| 1 |
#ifndef lint
|
| 2 |
static const char RCSid[] = "$Id: gensurf.c,v 2.32 2025/04/18 23:02:53 greg Exp $";
|
| 3 |
#endif
|
| 4 |
/*
|
| 5 |
* gensurf.c - program to generate functional surfaces
|
| 6 |
*
|
| 7 |
* Parametric functions x(s,t), y(s,t) and z(s,t)
|
| 8 |
* specify the surface, which is tesselated into an m by n
|
| 9 |
* array of paired triangles.
|
| 10 |
* The surface normal is defined by the right hand
|
| 11 |
* rule applied to (s,t).
|
| 12 |
*
|
| 13 |
* 4/3/87
|
| 14 |
*
|
| 15 |
* 4/16/02 Added conditional vertex output
|
| 16 |
*/
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| 17 |
|
| 18 |
#include "standard.h"
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| 19 |
|
| 20 |
#include "paths.h"
|
| 21 |
#include "resolu.h"
|
| 22 |
#include "rterror.h"
|
| 23 |
#include "calcomp.h"
|
| 24 |
|
| 25 |
char XNAME[] = "X`SYS"; /* x function name */
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| 26 |
char YNAME[] = "Y`SYS"; /* y function name */
|
| 27 |
char ZNAME[] = "Z`SYS"; /* z function name */
|
| 28 |
|
| 29 |
char VNAME[] = "valid"; /* valid vertex name */
|
| 30 |
|
| 31 |
#define ABS(x) ((x)>=0 ? (x) : -(x))
|
| 32 |
|
| 33 |
#define ZEROVECT(v) (DOT(v,v) <= FTINY*FTINY)
|
| 34 |
|
| 35 |
#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2])
|
| 36 |
|
| 37 |
char vformat[] = "%18.12g %18.12g %18.12g\n";
|
| 38 |
char tsargs[] = "4 surf_dx surf_dy surf_dz surf.cal";
|
| 39 |
char texname[] = "Phong";
|
| 40 |
|
| 41 |
int smooth = 0; /* apply smoothing? */
|
| 42 |
int objout = 0; /* output .OBJ format? */
|
| 43 |
int rev = 0; /* invert normal directions? */
|
| 44 |
|
| 45 |
char *modname, *surfname;
|
| 46 |
|
| 47 |
/* recorded data flags */
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| 48 |
#define HASBORDER 01
|
| 49 |
#define TRIPLETS 02
|
| 50 |
/* a data structure */
|
| 51 |
struct {
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| 52 |
int flags; /* data type */
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| 53 |
short m, n; /* number of s and t values */
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| 54 |
RREAL *data; /* the data itself, s major sort */
|
| 55 |
} datarec; /* our recorded data */
|
| 56 |
|
| 57 |
/* XXX this is redundant with rt/noise3.c, should go to a library */
|
| 58 |
double l_hermite(char *), l_bezier(char *),
|
| 59 |
l_bspline(char *), l_dataval(char *);
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| 60 |
|
| 61 |
typedef struct {
|
| 62 |
int valid; /* point is valid (vertex number) */
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| 63 |
int nvalid; /* normal is valid (normal number) */
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| 64 |
FVECT p; /* vertex position */
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| 65 |
FVECT n; /* average normal */
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| 66 |
RREAL uv[2]; /* (u,v) position */
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| 67 |
} POINT;
|
| 68 |
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| 69 |
int nverts = 0; /* vertex output count */
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| 70 |
int nnorms = 0; /* normal output count */
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| 71 |
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| 72 |
void loaddata(char *file, int m, int n, int pointsize);
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| 73 |
double l_dataval(char *nam);
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| 74 |
void putobjrow(POINT *rp, int n);
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| 75 |
void putobjvert(POINT *p);
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| 76 |
void putsquare(POINT *p0, POINT *p1, POINT *p2, POINT *p3);
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| 77 |
void comprow(double s, POINT *row, int siz);
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| 78 |
void compnorms(POINT *r0, POINT *r1, POINT *r2, int siz);
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| 79 |
int norminterp(FVECT resmat[4], POINT *p0, POINT *p1, POINT *p2, POINT *p3);
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| 80 |
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| 81 |
|
| 82 |
int
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| 83 |
main(int argc, char *argv[])
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| 84 |
{
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| 85 |
POINT *row0, *row1, *row2, *rp;
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| 86 |
int i, j, m, n;
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| 87 |
char stmp[256];
|
| 88 |
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| 89 |
esupport |= E_VARIABLE|E_FUNCTION|E_RCONST;
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| 90 |
esupport &= ~(E_OUTCHAN|E_INCHAN);
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| 91 |
varset("PI", ':', PI);
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| 92 |
funset("hermite", 5, ':', l_hermite);
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| 93 |
funset("bezier", 5, ':', l_bezier);
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| 94 |
funset("bspline", 5, ':', l_bspline);
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| 95 |
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| 96 |
if (argc < 8)
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| 97 |
goto userror;
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| 98 |
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| 99 |
for (i = 8; i < argc; i++)
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| 100 |
if (!strcmp(argv[i], "-e"))
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| 101 |
scompile(argv[++i], NULL, 0);
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| 102 |
else if (!strcmp(argv[i], "-f")) {
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| 103 |
char *fpath = getpath(argv[++i], getrlibpath(), 0);
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| 104 |
if (fpath == NULL) {
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| 105 |
fprintf(stderr, "%s: cannot find file '%s'\n",
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| 106 |
argv[0], argv[i]);
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| 107 |
quit(1);
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| 108 |
}
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| 109 |
fcompile(fpath);
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} else if (!strcmp(argv[i], "-s"))
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smooth++;
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| 112 |
else if (!strcmp(argv[i], "-o"))
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objout++;
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| 114 |
else if (!strcmp(argv[i], "-i"))
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| 115 |
rev = 1;
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| 116 |
else
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goto userror;
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| 118 |
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| 119 |
modname = argv[1];
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| 120 |
surfname = argv[2];
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| 121 |
m = eval(argv[6]) + .5;
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| 122 |
n = eval(argv[7]) + .5;
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| 123 |
if (m <= 0 || n <= 0)
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| 124 |
goto userror;
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| 125 |
if (!strcmp(argv[5], "-") || access(argv[5], 4) == 0) { /* file? */
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| 126 |
funset(ZNAME, 2, ':', l_dataval);
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| 127 |
if (!strcmp(argv[5],argv[3]) && !strcmp(argv[5],argv[4])) {
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| 128 |
loaddata(argv[5], m, n, 3);
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| 129 |
funset(XNAME, 2, ':', l_dataval);
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| 130 |
funset(YNAME, 2, ':', l_dataval);
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| 131 |
} else {
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| 132 |
loaddata(argv[5], m, n, 1);
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| 133 |
sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]);
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| 134 |
scompile(stmp, NULL, 0);
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| 135 |
sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]);
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| 136 |
scompile(stmp, NULL, 0);
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| 137 |
}
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| 138 |
} else {
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| 139 |
sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]);
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| 140 |
scompile(stmp, NULL, 0);
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| 141 |
sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]);
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| 142 |
scompile(stmp, NULL, 0);
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| 143 |
sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]);
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| 144 |
scompile(stmp, NULL, 0);
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| 145 |
}
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| 146 |
row0 = (POINT *)malloc((n+3)*sizeof(POINT));
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| 147 |
row1 = (POINT *)malloc((n+3)*sizeof(POINT));
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| 148 |
row2 = (POINT *)malloc((n+3)*sizeof(POINT));
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| 149 |
if (row0 == NULL || row1 == NULL || row2 == NULL) {
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| 150 |
fprintf(stderr, "%s: out of memory\n", argv[0]);
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| 151 |
quit(1);
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| 152 |
}
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| 153 |
row0++; row1++; row2++;
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/* print header */
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fputs("# ", stdout);
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| 156 |
printargs(argc, argv, stdout);
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doptimize(1);
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| 158 |
eclock++;
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| 159 |
/* initialize */
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| 160 |
comprow(-1.0/m, row0, n);
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| 161 |
comprow(0.0, row1, n);
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| 162 |
comprow(1.0/m, row2, n);
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| 163 |
compnorms(row0, row1, row2, n);
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| 164 |
if (objout) {
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| 165 |
printf("\nusemtl %s\n\n", modname);
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printf("o %s\n\n", surfname);
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| 167 |
putobjrow(row1, n);
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}
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| 169 |
/* for each row */
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| 170 |
for (i = 0; i < m; i++) {
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| 171 |
/* compute next row */
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rp = row0;
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| 173 |
row0 = row1;
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row1 = row2;
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row2 = rp;
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| 176 |
comprow((double)(i+2)/m, row2, n);
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compnorms(row0, row1, row2, n);
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| 178 |
if (objout)
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putobjrow(row1, n);
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for (j = 0; j < n; j++) {
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int orient = (j & 1);
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/* put polygons */
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if (!(row0[j].valid && row1[j+1].valid))
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orient = 1;
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else if (!(row1[j].valid && row0[j+1].valid))
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orient = 0;
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if (orient)
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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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return 0;
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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][-o][-e expr][-f file]\n");
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return 1;
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}
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void
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loaddata( /* load point data from file */
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char *file,
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int m,
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int n,
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int pointsize
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)
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{
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FILE *fp;
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char word[64];
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int size;
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RREAL *dp;
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datarec.flags = HASBORDER; /* assume border values */
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datarec.m = m+1;
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datarec.n = n+1;
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size = datarec.m*datarec.n*pointsize;
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if (pointsize == 3)
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datarec.flags |= TRIPLETS;
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dp = (RREAL *)malloc(size*sizeof(RREAL));
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if ((datarec.data = dp) == NULL) {
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| 227 |
fputs("Out of memory\n", stderr);
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| 228 |
exit(1);
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| 229 |
}
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| 230 |
if (!strcmp(file, "-")) {
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| 231 |
file = "<stdin>";
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fp = stdin;
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} else if ((fp = fopen(file, "r")) == NULL) {
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| 234 |
fputs(file, stderr);
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| 235 |
fputs(": cannot open\n", stderr);
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| 236 |
exit(1);
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| 237 |
}
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| 238 |
while (size > 0 && fgetword(word, sizeof(word), fp) != NULL) {
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| 239 |
if (!isflt(word)) {
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| 240 |
fprintf(stderr, "%s: garbled data value: %s\n",
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| 241 |
file, word);
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| 242 |
exit(1);
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| 243 |
}
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| 244 |
*dp++ = atof(word);
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| 245 |
size--;
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| 246 |
}
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| 247 |
if (size == (m+n+1)*pointsize) { /* no border after all */
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| 248 |
dp = (RREAL *)realloc(datarec.data,
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| 249 |
m*n*pointsize*sizeof(RREAL));
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| 250 |
if (dp != NULL)
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| 251 |
datarec.data = dp;
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| 252 |
datarec.flags &= ~HASBORDER;
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| 253 |
datarec.m = m;
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| 254 |
datarec.n = n;
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| 255 |
size = 0;
|
| 256 |
}
|
| 257 |
if (datarec.m < 2 || datarec.n < 2 || size != 0 ||
|
| 258 |
fgetword(word, sizeof(word), fp) != NULL) {
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| 259 |
fputs(file, stderr);
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| 260 |
fputs(": bad number of data points\n", stderr);
|
| 261 |
exit(1);
|
| 262 |
}
|
| 263 |
fclose(fp);
|
| 264 |
}
|
| 265 |
|
| 266 |
|
| 267 |
double
|
| 268 |
l_dataval( /* return recorded data value */
|
| 269 |
char *nam
|
| 270 |
)
|
| 271 |
{
|
| 272 |
double u, v;
|
| 273 |
int i, j;
|
| 274 |
RREAL *dp;
|
| 275 |
double d00, d01, d10, d11;
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| 276 |
/* compute coordinates */
|
| 277 |
u = argument(1); v = argument(2);
|
| 278 |
if (datarec.flags & HASBORDER) {
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| 279 |
i = u *= datarec.m-1;
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| 280 |
j = v *= datarec.n-1;
|
| 281 |
} else {
|
| 282 |
i = u = u*datarec.m - .5;
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| 283 |
j = v = v*datarec.n - .5;
|
| 284 |
}
|
| 285 |
if (i < 0) i = 0;
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| 286 |
else if (i > datarec.m-2) i = datarec.m-2;
|
| 287 |
if (j < 0) j = 0;
|
| 288 |
else if (j > datarec.n-2) j = datarec.n-2;
|
| 289 |
/* compute value */
|
| 290 |
if (datarec.flags & TRIPLETS) {
|
| 291 |
dp = datarec.data + 3*(j*datarec.m + i);
|
| 292 |
if (nam == ZNAME)
|
| 293 |
dp += 2;
|
| 294 |
else if (nam == YNAME)
|
| 295 |
dp++;
|
| 296 |
d00 = dp[0]; d01 = dp[3];
|
| 297 |
dp += 3*datarec.m;
|
| 298 |
d10 = dp[0]; d11 = dp[3];
|
| 299 |
} else {
|
| 300 |
dp = datarec.data + j*datarec.m + i;
|
| 301 |
d00 = dp[0]; d01 = dp[1];
|
| 302 |
dp += datarec.m;
|
| 303 |
d10 = dp[0]; d11 = dp[1];
|
| 304 |
}
|
| 305 |
/* bilinear interpolation */
|
| 306 |
return((j+1-v)*((i+1-u)*d00+(u-i)*d01)+(v-j)*((i+1-u)*d10+(u-i)*d11));
|
| 307 |
}
|
| 308 |
|
| 309 |
|
| 310 |
void
|
| 311 |
putobjrow( /* output vertex row to .OBJ */
|
| 312 |
POINT *rp,
|
| 313 |
int n
|
| 314 |
)
|
| 315 |
{
|
| 316 |
static FVECT prevNorm;
|
| 317 |
|
| 318 |
for ( ; n-- >= 0; rp++) {
|
| 319 |
if (!rp->valid)
|
| 320 |
continue;
|
| 321 |
fputs("v ", stdout);
|
| 322 |
pvect(rp->p);
|
| 323 |
rp->valid = ++nverts;
|
| 324 |
printf("\tvt %.9g %.9g\n", rp->uv[0], rp->uv[1]);
|
| 325 |
if (!smooth || ZEROVECT(rp->n))
|
| 326 |
rp->nvalid = 0;
|
| 327 |
else if (VABSEQ(rp->n, prevNorm))
|
| 328 |
rp->nvalid = nnorms;
|
| 329 |
else {
|
| 330 |
printf("\tvn %.9g %.9g %.9g\n",
|
| 331 |
rp->n[0], rp->n[1], rp->n[2]);
|
| 332 |
rp->nvalid = ++nnorms;
|
| 333 |
VCOPY(prevNorm, rp->n);
|
| 334 |
}
|
| 335 |
}
|
| 336 |
}
|
| 337 |
|
| 338 |
|
| 339 |
void
|
| 340 |
putobjvert( /* put out OBJ vertex index triplet */
|
| 341 |
POINT *p
|
| 342 |
)
|
| 343 |
{
|
| 344 |
int pti = p->valid ? p->valid-nverts-1 : 0;
|
| 345 |
int ni = p->nvalid ? p->nvalid-nnorms-1 : 0;
|
| 346 |
|
| 347 |
printf(" %d/%d/%d", pti, pti, ni);
|
| 348 |
}
|
| 349 |
|
| 350 |
|
| 351 |
void
|
| 352 |
putsquare( /* put out a square */
|
| 353 |
POINT *p0,
|
| 354 |
POINT *p1,
|
| 355 |
POINT *p2,
|
| 356 |
POINT *p3
|
| 357 |
)
|
| 358 |
{
|
| 359 |
static int nout = 0;
|
| 360 |
FVECT norm[4];
|
| 361 |
int axis;
|
| 362 |
FVECT v1, v2, vc1, vc2;
|
| 363 |
int ok1, ok2;
|
| 364 |
|
| 365 |
if (rev) { /* reverse normals? */
|
| 366 |
POINT *pt = p1; p1 = p2; p2 = pt;
|
| 367 |
}
|
| 368 |
/* compute exact normals */
|
| 369 |
ok1 = (p0->valid && p1->valid && p2->valid);
|
| 370 |
if (ok1) {
|
| 371 |
VSUB(v1, p1->p, p0->p);
|
| 372 |
VSUB(v2, p2->p, p0->p);
|
| 373 |
fcross(vc1, v1, v2);
|
| 374 |
ok1 = (normalize(vc1) != 0.0);
|
| 375 |
}
|
| 376 |
ok2 = (p1->valid && p2->valid && p3->valid);
|
| 377 |
if (ok2) {
|
| 378 |
VSUB(v1, p2->p, p3->p);
|
| 379 |
VSUB(v2, p1->p, p3->p);
|
| 380 |
fcross(vc2, v1, v2);
|
| 381 |
ok2 = (normalize(vc2) != 0.0);
|
| 382 |
}
|
| 383 |
if (!(ok1 | ok2))
|
| 384 |
return;
|
| 385 |
if (objout) { /* output .OBJ faces */
|
| 386 |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
|
| 387 |
putc('f', stdout);
|
| 388 |
putobjvert(p0); putobjvert(p1);
|
| 389 |
putobjvert(p3); putobjvert(p2);
|
| 390 |
putc('\n', stdout);
|
| 391 |
return;
|
| 392 |
}
|
| 393 |
if (ok1) {
|
| 394 |
putc('f', stdout);
|
| 395 |
putobjvert(p0); putobjvert(p1); putobjvert(p2);
|
| 396 |
putc('\n', stdout);
|
| 397 |
}
|
| 398 |
if (ok2) {
|
| 399 |
putc('f', stdout);
|
| 400 |
putobjvert(p2); putobjvert(p1); putobjvert(p3);
|
| 401 |
putc('\n', stdout);
|
| 402 |
}
|
| 403 |
return;
|
| 404 |
}
|
| 405 |
/* compute normal interpolation */
|
| 406 |
axis = norminterp(norm, p0, p1, p2, p3);
|
| 407 |
|
| 408 |
/* put out quadrilateral? */
|
| 409 |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
|
| 410 |
printf("\n%s ", modname);
|
| 411 |
if (axis != -1) {
|
| 412 |
printf("texfunc %s\n%s\n", texname, tsargs);
|
| 413 |
printf("0\n13\t%d\n", axis);
|
| 414 |
pvect(norm[0]);
|
| 415 |
pvect(norm[1]);
|
| 416 |
pvect(norm[2]);
|
| 417 |
fvsum(v1, norm[3], vc1, -0.5);
|
| 418 |
fvsum(v1, v1, vc2, -0.5);
|
| 419 |
pvect(v1);
|
| 420 |
printf("\n%s ", texname);
|
| 421 |
}
|
| 422 |
printf("polygon %s.%d\n", surfname, ++nout);
|
| 423 |
printf("0\n0\n12\n");
|
| 424 |
pvect(p0->p);
|
| 425 |
pvect(p1->p);
|
| 426 |
pvect(p3->p);
|
| 427 |
pvect(p2->p);
|
| 428 |
return;
|
| 429 |
}
|
| 430 |
/* put out triangles? */
|
| 431 |
if (ok1) {
|
| 432 |
printf("\n%s ", modname);
|
| 433 |
if (axis != -1) {
|
| 434 |
printf("texfunc %s\n%s\n", texname, tsargs);
|
| 435 |
printf("0\n13\t%d\n", axis);
|
| 436 |
pvect(norm[0]);
|
| 437 |
pvect(norm[1]);
|
| 438 |
pvect(norm[2]);
|
| 439 |
fvsum(v1, norm[3], vc1, -1.0);
|
| 440 |
pvect(v1);
|
| 441 |
printf("\n%s ", texname);
|
| 442 |
}
|
| 443 |
printf("polygon %s.%d\n", surfname, ++nout);
|
| 444 |
printf("0\n0\n9\n");
|
| 445 |
pvect(p0->p);
|
| 446 |
pvect(p1->p);
|
| 447 |
pvect(p2->p);
|
| 448 |
}
|
| 449 |
if (ok2) {
|
| 450 |
printf("\n%s ", modname);
|
| 451 |
if (axis != -1) {
|
| 452 |
printf("texfunc %s\n%s\n", texname, tsargs);
|
| 453 |
printf("0\n13\t%d\n", axis);
|
| 454 |
pvect(norm[0]);
|
| 455 |
pvect(norm[1]);
|
| 456 |
pvect(norm[2]);
|
| 457 |
fvsum(v2, norm[3], vc2, -1.0);
|
| 458 |
pvect(v2);
|
| 459 |
printf("\n%s ", texname);
|
| 460 |
}
|
| 461 |
printf("polygon %s.%d\n", surfname, ++nout);
|
| 462 |
printf("0\n0\n9\n");
|
| 463 |
pvect(p2->p);
|
| 464 |
pvect(p1->p);
|
| 465 |
pvect(p3->p);
|
| 466 |
}
|
| 467 |
}
|
| 468 |
|
| 469 |
|
| 470 |
void
|
| 471 |
comprow( /* compute row of values */
|
| 472 |
double s,
|
| 473 |
POINT *row,
|
| 474 |
int siz
|
| 475 |
)
|
| 476 |
{
|
| 477 |
double st[2];
|
| 478 |
int end;
|
| 479 |
int checkvalid;
|
| 480 |
int i;
|
| 481 |
|
| 482 |
if (smooth) {
|
| 483 |
i = -1; /* compute one past each end */
|
| 484 |
end = siz+1;
|
| 485 |
} else {
|
| 486 |
if (s < -FTINY || s > 1.0+FTINY)
|
| 487 |
return;
|
| 488 |
i = 0;
|
| 489 |
end = siz;
|
| 490 |
}
|
| 491 |
st[0] = s;
|
| 492 |
checkvalid = (fundefined(VNAME) == 2);
|
| 493 |
while (i <= end) {
|
| 494 |
st[1] = (double)i/siz;
|
| 495 |
if (checkvalid && funvalue(VNAME, 2, st) <= 0.0) {
|
| 496 |
row[i].valid = 0;
|
| 497 |
row[i].p[0] = row[i].p[1] = row[i].p[2] = 0.0;
|
| 498 |
row[i].uv[0] = row[i].uv[1] = 0.0;
|
| 499 |
} else {
|
| 500 |
row[i].valid = 1;
|
| 501 |
row[i].p[0] = funvalue(XNAME, 2, st);
|
| 502 |
row[i].p[1] = funvalue(YNAME, 2, st);
|
| 503 |
row[i].p[2] = funvalue(ZNAME, 2, st);
|
| 504 |
row[i].uv[0] = st[0];
|
| 505 |
row[i].uv[1] = st[1];
|
| 506 |
}
|
| 507 |
i++;
|
| 508 |
}
|
| 509 |
}
|
| 510 |
|
| 511 |
|
| 512 |
void
|
| 513 |
compnorms( /* compute row of averaged normals */
|
| 514 |
POINT *r0,
|
| 515 |
POINT *r1,
|
| 516 |
POINT *r2,
|
| 517 |
int siz
|
| 518 |
)
|
| 519 |
{
|
| 520 |
FVECT v1, v2;
|
| 521 |
|
| 522 |
if (!smooth) /* not needed if no smoothing */
|
| 523 |
return;
|
| 524 |
/* compute row 1 normals */
|
| 525 |
while (siz-- >= 0) {
|
| 526 |
if (!r1[0].valid)
|
| 527 |
goto skip;
|
| 528 |
if (!r0[0].valid) {
|
| 529 |
if (!r2[0].valid) {
|
| 530 |
r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
|
| 531 |
goto skip;
|
| 532 |
}
|
| 533 |
fvsum(v1, r2[0].p, r1[0].p, -1.0);
|
| 534 |
} else if (!r2[0].valid)
|
| 535 |
fvsum(v1, r1[0].p, r0[0].p, -1.0);
|
| 536 |
else
|
| 537 |
fvsum(v1, r2[0].p, r0[0].p, -1.0);
|
| 538 |
if (!r1[-1].valid) {
|
| 539 |
if (!r1[1].valid) {
|
| 540 |
r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
|
| 541 |
goto skip;
|
| 542 |
}
|
| 543 |
fvsum(v2, r1[1].p, r1[0].p, -1.0);
|
| 544 |
} else if (!r1[1].valid)
|
| 545 |
fvsum(v2, r1[0].p, r1[-1].p, -1.0);
|
| 546 |
else
|
| 547 |
fvsum(v2, r1[1].p, r1[-1].p, -1.0);
|
| 548 |
if (rev)
|
| 549 |
fcross(r1[0].n, v2, v1);
|
| 550 |
else
|
| 551 |
fcross(r1[0].n, v1, v2);
|
| 552 |
normalize(r1[0].n);
|
| 553 |
skip:
|
| 554 |
r0++; r1++; r2++;
|
| 555 |
}
|
| 556 |
}
|
| 557 |
|
| 558 |
|
| 559 |
int
|
| 560 |
norminterp( /* compute normal interpolation */
|
| 561 |
FVECT resmat[4],
|
| 562 |
POINT *p0,
|
| 563 |
POINT *p1,
|
| 564 |
POINT *p2,
|
| 565 |
POINT *p3
|
| 566 |
)
|
| 567 |
{
|
| 568 |
#define u ((ax+1)%3)
|
| 569 |
#define v ((ax+2)%3)
|
| 570 |
|
| 571 |
int ax;
|
| 572 |
MAT4 eqnmat;
|
| 573 |
FVECT v1;
|
| 574 |
int i, j;
|
| 575 |
|
| 576 |
if (!smooth) /* no interpolation if no smoothing */
|
| 577 |
return(-1);
|
| 578 |
/* find dominant axis */
|
| 579 |
VCOPY(v1, p0->n);
|
| 580 |
fvsum(v1, v1, p1->n, 1.0);
|
| 581 |
fvsum(v1, v1, p2->n, 1.0);
|
| 582 |
fvsum(v1, v1, p3->n, 1.0);
|
| 583 |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1;
|
| 584 |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2;
|
| 585 |
/* assign equation matrix */
|
| 586 |
eqnmat[0][0] = p0->p[u]*p0->p[v];
|
| 587 |
eqnmat[0][1] = p0->p[u];
|
| 588 |
eqnmat[0][2] = p0->p[v];
|
| 589 |
eqnmat[0][3] = 1.0;
|
| 590 |
eqnmat[1][0] = p1->p[u]*p1->p[v];
|
| 591 |
eqnmat[1][1] = p1->p[u];
|
| 592 |
eqnmat[1][2] = p1->p[v];
|
| 593 |
eqnmat[1][3] = 1.0;
|
| 594 |
eqnmat[2][0] = p2->p[u]*p2->p[v];
|
| 595 |
eqnmat[2][1] = p2->p[u];
|
| 596 |
eqnmat[2][2] = p2->p[v];
|
| 597 |
eqnmat[2][3] = 1.0;
|
| 598 |
eqnmat[3][0] = p3->p[u]*p3->p[v];
|
| 599 |
eqnmat[3][1] = p3->p[u];
|
| 600 |
eqnmat[3][2] = p3->p[v];
|
| 601 |
eqnmat[3][3] = 1.0;
|
| 602 |
/* invert matrix (solve system) */
|
| 603 |
if (!invmat4(eqnmat, eqnmat))
|
| 604 |
return(-1); /* no solution */
|
| 605 |
/* compute result matrix */
|
| 606 |
for (j = 0; j < 4; j++)
|
| 607 |
for (i = 0; i < 3; i++)
|
| 608 |
resmat[j][i] = eqnmat[j][0]*p0->n[i] +
|
| 609 |
eqnmat[j][1]*p1->n[i] +
|
| 610 |
eqnmat[j][2]*p2->n[i] +
|
| 611 |
eqnmat[j][3]*p3->n[i];
|
| 612 |
return(ax);
|
| 613 |
|
| 614 |
#undef u
|
| 615 |
#undef v
|
| 616 |
}
|
| 617 |
|
| 618 |
|
| 619 |
double
|
| 620 |
l_hermite(char *nm)
|
| 621 |
{
|
| 622 |
double t;
|
| 623 |
|
| 624 |
t = argument(5);
|
| 625 |
return( argument(1)*((2.0*t-3.0)*t*t+1.0) +
|
| 626 |
argument(2)*(-2.0*t+3.0)*t*t +
|
| 627 |
argument(3)*((t-2.0)*t+1.0)*t +
|
| 628 |
argument(4)*(t-1.0)*t*t );
|
| 629 |
}
|
| 630 |
|
| 631 |
|
| 632 |
double
|
| 633 |
l_bezier(char *nm)
|
| 634 |
{
|
| 635 |
double t;
|
| 636 |
|
| 637 |
t = argument(5);
|
| 638 |
return( argument(1) * (1.+t*(-3.+t*(3.-t))) +
|
| 639 |
argument(2) * 3.*t*(1.+t*(-2.+t)) +
|
| 640 |
argument(3) * 3.*t*t*(1.-t) +
|
| 641 |
argument(4) * t*t*t );
|
| 642 |
}
|
| 643 |
|
| 644 |
|
| 645 |
double
|
| 646 |
l_bspline(char *nm)
|
| 647 |
{
|
| 648 |
double t;
|
| 649 |
|
| 650 |
t = argument(5);
|
| 651 |
return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) +
|
| 652 |
argument(2) * (2./3.+t*t*(-1.+1./2.*t)) +
|
| 653 |
argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) +
|
| 654 |
argument(4) * (1./6.*t*t*t) );
|
| 655 |
}
|
