECT ivec) |
91 |
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{ |
92 |
greg |
2.4 |
double cos_a, cos_b, cos_c, cos_aplusb; |
93 |
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/* use triangle inequality */ |
94 |
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cos_a = DOT(ej->rbfv[0]->invec, ivec); |
95 |
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if (cos_a <= 0) |
96 |
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return(0); |
97 |
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98 |
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cos_b = DOT(ej->rbfv[1]->invec, ivec); |
99 |
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if (cos_b <= 0) |
100 |
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return(0); |
101 |
greg |
2.3 |
|
102 |
greg |
2.4 |
cos_aplusb = cos_a*cos_b - sqrt((1.-cos_a*cos_a)*(1.-cos_b*cos_b)); |
103 |
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if (cos_aplusb <= 0) |
104 |
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return(0); |
105 |
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106 |
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cos_c = DOT(ej->rbfv[0]->invec, ej->rbfv[1]->invec); |
107 |
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108 |
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return(cos_c - cos_aplusb < .001); |
109 |
greg |
2.3 |
} |
110 |
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111 |
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/* Determine if we are inside the given triangle */ |
112 |
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static int |
113 |
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in_tri(const RBFNODE *v1, const RBFNODE *v2, const RBFNODE *v3, const FVECT p) |
114 |
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{ |
115 |
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FVECT vc; |
116 |
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int sgn1, sgn2, sgn3; |
117 |
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/* signed volume test */ |
118 |
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VCROSS(vc, v1->invec, v2->invec); |
119 |
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sgn1 = (DOT(p, vc) > 0); |
120 |
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VCROSS(vc, v2->invec, v3->invec); |
121 |
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sgn2 = (DOT(p, vc) > 0); |
122 |
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if (sgn1 != sgn2) |
123 |
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return(0); |
124 |
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VCROSS(vc, v3->invec, v1->invec); |
125 |
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sgn3 = (DOT(p, vc) > 0); |
126 |
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return(sgn2 == sgn3); |
127 |
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} |
128 |
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129 |
greg |
2.6 |
/* Test (and set) bitmap for edge */ |
130 |
greg |
2.4 |
static int |
131 |
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check_edge(unsigned char *emap, int nedges, const MIGRATION *mig, int mark) |
132 |
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{ |
133 |
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int ejndx, bit2check; |
134 |
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135 |
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if (mig->rbfv[0]->ord > mig->rbfv[1]->ord) |
136 |
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ejndx = mig->rbfv[1]->ord + (nedges-1)*mig->rbfv[0]->ord; |
137 |
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else |
138 |
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ejndx = mig->rbfv[0]->ord + (nedges-1)*mig->rbfv[1]->ord; |
139 |
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140 |
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bit2check = 1<<(ejndx&07); |
141 |
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142 |
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if (emap[ejndx>>3] & bit2check) |
143 |
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return(0); |
144 |
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if (mark) |
145 |
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emap[ejndx>>3] |= bit2check; |
146 |
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return(1); |
147 |
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} |
148 |
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149 |
greg |
2.3 |
/* Compute intersection with the given position over remaining mesh */ |
150 |
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static int |
151 |
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in_mesh(MIGRATION *miga[3], unsigned char *emap, int nedges, |
152 |
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const FVECT ivec, MIGRATION *mig) |
153 |
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{ |
154 |
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MIGRATION *ej1, *ej2; |
155 |
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RBFNODE *tv; |
156 |
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/* check visitation record */ |
157 |
greg |
2.4 |
if (!check_edge(emap, nedges, mig, 1)) |
158 |
greg |
2.3 |
return(0); |
159 |
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if (on_edge(mig, ivec)) { |
160 |
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miga[0] = mig; /* close enough to edge */ |
161 |
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return(1); |
162 |
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} |
163 |
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/* do triangles either side */ |
164 |
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for (ej1 = mig->rbfv[0]->ejl; ej1 != NULL; |
165 |
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ej1 = nextedge(mig->rbfv[0],ej1)) { |
166 |
greg |
2.4 |
if (ej1 == mig) |
167 |
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continue; |
168 |
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tv = opp_rbf(mig->rbfv[0],ej1); |
169 |
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for (ej2 = tv->ejl; ej2 != NULL; ej2 = nextedge(tv,ej2)) |
170 |
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if (opp_rbf(tv,ej2) == mig->rbfv[1]) { |
171 |
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int do_ej1 = check_edge(emap, nedges, ej1, 0); |
172 |
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int do_ej2 = check_edge(emap, nedges, ej2, 0); |
173 |
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if (do_ej1 && in_mesh(miga, emap, nedges, ivec, ej1)) |
174 |
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return(1); |
175 |
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if (do_ej2 && in_mesh(miga, emap, nedges, ivec, ej2)) |
176 |
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return(1); |
177 |
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/* check just once */ |
178 |
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if (do_ej1 & do_ej2 && in_tri(mig->rbfv[0], |
179 |
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mig->rbfv[1], tv, ivec)) { |
180 |
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miga[0] = mig; |
181 |
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miga[1] = ej1; |
182 |
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miga[2] = ej2; |
183 |
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return(1); |
184 |
greg |
2.3 |
} |
185 |
greg |
2.4 |
} |
186 |
greg |
2.3 |
} |
187 |
greg |
2.4 |
return(0); /* not near this edge */ |
188 |
greg |
2.3 |
} |
189 |
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|
190 |
greg |
2.1 |
/* Find edge(s) for interpolating the given vector, applying symmetry */ |
191 |
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int |
192 |
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get_interp(MIGRATION *miga[3], FVECT invec) |
193 |
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{ |
194 |
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miga[0] = miga[1] = miga[2] = NULL; |
195 |
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if (single_plane_incident) { /* isotropic BSDF? */ |
196 |
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RBFNODE *rbf; /* find edge we're on */ |
197 |
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for (rbf = dsf_list; rbf != NULL; rbf = rbf->next) { |
198 |
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if (input_orient*rbf->invec[2] < input_orient*invec[2]) |
199 |
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break; |
200 |
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if (rbf->next != NULL && |
201 |
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input_orient*rbf->next->invec[2] < |
202 |
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input_orient*invec[2]) { |
203 |
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for (miga[0] = rbf->ejl; miga[0] != NULL; |
204 |
|
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miga[0] = nextedge(rbf,miga[0])) |
205 |
greg |
2.5 |
if (opp_rbf(rbf,miga[0]) == rbf->next) { |
206 |
|
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double nf = 1.-rbf->invec[2]*rbf->invec[2]; |
207 |
|
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if (nf > FTINY) { |
208 |
|
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nf = sqrt((1.-invec[2]*invec[2])/nf); |
209 |
|
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invec[0] = nf*rbf->invec[0]; |
210 |
|
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invec[1] = nf*rbf->invec[1]; |
211 |
|
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} |
212 |
greg |
2.1 |
return(0); |
213 |
greg |
2.5 |
} |
214 |
greg |
2.1 |
break; |
215 |
|
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} |
216 |
|
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} |
217 |
|
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return(-1); /* outside range! */ |
218 |
|
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} |
219 |
|
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{ /* else use triangle mesh */ |
220 |
greg |
2.3 |
int sym = use_symmetry(invec); |
221 |
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int nedges = 0; |
222 |
|
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MIGRATION *mep; |
223 |
|
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unsigned char *emap; |
224 |
|
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/* clear visitation map */ |
225 |
|
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for (mep = mig_list; mep != NULL; mep = mep->next) |
226 |
|
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++nedges; |
227 |
|
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emap = (unsigned char *)calloc((nedges*(nedges-1) + 7)>>3, 1); |
228 |
|
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if (emap == NULL) { |
229 |
|
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fprintf(stderr, "%s: Out of memory in get_interp()\n", |
230 |
|
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progname); |
231 |
|
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exit(1); |
232 |
|
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} |
233 |
|
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/* identify intersection */ |
234 |
|
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if (!in_mesh(miga, emap, nedges, invec, mig_list)) |
235 |
|
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sym = -1; /* outside mesh */ |
236 |
|
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else if (miga[1] != NULL && |
237 |
|
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(miga[2] == NULL || !order_triangle(miga))) { |
238 |
greg |
2.1 |
#ifdef DEBUG |
239 |
|
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fputs("Munged triangle in get_interp()\n", stderr); |
240 |
|
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#endif |
241 |
greg |
2.3 |
sym = -1; |
242 |
greg |
2.1 |
} |
243 |
greg |
2.3 |
free(emap); |
244 |
greg |
2.1 |
return(sym); /* return in standard order */ |
245 |
|
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} |
246 |
|
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} |
247 |
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|
248 |
|
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/* Advect and allocate new RBF along edge */ |
249 |
|
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static RBFNODE * |
250 |
|
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e_advect_rbf(const MIGRATION *mig, const FVECT invec) |
251 |
|
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{ |
252 |
|
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RBFNODE *rbf; |
253 |
|
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int n, i, j; |
254 |
|
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double t, full_dist; |
255 |
|
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/* get relative position */ |
256 |
|
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t = acos(DOT(invec, mig->rbfv[0]->invec)); |
257 |
greg |
2.5 |
if (t < M_PI/grid_res) { /* near first DSF */ |
258 |
greg |
2.1 |
n = sizeof(RBFNODE) + sizeof(RBFVAL)*(mig->rbfv[0]->nrbf-1); |
259 |
|
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rbf = (RBFNODE *)malloc(n); |
260 |
|
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if (rbf == NULL) |
261 |
|
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goto memerr; |
262 |
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memcpy(rbf, mig->rbfv[0], n); /* just duplicate */ |
263 |
|
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return(rbf); |
264 |
|
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} |
265 |
|
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full_dist = acos(DOT(mig->rbfv[0]->invec, mig->rbfv[1]->invec)); |
266 |
greg |
2.5 |
if (t > full_dist-M_PI/grid_res) { /* near second DSF */ |
267 |
greg |
2.1 |
n = sizeof(RBFNODE) + sizeof(RBFVAL)*(mig->rbfv[1]->nrbf-1); |
268 |
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rbf = (RBFNODE *)malloc(n); |
269 |
|
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if (rbf == NULL) |
270 |
|
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goto memerr; |
271 |
|
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memcpy(rbf, mig->rbfv[1], n); /* just duplicate */ |
272 |
|
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return(rbf); |
273 |
|
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} |
274 |
|
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t /= full_dist; |
275 |
|
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n = 0; /* count migrating particles */ |
276 |
|
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for (i = 0; i < mtx_nrows(mig); i++) |
277 |
|
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for (j = 0; j < mtx_ncols(mig); j++) |
278 |
greg |
2.2 |
n += (mtx_coef(mig,i,j) > FTINY); |
279 |
greg |
2.1 |
#ifdef DEBUG |
280 |
|
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fprintf(stderr, "Input RBFs have %d, %d nodes -> output has %d\n", |
281 |
|
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mig->rbfv[0]->nrbf, mig->rbfv[1]->nrbf, n); |
282 |
|
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#endif |
283 |
|
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rbf = (RBFNODE *)malloc(sizeof(RBFNODE) + sizeof(RBFVAL)*(n-1)); |
284 |
|
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if (rbf == NULL) |
285 |
|
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goto memerr; |
286 |
|
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rbf->next = NULL; rbf->ejl = NULL; |
287 |
|
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VCOPY(rbf->invec, invec); |
288 |
|
|
rbf->nrbf = n; |
289 |
|
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rbf->vtotal = 1.-t + t*mig->rbfv[1]->vtotal/mig->rbfv[0]->vtotal; |
290 |
|
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n = 0; /* advect RBF lobes */ |
291 |
|
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for (i = 0; i < mtx_nrows(mig); i++) { |
292 |
|
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const RBFVAL *rbf0i = &mig->rbfv[0]->rbfa[i]; |
293 |
|
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const float peak0 = rbf0i->peak; |
294 |
|
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const double rad0 = R2ANG(rbf0i->crad); |
295 |
|
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FVECT v0; |
296 |
|
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float mv; |
297 |
|
|
ovec_from_pos(v0, rbf0i->gx, rbf0i->gy); |
298 |
|
|
for (j = 0; j < mtx_ncols(mig); j++) |
299 |
greg |
2.2 |
if ((mv = mtx_coef(mig,i,j)) > FTINY) { |
300 |
greg |
2.1 |
const RBFVAL *rbf1j = &mig->rbfv[1]->rbfa[j]; |
301 |
|
|
double rad1 = R2ANG(rbf1j->crad); |
302 |
|
|
FVECT v; |
303 |
|
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int pos[2]; |
304 |
|
|
rbf->rbfa[n].peak = peak0 * mv * rbf->vtotal; |
305 |
|
|
rbf->rbfa[n].crad = ANG2R(sqrt(rad0*rad0*(1.-t) + |
306 |
|
|
rad1*rad1*t)); |
307 |
|
|
ovec_from_pos(v, rbf1j->gx, rbf1j->gy); |
308 |
greg |
2.6 |
geodesic(v, v0, v, t*full_dist, GEOD_RAD); |
309 |
greg |
2.1 |
pos_from_vec(pos, v); |
310 |
|
|
rbf->rbfa[n].gx = pos[0]; |
311 |
|
|
rbf->rbfa[n].gy = pos[1]; |
312 |
|
|
++n; |
313 |
|
|
} |
314 |
|
|
} |
315 |
|
|
rbf->vtotal *= mig->rbfv[0]->vtotal; /* turn ratio into actual */ |
316 |
|
|
return(rbf); |
317 |
|
|
memerr: |
318 |
|
|
fprintf(stderr, "%s: Out of memory in e_advect_rbf()\n", progname); |
319 |
|
|
exit(1); |
320 |
|
|
return(NULL); /* pro forma return */ |
321 |
|
|
} |
322 |
|
|
|
323 |
|
|
/* Partially advect between recorded incident angles and allocate new RBF */ |
324 |
|
|
RBFNODE * |
325 |
|
|
advect_rbf(const FVECT invec) |
326 |
|
|
{ |
327 |
|
|
FVECT sivec; |
328 |
|
|
MIGRATION *miga[3]; |
329 |
|
|
RBFNODE *rbf; |
330 |
|
|
int sym; |
331 |
|
|
float mbfact, mcfact; |
332 |
|
|
int n, i, j, k; |
333 |
|
|
FVECT v0, v1, v2; |
334 |
greg |
2.6 |
double s, t, s_full, t_full; |
335 |
greg |
2.1 |
|
336 |
|
|
VCOPY(sivec, invec); /* find triangle/edge */ |
337 |
|
|
sym = get_interp(miga, sivec); |
338 |
|
|
if (sym < 0) /* can't interpolate? */ |
339 |
|
|
return(NULL); |
340 |
|
|
if (miga[1] == NULL) { /* advect along edge? */ |
341 |
|
|
rbf = e_advect_rbf(miga[0], sivec); |
342 |
greg |
2.5 |
if (single_plane_incident) |
343 |
|
|
rotate_rbf(rbf, invec); |
344 |
|
|
else |
345 |
|
|
rev_rbf_symmetry(rbf, sym); |
346 |
greg |
2.1 |
return(rbf); |
347 |
|
|
} |
348 |
|
|
#ifdef DEBUG |
349 |
|
|
if (miga[0]->rbfv[0] != miga[2]->rbfv[0] | |
350 |
|
|
miga[0]->rbfv[1] != miga[1]->rbfv[0] | |
351 |
|
|
miga[1]->rbfv[1] != miga[2]->rbfv[1]) { |
352 |
|
|
fprintf(stderr, "%s: Triangle vertex screw-up!\n", progname); |
353 |
|
|
exit(1); |
354 |
|
|
} |
355 |
|
|
#endif |
356 |
|
|
/* figure out position */ |
357 |
|
|
fcross(v0, miga[2]->rbfv[0]->invec, miga[2]->rbfv[1]->invec); |
358 |
|
|
normalize(v0); |
359 |
|
|
fcross(v2, miga[1]->rbfv[0]->invec, miga[1]->rbfv[1]->invec); |
360 |
|
|
normalize(v2); |
361 |
|
|
fcross(v1, sivec, miga[1]->rbfv[1]->invec); |
362 |
|
|
normalize(v1); |
363 |
greg |
2.6 |
s = acos(DOT(v0,v1)); |
364 |
greg |
2.1 |
geodesic(v1, miga[0]->rbfv[0]->invec, miga[0]->rbfv[1]->invec, |
365 |
greg |
2.6 |
s, GEOD_RAD); |
366 |
|
|
s /= s_full = acos(DOT(v0,v2)); |
367 |
|
|
t = acos(DOT(v1,sivec)) / |
368 |
|
|
(t_full = acos(DOT(v1,miga[1]->rbfv[1]->invec))); |
369 |
greg |
2.1 |
n = 0; /* count migrating particles */ |
370 |
|
|
for (i = 0; i < mtx_nrows(miga[0]); i++) |
371 |
|
|
for (j = 0; j < mtx_ncols(miga[0]); j++) |
372 |
greg |
2.2 |
for (k = (mtx_coef(miga[0],i,j) > FTINY) * |
373 |
greg |
2.1 |
mtx_ncols(miga[2]); k--; ) |
374 |
greg |
2.4 |
n += (mtx_coef(miga[2],i,k) > FTINY || |
375 |
greg |
2.2 |
mtx_coef(miga[1],j,k) > FTINY); |
376 |
greg |
2.1 |
#ifdef DEBUG |
377 |
|
|
fprintf(stderr, "Input RBFs have %d, %d, %d nodes -> output has %d\n", |
378 |
|
|
miga[0]->rbfv[0]->nrbf, miga[0]->rbfv[1]->nrbf, |
379 |
|
|
miga[2]->rbfv[1]->nrbf, n); |
380 |
|
|
#endif |
381 |
|
|
rbf = (RBFNODE *)malloc(sizeof(RBFNODE) + sizeof(RBFVAL)*(n-1)); |
382 |
|
|
if (rbf == NULL) { |
383 |
|
|
fprintf(stderr, "%s: Out of memory in advect_rbf()\n", progname); |
384 |
|
|
exit(1); |
385 |
|
|
} |
386 |
|
|
rbf->next = NULL; rbf->ejl = NULL; |
387 |
|
|
VCOPY(rbf->invec, sivec); |
388 |
|
|
rbf->nrbf = n; |
389 |
|
|
n = 0; /* compute RBF lobes */ |
390 |
|
|
mbfact = s * miga[0]->rbfv[1]->vtotal/miga[0]->rbfv[0]->vtotal * |
391 |
|
|
(1.-t + t*miga[1]->rbfv[1]->vtotal/miga[1]->rbfv[0]->vtotal); |
392 |
|
|
mcfact = (1.-s) * |
393 |
|
|
(1.-t + t*miga[2]->rbfv[1]->vtotal/miga[2]->rbfv[0]->vtotal); |
394 |
|
|
for (i = 0; i < mtx_nrows(miga[0]); i++) { |
395 |
|
|
const RBFVAL *rbf0i = &miga[0]->rbfv[0]->rbfa[i]; |
396 |
|
|
const float w0i = rbf0i->peak; |
397 |
|
|
const double rad0i = R2ANG(rbf0i->crad); |
398 |
|
|
ovec_from_pos(v0, rbf0i->gx, rbf0i->gy); |
399 |
|
|
for (j = 0; j < mtx_ncols(miga[0]); j++) { |
400 |
greg |
2.2 |
const float ma = mtx_coef(miga[0],i,j); |
401 |
greg |
2.1 |
const RBFVAL *rbf1j; |
402 |
|
|
double rad1j, srad2; |
403 |
|
|
if (ma <= FTINY) |
404 |
|
|
continue; |
405 |
|
|
rbf1j = &miga[0]->rbfv[1]->rbfa[j]; |
406 |
|
|
rad1j = R2ANG(rbf1j->crad); |
407 |
|
|
srad2 = (1.-s)*(1.-t)*rad0i*rad0i + s*(1.-t)*rad1j*rad1j; |
408 |
|
|
ovec_from_pos(v1, rbf1j->gx, rbf1j->gy); |
409 |
greg |
2.6 |
geodesic(v1, v0, v1, s*s_full, GEOD_RAD); |
410 |
greg |
2.1 |
for (k = 0; k < mtx_ncols(miga[2]); k++) { |
411 |
greg |
2.2 |
float mb = mtx_coef(miga[1],j,k); |
412 |
|
|
float mc = mtx_coef(miga[2],i,k); |
413 |
greg |
2.1 |
const RBFVAL *rbf2k; |
414 |
|
|
double rad2k; |
415 |
|
|
FVECT vout; |
416 |
|
|
int pos[2]; |
417 |
greg |
2.4 |
if ((mb <= FTINY) & (mc <= FTINY)) |
418 |
greg |
2.1 |
continue; |
419 |
|
|
rbf2k = &miga[2]->rbfv[1]->rbfa[k]; |
420 |
|
|
rbf->rbfa[n].peak = w0i * ma * (mb*mbfact + mc*mcfact); |
421 |
|
|
rad2k = R2ANG(rbf2k->crad); |
422 |
|
|
rbf->rbfa[n].crad = ANG2R(sqrt(srad2 + t*rad2k*rad2k)); |
423 |
|
|
ovec_from_pos(v2, rbf2k->gx, rbf2k->gy); |
424 |
greg |
2.6 |
geodesic(vout, v1, v2, t*t_full, GEOD_RAD); |
425 |
greg |
2.1 |
pos_from_vec(pos, vout); |
426 |
|
|
rbf->rbfa[n].gx = pos[0]; |
427 |
|
|
rbf->rbfa[n].gy = pos[1]; |
428 |
|
|
++n; |
429 |
|
|
} |
430 |
|
|
} |
431 |
|
|
} |
432 |
|
|
rbf->vtotal = miga[0]->rbfv[0]->vtotal * (mbfact + mcfact); |
433 |
|
|
rev_rbf_symmetry(rbf, sym); |
434 |
|
|
return(rbf); |
435 |
|
|
} |