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#ifndef lint |
| 2 |
static char SCCSid[] = "$SunId$ LBL"; |
| 3 |
#endif |
| 4 |
|
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/* Copyright (c) 1989 Regents of the University of California */ |
| 6 |
|
| 7 |
/* |
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* gensurf.c - program to generate functional surfaces |
| 9 |
* |
| 10 |
* Parametric functions x(s,t), y(s,t) and z(s,t) |
| 11 |
* specify the surface, which is tesselated into an m by n |
| 12 |
* array of paired triangles. |
| 13 |
* The surface normal is defined by the right hand |
| 14 |
* rule applied to (s,t). |
| 15 |
* |
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* 4/3/87 |
| 17 |
*/ |
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|
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#include "standard.h" |
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|
| 21 |
#define XNAME "X_" /* x function name */ |
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#define YNAME "Y_" /* y function name */ |
| 23 |
#define ZNAME "Z_" /* z function name */ |
| 24 |
|
| 25 |
#define ABS(x) ((x)>=0 ? (x) : -(x)) |
| 26 |
|
| 27 |
#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
| 28 |
|
| 29 |
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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|
| 33 |
int smooth = 0; /* apply smoothing? */ |
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|
| 35 |
char *modname, *surfname; |
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|
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double funvalue(), l_hermite(), l_bezier(), l_bspline(), argument(); |
| 38 |
|
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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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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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|
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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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|
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for (i = 8; i < argc; i++) |
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if (!strcmp(argv[i], "-e")) |
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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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scompile(NULL, stmp); |
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sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]); |
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scompile(NULL, stmp); |
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m = atoi(argv[6]); |
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n = atoi(argv[7]); |
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if (m <= 0 || n <= 0) |
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goto userror; |
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|
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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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/* 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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rp = row0; |
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row0 = row1; |
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row1 = row2; |
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row2 = rp; |
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comprow((double)(i+2)/m, row2, n); |
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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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/* 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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quit(0); |
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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 [-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 */ |
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fvsum(v1, p1->p, p0->p, -1.0); |
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fvsum(v2, p2->p, p0->p, -1.0); |
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fcross(vc1, v1, v2); |
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ok1 = normalize(vc1) != 0.0; |
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fvsum(v1, p2->p, p3->p, -1.0); |
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fvsum(v2, p1->p, p3->p, -1.0); |
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fcross(vc2, v1, v2); |
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ok2 = normalize(vc2) != 0.0; |
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if (!(ok1 | ok2)) |
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return; |
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/* compute normal interpolation */ |
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axis = norminterp(norm, p0, p1, p2, p3); |
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|
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/* put out quadrilateral? */ |
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if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) { |
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printf("\n%s ", modname); |
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if (axis != -1) { |
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printf("texfunc %s\n", texname); |
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printf(tsargs); |
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printf("0\n13\t%d\n", axis); |
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pvect(norm[0]); |
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pvect(norm[1]); |
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pvect(norm[2]); |
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fvsum(v1, norm[3], vc1, -0.5); |
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fvsum(v1, v1, vc2, -0.5); |
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pvect(v1); |
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printf("\n%s ", texname); |
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} |
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printf("polygon %s.%d\n", surfname, ++nout); |
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printf("0\n0\n12\n"); |
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pvect(p0->p); |
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pvect(p1->p); |
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pvect(p3->p); |
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pvect(p2->p); |
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return; |
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} |
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/* put out triangles? */ |
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if (ok1) { |
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printf("\n%s ", modname); |
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if (axis != -1) { |
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printf("texfunc %s\n", texname); |
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printf(tsargs); |
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printf("0\n13\t%d\n", axis); |
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pvect(norm[0]); |
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pvect(norm[1]); |
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pvect(norm[2]); |
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fvsum(v1, norm[3], vc1, -1.0); |
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pvect(v1); |
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printf("\n%s ", texname); |
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} |
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printf("polygon %s.%d\n", surfname, ++nout); |
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printf("0\n0\n9\n"); |
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pvect(p0->p); |
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pvect(p1->p); |
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pvect(p2->p); |
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} |
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if (ok2) { |
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printf("\n%s ", modname); |
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if (axis != -1) { |
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printf("texfunc %s\n", texname); |
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printf(tsargs); |
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printf("0\n13\t%d\n", axis); |
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pvect(norm[0]); |
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pvect(norm[1]); |
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pvect(norm[2]); |
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fvsum(v2, norm[3], vc2, -1.0); |
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pvect(v2); |
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printf("\n%s ", texname); |
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} |
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printf("polygon %s.%d\n", surfname, ++nout); |
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printf("0\n0\n9\n"); |
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pvect(p2->p); |
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pvect(p1->p); |
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pvect(p3->p); |
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} |
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} |
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|
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|
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comprow(s, row, siz) /* compute row of values */ |
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double s; |
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register POINT *row; |
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int siz; |
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{ |
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double st[2]; |
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register int i; |
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/* compute one past each end */ |
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st[0] = s; |
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for (i = -1; i <= siz+1; i++) { |
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st[1] = (double)i/siz; |
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row[i].p[0] = funvalue(XNAME, 2, st); |
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row[i].p[1] = funvalue(YNAME, 2, st); |
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row[i].p[2] = funvalue(ZNAME, 2, st); |
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} |
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} |
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|
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|
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compnorms(r0, r1, r2, siz) /* compute row of averaged normals */ |
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register POINT *r0, *r1, *r2; |
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int siz; |
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{ |
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FVECT v1, v2, vc; |
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register int i; |
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|
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if (!smooth) /* not needed if no smoothing */ |
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return; |
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/* compute middle points */ |
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while (siz-- >= 0) { |
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fvsum(v1, r2[0].p, r1[0].p, -1.0); |
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fvsum(v2, r1[1].p, r1[0].p, -1.0); |
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fcross(r1[0].n, v1, v2); |
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fvsum(v1, r0[0].p, r1[0].p, -1.0); |
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fcross(vc, v2, v1); |
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fvsum(r1[0].n, r1[0].n, vc, 1.0); |
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fvsum(v2, r1[-1].p, r1[0].p, -1.0); |
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fcross(vc, v1, v2); |
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fvsum(r1[0].n, r1[0].n, vc, 1.0); |
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fvsum(v1, r2[0].p, r1[0].p, -1.0); |
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fcross(vc, v2, v1); |
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fvsum(r1[0].n, r1[0].n, vc, 1.0); |
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normalize(r1[0].n); |
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r0++; r1++; r2++; |
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} |
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} |
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|
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|
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int |
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norminterp(resmat, p0, p1, p2, p3) /* compute normal interpolation */ |
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register FVECT resmat[4]; |
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POINT *p0, *p1, *p2, *p3; |
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{ |
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#define u ((ax+1)%3) |
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#define v ((ax+2)%3) |
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|
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register int ax; |
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double eqnmat[4][4]; |
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FVECT v1; |
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register int i, j; |
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|
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if (!smooth) /* no interpolation if no smoothing */ |
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return(-1); |
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/* find dominant axis */ |
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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); |
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ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
| 284 |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
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/* 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]; |
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eqnmat[1][3] = 1.0; |
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eqnmat[2][0] = p2->p[u]*p2->p[v]; |
| 295 |
eqnmat[2][1] = p2->p[u]; |
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eqnmat[2][2] = p2->p[v]; |
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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]; |
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eqnmat[3][3] = 1.0; |
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/* invert matrix (solve system) */ |
| 303 |
if (!invmat(eqnmat, eqnmat)) |
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return(-1); /* no solution */ |
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/* compute result matrix */ |
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for (j = 0; j < 4; j++) |
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for (i = 0; i < 3; i++) |
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resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
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eqnmat[j][1]*p1->n[i] + |
| 310 |
eqnmat[j][2]*p2->n[i] + |
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eqnmat[j][3]*p3->n[i]; |
| 312 |
return(ax); |
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|
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#undef u |
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#undef v |
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} |
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|
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|
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/* |
| 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. |
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*/ |
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|
| 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 |
{ |
| 380 |
fputs(msg, stderr); |
| 381 |
} |
| 382 |
|
| 383 |
|
| 384 |
wputs(msg) |
| 385 |
char *msg; |
| 386 |
{ |
| 387 |
eputs(msg); |
| 388 |
} |
| 389 |
|
| 390 |
|
| 391 |
quit(code) |
| 392 |
{ |
| 393 |
exit(code); |
| 394 |
} |
| 395 |
|
| 396 |
|
| 397 |
printhead(ac, av) /* print command header */ |
| 398 |
register int ac; |
| 399 |
register char **av; |
| 400 |
{ |
| 401 |
putchar('#'); |
| 402 |
while (ac--) { |
| 403 |
putchar(' '); |
| 404 |
fputs(*av++, stdout); |
| 405 |
} |
| 406 |
putchar('\n'); |
| 407 |
} |
| 408 |
|
| 409 |
|
| 410 |
double |
| 411 |
l_hermite() |
| 412 |
{ |
| 413 |
double t; |
| 414 |
|
| 415 |
t = argument(5); |
| 416 |
return( argument(1)*((2.0*t-3.0)*t*t+1.0) + |
| 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 |
} |
