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/* Copyright (c) 1989 Regents of the University of California */ |
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|
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#ifndef lint |
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static char SCCSid[] = "$SunId$ LBL"; |
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#endif |
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|
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/* Copyright (c) 1989 Regents of the University of California */ |
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|
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/* |
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* gensurf.c - program to generate functional surfaces |
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* |
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* 4/3/87 |
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*/ |
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|
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< |
#include <stdio.h> |
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#include "standard.h" |
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|
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#define XNAME "X_" /* x function name */ |
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#define YNAME "Y_" /* y function name */ |
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#define ZNAME "Z_" /* z function name */ |
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|
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< |
#define PI 3.14159265358979323846 |
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> |
#define ABS(x) ((x)>=0 ? (x) : -(x)) |
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|
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< |
#define FTINY 1e-7 |
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> |
#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
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|
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#define vertex(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
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|
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char vformat[] = "%15.9g %15.9g %15.9g\n"; |
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char tsargs[] = "4 surf_dx surf_dy surf_dz surf.cal\n"; |
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char texname[] = "Phong"; |
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|
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double funvalue(), dist2(), fdot(), l_hermite(), argument(); |
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int smooth = 0; /* apply smoothing? */ |
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|
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char *modname, *surfname; |
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|
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double funvalue(), l_hermite(), l_bezier(), l_bspline(), argument(); |
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|
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typedef struct { |
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FVECT p; /* vertex position */ |
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FVECT n; /* average normal */ |
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} POINT; |
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|
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|
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main(argc, argv) |
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int argc; |
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char *argv[]; |
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{ |
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static double *xyz[4]; |
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double *row0, *row1, *dp; |
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double v1[3], v2[3], vc1[3], vc2[3]; |
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double a1, a2; |
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> |
POINT *row0, *row1, *row2, *rp; |
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int i, j, m, n; |
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char stmp[256]; |
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double d; |
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register int k; |
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|
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varset("PI", PI); |
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funset("hermite", 5, l_hermite); |
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funset("bezier", 5, l_bezier); |
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funset("bspline", 5, l_bspline); |
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|
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if (argc < 8) |
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goto userror; |
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scompile(NULL, argv[++i]); |
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else if (!strcmp(argv[i], "-f")) |
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fcompile(argv[++i]); |
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else if (!strcmp(argv[i], "-s")) |
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smooth++; |
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else |
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goto userror; |
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|
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modname = argv[1]; |
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surfname = argv[2]; |
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sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
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scompile(NULL, stmp); |
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sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
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if (m <= 0 || n <= 0) |
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goto userror; |
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|
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row0 = (double *)malloc((n+1)*3*sizeof(double)); |
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row1 = (double *)malloc((n+1)*3*sizeof(double)); |
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if (row0 == NULL || row1 == NULL) { |
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row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
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row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
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row2 = (POINT *)malloc((n+3)*sizeof(POINT)); |
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if (row0 == NULL || row1 == NULL || row2 == NULL) { |
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fprintf(stderr, "%s: out of memory\n", argv[0]); |
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quit(1); |
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} |
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row0++; row1++; row2++; |
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/* print header */ |
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printhead(argc, argv); |
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comprow(0.0, row1, n); /* compute zeroeth row */ |
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/* initialize */ |
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comprow(-1.0/m, row0, n); |
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comprow(0.0, row1, n); |
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comprow(1.0/m, row2, n); |
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compnorms(row0, row1, row2, n); |
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/* for each row */ |
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for (i = 0; i < m; i++) { |
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/* compute next row */ |
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dp = row0; |
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rp = row0; |
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row0 = row1; |
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row1 = dp; |
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comprow((double)(i+1)/m, row1, n); |
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row1 = row2; |
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row2 = rp; |
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comprow((double)(i+2)/m, row2, n); |
| 107 |
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compnorms(row0, row1, row2, n); |
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|
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for (j = 0; j < n; j++) { |
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/* get vertices */ |
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xyz[0] = row0 + 3*j; |
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xyz[1] = row1 + 3*j; |
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xyz[2] = xyz[0] + 3; |
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xyz[3] = xyz[1] + 3; |
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/* rotate vertices */ |
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if (dist2(xyz[0],xyz[3]) < dist2(xyz[1],xyz[2])-FTINY) { |
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dp = xyz[0]; |
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< |
xyz[0] = xyz[1]; |
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< |
xyz[1] = xyz[3]; |
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xyz[3] = xyz[2]; |
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xyz[2] = dp; |
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} |
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/* get normals */ |
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for (k = 0; k < 3; k++) { |
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v1[k] = xyz[1][k] - xyz[0][k]; |
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< |
v2[k] = xyz[2][k] - xyz[0][k]; |
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} |
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fcross(vc1, v1, v2); |
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a1 = fdot(vc1, vc1); |
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for (k = 0; k < 3; k++) { |
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v1[k] = xyz[2][k] - xyz[3][k]; |
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v2[k] = xyz[1][k] - xyz[3][k]; |
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} |
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fcross(vc2, v1, v2); |
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a2 = fdot(vc2, vc2); |
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/* check coplanar */ |
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if (a1 > FTINY*FTINY && a2 > FTINY*FTINY) { |
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< |
d = fdot(vc1, vc2); |
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if (d*d/a1/a2 >= 1.0-FTINY*FTINY) { |
| 123 |
< |
if (d > 0.0) { /* coplanar */ |
| 124 |
< |
printf( |
| 125 |
< |
"\n%s polygon %s.%d.%d\n", |
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< |
argv[1], argv[2], i+1, j+1); |
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< |
printf("0\n0\n12\n"); |
| 128 |
< |
vertex(xyz[0]); |
| 129 |
< |
vertex(xyz[1]); |
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< |
vertex(xyz[3]); |
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< |
vertex(xyz[2]); |
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< |
} /* else overlapped */ |
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continue; |
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< |
} /* else bent */ |
| 135 |
< |
} |
| 136 |
< |
/* check triangles */ |
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< |
if (a1 > FTINY*FTINY) { |
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< |
printf("\n%s polygon %s.%da%d\n", |
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< |
argv[1], argv[2], i+1, j+1); |
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< |
printf("0\n0\n9\n"); |
| 141 |
< |
vertex(xyz[0]); |
| 142 |
< |
vertex(xyz[1]); |
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< |
vertex(xyz[2]); |
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< |
} |
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< |
if (a2 > FTINY*FTINY) { |
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< |
printf("\n%s polygon %s.%db%d\n", |
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< |
argv[1], argv[2], i+1, j+1); |
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< |
printf("0\n0\n9\n"); |
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< |
vertex(xyz[2]); |
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< |
vertex(xyz[1]); |
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< |
vertex(xyz[3]); |
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< |
} |
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> |
/* put polygons */ |
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> |
if ((i+j) & 1) |
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> |
putsquare(&row0[j], &row1[j], |
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> |
&row0[j+1], &row1[j+1]); |
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> |
else |
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> |
putsquare(&row1[j], &row1[j+1], |
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> |
&row0[j], &row0[j+1]); |
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} |
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} |
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|
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|
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userror: |
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fprintf(stderr, "Usage: %s material name ", argv[0]); |
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< |
fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-e expr] [-f file]\n"); |
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> |
fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-s][-e expr][-f file]\n"); |
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quit(1); |
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} |
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|
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|
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+ |
putsquare(p0, p1, p2, p3) /* put out a square */ |
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POINT *p0, *p1, *p2, *p3; |
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{ |
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static int nout = 0; |
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FVECT norm[4]; |
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+ |
int axis; |
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FVECT v1, v2, vc1, vc2; |
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+ |
int ok1, ok2; |
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+ |
/* compute exact normals */ |
| 138 |
+ |
fvsum(v1, p1->p, p0->p, -1.0); |
| 139 |
+ |
fvsum(v2, p2->p, p0->p, -1.0); |
| 140 |
+ |
fcross(vc1, v1, v2); |
| 141 |
+ |
ok1 = normalize(vc1) != 0.0; |
| 142 |
+ |
fvsum(v1, p2->p, p3->p, -1.0); |
| 143 |
+ |
fvsum(v2, p1->p, p3->p, -1.0); |
| 144 |
+ |
fcross(vc2, v1, v2); |
| 145 |
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ok2 = normalize(vc2) != 0.0; |
| 146 |
+ |
if (!(ok1 | ok2)) |
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+ |
return; |
| 148 |
+ |
/* compute normal interpolation */ |
| 149 |
+ |
axis = norminterp(norm, p0, p1, p2, p3); |
| 150 |
+ |
|
| 151 |
+ |
/* put out quadrilateral? */ |
| 152 |
+ |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) { |
| 153 |
+ |
printf("\n%s ", modname); |
| 154 |
+ |
if (axis != -1) { |
| 155 |
+ |
printf("texfunc %s\n", texname); |
| 156 |
+ |
printf(tsargs); |
| 157 |
+ |
printf("0\n13\t%d\n", axis); |
| 158 |
+ |
pvect(norm[0]); |
| 159 |
+ |
pvect(norm[1]); |
| 160 |
+ |
pvect(norm[2]); |
| 161 |
+ |
fvsum(v1, norm[3], vc1, -0.5); |
| 162 |
+ |
fvsum(v1, v1, vc2, -0.5); |
| 163 |
+ |
pvect(v1); |
| 164 |
+ |
printf("\n%s ", texname); |
| 165 |
+ |
} |
| 166 |
+ |
printf("polygon %s.%d\n", surfname, ++nout); |
| 167 |
+ |
printf("0\n0\n12\n"); |
| 168 |
+ |
pvect(p0->p); |
| 169 |
+ |
pvect(p1->p); |
| 170 |
+ |
pvect(p3->p); |
| 171 |
+ |
pvect(p2->p); |
| 172 |
+ |
return; |
| 173 |
+ |
} |
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+ |
/* put out triangles? */ |
| 175 |
+ |
if (ok1) { |
| 176 |
+ |
printf("\n%s ", modname); |
| 177 |
+ |
if (axis != -1) { |
| 178 |
+ |
printf("texfunc %s\n", texname); |
| 179 |
+ |
printf(tsargs); |
| 180 |
+ |
printf("0\n13\t%d\n", axis); |
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+ |
pvect(norm[0]); |
| 182 |
+ |
pvect(norm[1]); |
| 183 |
+ |
pvect(norm[2]); |
| 184 |
+ |
fvsum(v1, norm[3], vc1, -1.0); |
| 185 |
+ |
pvect(v1); |
| 186 |
+ |
printf("\n%s ", texname); |
| 187 |
+ |
} |
| 188 |
+ |
printf("polygon %s.%d\n", surfname, ++nout); |
| 189 |
+ |
printf("0\n0\n9\n"); |
| 190 |
+ |
pvect(p0->p); |
| 191 |
+ |
pvect(p1->p); |
| 192 |
+ |
pvect(p2->p); |
| 193 |
+ |
} |
| 194 |
+ |
if (ok2) { |
| 195 |
+ |
printf("\n%s ", modname); |
| 196 |
+ |
if (axis != -1) { |
| 197 |
+ |
printf("texfunc %s\n", texname); |
| 198 |
+ |
printf(tsargs); |
| 199 |
+ |
printf("0\n13\t%d\n", axis); |
| 200 |
+ |
pvect(norm[0]); |
| 201 |
+ |
pvect(norm[1]); |
| 202 |
+ |
pvect(norm[2]); |
| 203 |
+ |
fvsum(v2, norm[3], vc2, -1.0); |
| 204 |
+ |
pvect(v2); |
| 205 |
+ |
printf("\n%s ", texname); |
| 206 |
+ |
} |
| 207 |
+ |
printf("polygon %s.%d\n", surfname, ++nout); |
| 208 |
+ |
printf("0\n0\n9\n"); |
| 209 |
+ |
pvect(p2->p); |
| 210 |
+ |
pvect(p1->p); |
| 211 |
+ |
pvect(p3->p); |
| 212 |
+ |
} |
| 213 |
+ |
} |
| 214 |
+ |
|
| 215 |
+ |
|
| 216 |
|
comprow(s, row, siz) /* compute row of values */ |
| 217 |
|
double s; |
| 218 |
< |
register double *row; |
| 218 |
> |
register POINT *row; |
| 219 |
|
int siz; |
| 220 |
|
{ |
| 221 |
< |
double st[2], step; |
| 222 |
< |
|
| 221 |
> |
double st[2]; |
| 222 |
> |
register int i; |
| 223 |
> |
/* compute one past each end */ |
| 224 |
|
st[0] = s; |
| 225 |
< |
st[1] = 0.0; |
| 226 |
< |
step = 1.0 / siz; |
| 225 |
> |
for (i = -1; i <= siz+1; i++) { |
| 226 |
> |
st[1] = (double)i/siz; |
| 227 |
> |
row[i].p[0] = funvalue(XNAME, 2, st); |
| 228 |
> |
row[i].p[1] = funvalue(YNAME, 2, st); |
| 229 |
> |
row[i].p[2] = funvalue(ZNAME, 2, st); |
| 230 |
> |
} |
| 231 |
> |
} |
| 232 |
> |
|
| 233 |
> |
|
| 234 |
> |
compnorms(r0, r1, r2, siz) /* compute row of averaged normals */ |
| 235 |
> |
register POINT *r0, *r1, *r2; |
| 236 |
> |
int siz; |
| 237 |
> |
{ |
| 238 |
> |
FVECT v1, v2, vc; |
| 239 |
> |
register int i; |
| 240 |
> |
|
| 241 |
> |
if (!smooth) /* not needed if no smoothing */ |
| 242 |
> |
return; |
| 243 |
> |
/* compute middle points */ |
| 244 |
|
while (siz-- >= 0) { |
| 245 |
< |
*row++ = funvalue(XNAME, 2, st); |
| 246 |
< |
*row++ = funvalue(YNAME, 2, st); |
| 247 |
< |
*row++ = funvalue(ZNAME, 2, st); |
| 248 |
< |
st[1] += step; |
| 245 |
> |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
| 246 |
> |
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
| 247 |
> |
fcross(r1[0].n, v1, v2); |
| 248 |
> |
fvsum(v1, r0[0].p, r1[0].p, -1.0); |
| 249 |
> |
fcross(vc, v2, v1); |
| 250 |
> |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
| 251 |
> |
fvsum(v2, r1[-1].p, r1[0].p, -1.0); |
| 252 |
> |
fcross(vc, v1, v2); |
| 253 |
> |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
| 254 |
> |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
| 255 |
> |
fcross(vc, v2, v1); |
| 256 |
> |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
| 257 |
> |
normalize(r1[0].n); |
| 258 |
> |
r0++; r1++; r2++; |
| 259 |
|
} |
| 260 |
|
} |
| 261 |
|
|
| 262 |
|
|
| 263 |
+ |
int |
| 264 |
+ |
norminterp(resmat, p0, p1, p2, p3) /* compute normal interpolation */ |
| 265 |
+ |
register FVECT resmat[4]; |
| 266 |
+ |
POINT *p0, *p1, *p2, *p3; |
| 267 |
+ |
{ |
| 268 |
+ |
#define u ((ax+1)%3) |
| 269 |
+ |
#define v ((ax+2)%3) |
| 270 |
+ |
|
| 271 |
+ |
register int ax; |
| 272 |
+ |
double eqnmat[4][4]; |
| 273 |
+ |
FVECT v1; |
| 274 |
+ |
register int i, j; |
| 275 |
+ |
|
| 276 |
+ |
if (!smooth) /* no interpolation if no smoothing */ |
| 277 |
+ |
return(-1); |
| 278 |
+ |
/* find dominant axis */ |
| 279 |
+ |
VCOPY(v1, p0->n); |
| 280 |
+ |
fvsum(v1, v1, p1->n, 1.0); |
| 281 |
+ |
fvsum(v1, v1, p2->n, 1.0); |
| 282 |
+ |
fvsum(v1, v1, p3->n, 1.0); |
| 283 |
+ |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
| 284 |
+ |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
| 285 |
+ |
/* assign equation matrix */ |
| 286 |
+ |
eqnmat[0][0] = p0->p[u]*p0->p[v]; |
| 287 |
+ |
eqnmat[0][1] = p0->p[u]; |
| 288 |
+ |
eqnmat[0][2] = p0->p[v]; |
| 289 |
+ |
eqnmat[0][3] = 1.0; |
| 290 |
+ |
eqnmat[1][0] = p1->p[u]*p1->p[v]; |
| 291 |
+ |
eqnmat[1][1] = p1->p[u]; |
| 292 |
+ |
eqnmat[1][2] = p1->p[v]; |
| 293 |
+ |
eqnmat[1][3] = 1.0; |
| 294 |
+ |
eqnmat[2][0] = p2->p[u]*p2->p[v]; |
| 295 |
+ |
eqnmat[2][1] = p2->p[u]; |
| 296 |
+ |
eqnmat[2][2] = p2->p[v]; |
| 297 |
+ |
eqnmat[2][3] = 1.0; |
| 298 |
+ |
eqnmat[3][0] = p3->p[u]*p3->p[v]; |
| 299 |
+ |
eqnmat[3][1] = p3->p[u]; |
| 300 |
+ |
eqnmat[3][2] = p3->p[v]; |
| 301 |
+ |
eqnmat[3][3] = 1.0; |
| 302 |
+ |
/* invert matrix (solve system) */ |
| 303 |
+ |
if (!invmat(eqnmat, eqnmat)) |
| 304 |
+ |
return(-1); /* no solution */ |
| 305 |
+ |
/* compute result matrix */ |
| 306 |
+ |
for (j = 0; j < 4; j++) |
| 307 |
+ |
for (i = 0; i < 3; i++) |
| 308 |
+ |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
| 309 |
+ |
eqnmat[j][1]*p1->n[i] + |
| 310 |
+ |
eqnmat[j][2]*p2->n[i] + |
| 311 |
+ |
eqnmat[j][3]*p3->n[i]; |
| 312 |
+ |
return(ax); |
| 313 |
+ |
|
| 314 |
+ |
#undef u |
| 315 |
+ |
#undef v |
| 316 |
+ |
} |
| 317 |
+ |
|
| 318 |
+ |
|
| 319 |
+ |
/* |
| 320 |
+ |
* invmat - computes the inverse of mat into inverse. Returns 1 |
| 321 |
+ |
* if there exists an inverse, 0 otherwise. It uses Gaussian Elimination |
| 322 |
+ |
* method. |
| 323 |
+ |
*/ |
| 324 |
+ |
|
| 325 |
+ |
invmat(inverse,mat) |
| 326 |
+ |
double mat[4][4],inverse[4][4]; |
| 327 |
+ |
{ |
| 328 |
+ |
#define SWAP(a,b,t) (t=a,a=b,b=t) |
| 329 |
+ |
|
| 330 |
+ |
double m4tmp[4][4]; |
| 331 |
+ |
register int i,j,k; |
| 332 |
+ |
register double temp; |
| 333 |
+ |
|
| 334 |
+ |
bcopy((char *)mat, (char *)m4tmp, sizeof(m4tmp)); |
| 335 |
+ |
/* set inverse to identity */ |
| 336 |
+ |
for (i = 0; i < 4; i++) |
| 337 |
+ |
for (j = 0; j < 4; j++) |
| 338 |
+ |
inverse[i][j] = i==j ? 1.0 : 0.0; |
| 339 |
+ |
|
| 340 |
+ |
for(i = 0; i < 4; i++) { |
| 341 |
+ |
/* Look for raw with largest pivot and swap raws */ |
| 342 |
+ |
temp = FTINY; j = -1; |
| 343 |
+ |
for(k = i; k < 4; k++) |
| 344 |
+ |
if(ABS(m4tmp[k][i]) > temp) { |
| 345 |
+ |
temp = ABS(m4tmp[k][i]); |
| 346 |
+ |
j = k; |
| 347 |
+ |
} |
| 348 |
+ |
if(j == -1) /* No replacing raw -> no inverse */ |
| 349 |
+ |
return(0); |
| 350 |
+ |
if (j != i) |
| 351 |
+ |
for(k = 0; k < 4; k++) { |
| 352 |
+ |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
| 353 |
+ |
SWAP(inverse[i][k],inverse[j][k],temp); |
| 354 |
+ |
} |
| 355 |
+ |
|
| 356 |
+ |
temp = m4tmp[i][i]; |
| 357 |
+ |
for(k = 0; k < 4; k++) { |
| 358 |
+ |
m4tmp[i][k] /= temp; |
| 359 |
+ |
inverse[i][k] /= temp; |
| 360 |
+ |
} |
| 361 |
+ |
for(j = 0; j < 4; j++) { |
| 362 |
+ |
if(j != i) { |
| 363 |
+ |
temp = m4tmp[j][i]; |
| 364 |
+ |
for(k = 0; k < 4; k++) { |
| 365 |
+ |
m4tmp[j][k] -= m4tmp[i][k]*temp; |
| 366 |
+ |
inverse[j][k] -= inverse[i][k]*temp; |
| 367 |
+ |
} |
| 368 |
+ |
} |
| 369 |
+ |
} |
| 370 |
+ |
} |
| 371 |
+ |
return(1); |
| 372 |
+ |
|
| 373 |
+ |
#undef SWAP |
| 374 |
+ |
} |
| 375 |
+ |
|
| 376 |
+ |
|
| 377 |
|
eputs(msg) |
| 378 |
|
char *msg; |
| 379 |
|
{ |
| 417 |
|
argument(2)*(-2.0*t+3.0)*t*t + |
| 418 |
|
argument(3)*((t-2.0)*t+1.0)*t + |
| 419 |
|
argument(4)*(t-1.0)*t*t ); |
| 420 |
+ |
} |
| 421 |
+ |
|
| 422 |
+ |
|
| 423 |
+ |
double |
| 424 |
+ |
l_bezier() |
| 425 |
+ |
{ |
| 426 |
+ |
double t; |
| 427 |
+ |
|
| 428 |
+ |
t = argument(5); |
| 429 |
+ |
return( argument(1) * (1.+t*(-3.+t*(3.-t))) + |
| 430 |
+ |
argument(2) * 3.*t*(1.+t*(-2.+t)) + |
| 431 |
+ |
argument(3) * 3.*t*t*(1.-t) + |
| 432 |
+ |
argument(4) * t*t*t ); |
| 433 |
+ |
} |
| 434 |
+ |
|
| 435 |
+ |
|
| 436 |
+ |
double |
| 437 |
+ |
l_bspline() |
| 438 |
+ |
{ |
| 439 |
+ |
double t; |
| 440 |
+ |
|
| 441 |
+ |
t = argument(5); |
| 442 |
+ |
return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) + |
| 443 |
+ |
argument(2) * (2./3.+t*t*(-1.+1./2.*t)) + |
| 444 |
+ |
argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) + |
| 445 |
+ |
argument(4) * (1./6.*t*t*t) ); |
| 446 |
|
} |
