| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id: gensurf.c,v 2.23 2017/01/28 23:09:24 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 |
*/ |
| 17 |
|
| 18 |
#include "standard.h" |
| 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 */ |
| 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 |
|
| 44 |
char *modname, *surfname; |
| 45 |
|
| 46 |
/* recorded data flags */ |
| 47 |
#define HASBORDER 01 |
| 48 |
#define TRIPLETS 02 |
| 49 |
/* a data structure */ |
| 50 |
struct { |
| 51 |
int flags; /* data type */ |
| 52 |
short m, n; /* number of s and t values */ |
| 53 |
RREAL *data; /* the data itself, s major sort */ |
| 54 |
} datarec; /* our recorded data */ |
| 55 |
|
| 56 |
/* XXX this is redundant with rt/noise3.c, should go to a library */ |
| 57 |
double l_hermite(), l_bezier(), l_bspline(), l_dataval(); |
| 58 |
|
| 59 |
typedef struct { |
| 60 |
int valid; /* point is valid (vertex number) */ |
| 61 |
int nvalid; /* normal is valid */ |
| 62 |
FVECT p; /* vertex position */ |
| 63 |
FVECT n; /* average normal */ |
| 64 |
RREAL uv[2]; /* (u,v) position */ |
| 65 |
} POINT; |
| 66 |
|
| 67 |
int nverts = 0; /* vertex output count */ |
| 68 |
int nnorms = 0; /* normal output count */ |
| 69 |
|
| 70 |
void loaddata(char *file, int m, int n, int pointsize); |
| 71 |
double l_dataval(char *nam); |
| 72 |
void putobjrow(POINT *rp, int n); |
| 73 |
void putobjvert(POINT *p); |
| 74 |
void putsquare(POINT *p0, POINT *p1, POINT *p2, POINT *p3); |
| 75 |
void comprow(double s, POINT *row, int siz); |
| 76 |
void compnorms(POINT *r0, POINT *r1, POINT *r2, int siz); |
| 77 |
int norminterp(FVECT resmat[4], POINT *p0, POINT *p1, POINT *p2, POINT *p3); |
| 78 |
|
| 79 |
|
| 80 |
int |
| 81 |
main(argc, argv) |
| 82 |
int argc; |
| 83 |
char *argv[]; |
| 84 |
{ |
| 85 |
POINT *row0, *row1, *row2, *rp; |
| 86 |
int i, j, m, n; |
| 87 |
char stmp[256]; |
| 88 |
|
| 89 |
esupport |= E_VARIABLE|E_FUNCTION|E_RCONST; |
| 90 |
esupport &= ~(E_OUTCHAN|E_INCHAN); |
| 91 |
varset("PI", ':', PI); |
| 92 |
funset("hermite", 5, ':', l_hermite); |
| 93 |
funset("bezier", 5, ':', l_bezier); |
| 94 |
funset("bspline", 5, ':', l_bspline); |
| 95 |
|
| 96 |
if (argc < 8) |
| 97 |
goto userror; |
| 98 |
|
| 99 |
for (i = 8; i < argc; i++) |
| 100 |
if (!strcmp(argv[i], "-e")) |
| 101 |
scompile(argv[++i], NULL, 0); |
| 102 |
else if (!strcmp(argv[i], "-f")) |
| 103 |
fcompile(argv[++i]); |
| 104 |
else if (!strcmp(argv[i], "-s")) |
| 105 |
smooth++; |
| 106 |
else if (!strcmp(argv[i], "-o")) |
| 107 |
objout++; |
| 108 |
else |
| 109 |
goto userror; |
| 110 |
|
| 111 |
modname = argv[1]; |
| 112 |
surfname = argv[2]; |
| 113 |
m = atoi(argv[6]); |
| 114 |
n = atoi(argv[7]); |
| 115 |
if (m <= 0 || n <= 0) |
| 116 |
goto userror; |
| 117 |
if (!strcmp(argv[5], "-") || access(argv[5], 4) == 0) { /* file? */ |
| 118 |
funset(ZNAME, 2, ':', l_dataval); |
| 119 |
if (!strcmp(argv[5],argv[3]) && !strcmp(argv[5],argv[4])) { |
| 120 |
loaddata(argv[5], m, n, 3); |
| 121 |
funset(XNAME, 2, ':', l_dataval); |
| 122 |
funset(YNAME, 2, ':', l_dataval); |
| 123 |
} else { |
| 124 |
loaddata(argv[5], m, n, 1); |
| 125 |
sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
| 126 |
scompile(stmp, NULL, 0); |
| 127 |
sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
| 128 |
scompile(stmp, NULL, 0); |
| 129 |
} |
| 130 |
} else { |
| 131 |
sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
| 132 |
scompile(stmp, NULL, 0); |
| 133 |
sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
| 134 |
scompile(stmp, NULL, 0); |
| 135 |
sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]); |
| 136 |
scompile(stmp, NULL, 0); |
| 137 |
} |
| 138 |
row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
| 139 |
row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
| 140 |
row2 = (POINT *)malloc((n+3)*sizeof(POINT)); |
| 141 |
if (row0 == NULL || row1 == NULL || row2 == NULL) { |
| 142 |
fprintf(stderr, "%s: out of memory\n", argv[0]); |
| 143 |
quit(1); |
| 144 |
} |
| 145 |
row0++; row1++; row2++; |
| 146 |
/* print header */ |
| 147 |
fputs("# ", stdout); |
| 148 |
printargs(argc, argv, stdout); |
| 149 |
eclock = 0; |
| 150 |
/* initialize */ |
| 151 |
comprow(-1.0/m, row0, n); |
| 152 |
comprow(0.0, row1, n); |
| 153 |
comprow(1.0/m, row2, n); |
| 154 |
compnorms(row0, row1, row2, n); |
| 155 |
if (objout) { |
| 156 |
printf("\nusemtl %s\n\n", modname); |
| 157 |
putobjrow(row1, n); |
| 158 |
} |
| 159 |
/* for each row */ |
| 160 |
for (i = 0; i < m; i++) { |
| 161 |
/* compute next row */ |
| 162 |
rp = row0; |
| 163 |
row0 = row1; |
| 164 |
row1 = row2; |
| 165 |
row2 = rp; |
| 166 |
comprow((double)(i+2)/m, row2, n); |
| 167 |
compnorms(row0, row1, row2, n); |
| 168 |
if (objout) |
| 169 |
putobjrow(row1, n); |
| 170 |
|
| 171 |
for (j = 0; j < n; j++) { |
| 172 |
int orient = (j & 1); |
| 173 |
/* put polygons */ |
| 174 |
if (!(row0[j].valid && row1[j+1].valid)) |
| 175 |
orient = 1; |
| 176 |
else if (!(row1[j].valid && row0[j+1].valid)) |
| 177 |
orient = 0; |
| 178 |
if (orient) |
| 179 |
putsquare(&row0[j], &row1[j], |
| 180 |
&row0[j+1], &row1[j+1]); |
| 181 |
else |
| 182 |
putsquare(&row1[j], &row1[j+1], |
| 183 |
&row0[j], &row0[j+1]); |
| 184 |
} |
| 185 |
} |
| 186 |
|
| 187 |
return 0; |
| 188 |
|
| 189 |
userror: |
| 190 |
fprintf(stderr, "Usage: %s material name ", argv[0]); |
| 191 |
fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-s][-o][-e expr][-f file]\n"); |
| 192 |
return 1; |
| 193 |
} |
| 194 |
|
| 195 |
|
| 196 |
void |
| 197 |
loaddata( /* load point data from file */ |
| 198 |
char *file, |
| 199 |
int m, |
| 200 |
int n, |
| 201 |
int pointsize |
| 202 |
) |
| 203 |
{ |
| 204 |
FILE *fp; |
| 205 |
char word[64]; |
| 206 |
int size; |
| 207 |
RREAL *dp; |
| 208 |
|
| 209 |
datarec.flags = HASBORDER; /* assume border values */ |
| 210 |
datarec.m = m+1; |
| 211 |
datarec.n = n+1; |
| 212 |
size = datarec.m*datarec.n*pointsize; |
| 213 |
if (pointsize == 3) |
| 214 |
datarec.flags |= TRIPLETS; |
| 215 |
dp = (RREAL *)malloc(size*sizeof(RREAL)); |
| 216 |
if ((datarec.data = dp) == NULL) { |
| 217 |
fputs("Out of memory\n", stderr); |
| 218 |
exit(1); |
| 219 |
} |
| 220 |
if (!strcmp(file, "-")) { |
| 221 |
file = "<stdin>"; |
| 222 |
fp = stdin; |
| 223 |
} else if ((fp = fopen(file, "r")) == NULL) { |
| 224 |
fputs(file, stderr); |
| 225 |
fputs(": cannot open\n", stderr); |
| 226 |
exit(1); |
| 227 |
} |
| 228 |
while (size > 0 && fgetword(word, sizeof(word), fp) != NULL) { |
| 229 |
if (!isflt(word)) { |
| 230 |
fprintf(stderr, "%s: garbled data value: %s\n", |
| 231 |
file, word); |
| 232 |
exit(1); |
| 233 |
} |
| 234 |
*dp++ = atof(word); |
| 235 |
size--; |
| 236 |
} |
| 237 |
if (size == (m+n+1)*pointsize) { /* no border after all */ |
| 238 |
dp = (RREAL *)realloc(datarec.data, |
| 239 |
m*n*pointsize*sizeof(RREAL)); |
| 240 |
if (dp != NULL) |
| 241 |
datarec.data = dp; |
| 242 |
datarec.flags &= ~HASBORDER; |
| 243 |
datarec.m = m; |
| 244 |
datarec.n = n; |
| 245 |
size = 0; |
| 246 |
} |
| 247 |
if (datarec.m < 2 || datarec.n < 2 || size != 0 || |
| 248 |
fgetword(word, sizeof(word), fp) != NULL) { |
| 249 |
fputs(file, stderr); |
| 250 |
fputs(": bad number of data points\n", stderr); |
| 251 |
exit(1); |
| 252 |
} |
| 253 |
fclose(fp); |
| 254 |
} |
| 255 |
|
| 256 |
|
| 257 |
double |
| 258 |
l_dataval( /* return recorded data value */ |
| 259 |
char *nam |
| 260 |
) |
| 261 |
{ |
| 262 |
double u, v; |
| 263 |
int i, j; |
| 264 |
RREAL *dp; |
| 265 |
double d00, d01, d10, d11; |
| 266 |
/* compute coordinates */ |
| 267 |
u = argument(1); v = argument(2); |
| 268 |
if (datarec.flags & HASBORDER) { |
| 269 |
i = u *= datarec.m-1; |
| 270 |
j = v *= datarec.n-1; |
| 271 |
} else { |
| 272 |
i = u = u*datarec.m - .5; |
| 273 |
j = v = v*datarec.n - .5; |
| 274 |
} |
| 275 |
if (i < 0) i = 0; |
| 276 |
else if (i > datarec.m-2) i = datarec.m-2; |
| 277 |
if (j < 0) j = 0; |
| 278 |
else if (j > datarec.n-2) j = datarec.n-2; |
| 279 |
/* compute value */ |
| 280 |
if (datarec.flags & TRIPLETS) { |
| 281 |
dp = datarec.data + 3*(j*datarec.m + i); |
| 282 |
if (nam == ZNAME) |
| 283 |
dp += 2; |
| 284 |
else if (nam == YNAME) |
| 285 |
dp++; |
| 286 |
d00 = dp[0]; d01 = dp[3]; |
| 287 |
dp += 3*datarec.m; |
| 288 |
d10 = dp[0]; d11 = dp[3]; |
| 289 |
} else { |
| 290 |
dp = datarec.data + j*datarec.m + i; |
| 291 |
d00 = dp[0]; d01 = dp[1]; |
| 292 |
dp += datarec.m; |
| 293 |
d10 = dp[0]; d11 = dp[1]; |
| 294 |
} |
| 295 |
/* bilinear interpolation */ |
| 296 |
return((j+1-v)*((i+1-u)*d00+(u-i)*d01)+(v-j)*((i+1-u)*d10+(u-i)*d11)); |
| 297 |
} |
| 298 |
|
| 299 |
|
| 300 |
void |
| 301 |
putobjrow( /* output vertex row to .OBJ */ |
| 302 |
POINT *rp, |
| 303 |
int n |
| 304 |
) |
| 305 |
{ |
| 306 |
for ( ; n-- >= 0; rp++) { |
| 307 |
if (!rp->valid) |
| 308 |
continue; |
| 309 |
fputs("v ", stdout); |
| 310 |
pvect(rp->p); |
| 311 |
if (smooth && !ZEROVECT(rp->n)) { |
| 312 |
printf("\tvn %.9g %.9g %.9g\n", |
| 313 |
rp->n[0], rp->n[1], rp->n[2]); |
| 314 |
rp->nvalid = ++nnorms; |
| 315 |
} else |
| 316 |
rp->nvalid = 0; |
| 317 |
printf("\tvt %.9g %.9g\n", rp->uv[0], rp->uv[1]); |
| 318 |
rp->valid = ++nverts; |
| 319 |
} |
| 320 |
} |
| 321 |
|
| 322 |
|
| 323 |
void |
| 324 |
putobjvert( /* put out OBJ vertex index triplet */ |
| 325 |
POINT *p |
| 326 |
) |
| 327 |
{ |
| 328 |
int pti = p->valid ? p->valid-nverts-1 : 0; |
| 329 |
int ni = p->nvalid ? p->nvalid-nnorms-1 : 0; |
| 330 |
|
| 331 |
printf(" %d/%d/%d", pti, pti, ni); |
| 332 |
} |
| 333 |
|
| 334 |
|
| 335 |
void |
| 336 |
putsquare( /* put out a square */ |
| 337 |
POINT *p0, |
| 338 |
POINT *p1, |
| 339 |
POINT *p2, |
| 340 |
POINT *p3 |
| 341 |
) |
| 342 |
{ |
| 343 |
static int nout = 0; |
| 344 |
FVECT norm[4]; |
| 345 |
int axis; |
| 346 |
FVECT v1, v2, vc1, vc2; |
| 347 |
int ok1, ok2; |
| 348 |
/* compute exact normals */ |
| 349 |
ok1 = (p0->valid && p1->valid && p2->valid); |
| 350 |
if (ok1) { |
| 351 |
VSUB(v1, p1->p, p0->p); |
| 352 |
VSUB(v2, p2->p, p0->p); |
| 353 |
fcross(vc1, v1, v2); |
| 354 |
ok1 = (normalize(vc1) != 0.0); |
| 355 |
} |
| 356 |
ok2 = (p1->valid && p2->valid && p3->valid); |
| 357 |
if (ok2) { |
| 358 |
VSUB(v1, p2->p, p3->p); |
| 359 |
VSUB(v2, p1->p, p3->p); |
| 360 |
fcross(vc2, v1, v2); |
| 361 |
ok2 = (normalize(vc2) != 0.0); |
| 362 |
} |
| 363 |
if (!(ok1 | ok2)) |
| 364 |
return; |
| 365 |
if (objout) { /* output .OBJ faces */ |
| 366 |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) { |
| 367 |
putc('f', stdout); |
| 368 |
putobjvert(p0); putobjvert(p1); |
| 369 |
putobjvert(p3); putobjvert(p2); |
| 370 |
putc('\n', stdout); |
| 371 |
return; |
| 372 |
} |
| 373 |
if (ok1) { |
| 374 |
putc('f', stdout); |
| 375 |
putobjvert(p0); putobjvert(p1); putobjvert(p2); |
| 376 |
putc('\n', stdout); |
| 377 |
} |
| 378 |
if (ok2) { |
| 379 |
putc('f', stdout); |
| 380 |
putobjvert(p2); putobjvert(p1); putobjvert(p3); |
| 381 |
putc('\n', stdout); |
| 382 |
} |
| 383 |
return; |
| 384 |
} |
| 385 |
/* compute normal interpolation */ |
| 386 |
axis = norminterp(norm, p0, p1, p2, p3); |
| 387 |
|
| 388 |
/* put out quadrilateral? */ |
| 389 |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) { |
| 390 |
printf("\n%s ", modname); |
| 391 |
if (axis != -1) { |
| 392 |
printf("texfunc %s\n%s\n", texname, tsargs); |
| 393 |
printf("0\n13\t%d\n", axis); |
| 394 |
pvect(norm[0]); |
| 395 |
pvect(norm[1]); |
| 396 |
pvect(norm[2]); |
| 397 |
fvsum(v1, norm[3], vc1, -0.5); |
| 398 |
fvsum(v1, v1, vc2, -0.5); |
| 399 |
pvect(v1); |
| 400 |
printf("\n%s ", texname); |
| 401 |
} |
| 402 |
printf("polygon %s.%d\n", surfname, ++nout); |
| 403 |
printf("0\n0\n12\n"); |
| 404 |
pvect(p0->p); |
| 405 |
pvect(p1->p); |
| 406 |
pvect(p3->p); |
| 407 |
pvect(p2->p); |
| 408 |
return; |
| 409 |
} |
| 410 |
/* put out triangles? */ |
| 411 |
if (ok1) { |
| 412 |
printf("\n%s ", modname); |
| 413 |
if (axis != -1) { |
| 414 |
printf("texfunc %s\n%s\n", texname, tsargs); |
| 415 |
printf("0\n13\t%d\n", axis); |
| 416 |
pvect(norm[0]); |
| 417 |
pvect(norm[1]); |
| 418 |
pvect(norm[2]); |
| 419 |
fvsum(v1, norm[3], vc1, -1.0); |
| 420 |
pvect(v1); |
| 421 |
printf("\n%s ", texname); |
| 422 |
} |
| 423 |
printf("polygon %s.%d\n", surfname, ++nout); |
| 424 |
printf("0\n0\n9\n"); |
| 425 |
pvect(p0->p); |
| 426 |
pvect(p1->p); |
| 427 |
pvect(p2->p); |
| 428 |
} |
| 429 |
if (ok2) { |
| 430 |
printf("\n%s ", modname); |
| 431 |
if (axis != -1) { |
| 432 |
printf("texfunc %s\n%s\n", texname, tsargs); |
| 433 |
printf("0\n13\t%d\n", axis); |
| 434 |
pvect(norm[0]); |
| 435 |
pvect(norm[1]); |
| 436 |
pvect(norm[2]); |
| 437 |
fvsum(v2, norm[3], vc2, -1.0); |
| 438 |
pvect(v2); |
| 439 |
printf("\n%s ", texname); |
| 440 |
} |
| 441 |
printf("polygon %s.%d\n", surfname, ++nout); |
| 442 |
printf("0\n0\n9\n"); |
| 443 |
pvect(p2->p); |
| 444 |
pvect(p1->p); |
| 445 |
pvect(p3->p); |
| 446 |
} |
| 447 |
} |
| 448 |
|
| 449 |
|
| 450 |
void |
| 451 |
comprow( /* compute row of values */ |
| 452 |
double s, |
| 453 |
POINT *row, |
| 454 |
int siz |
| 455 |
) |
| 456 |
{ |
| 457 |
double st[2]; |
| 458 |
int end; |
| 459 |
int checkvalid; |
| 460 |
int i; |
| 461 |
|
| 462 |
if (smooth) { |
| 463 |
i = -1; /* compute one past each end */ |
| 464 |
end = siz+1; |
| 465 |
} else { |
| 466 |
if (s < -FTINY || s > 1.0+FTINY) |
| 467 |
return; |
| 468 |
i = 0; |
| 469 |
end = siz; |
| 470 |
} |
| 471 |
st[0] = s; |
| 472 |
checkvalid = (fundefined(VNAME) == 2); |
| 473 |
while (i <= end) { |
| 474 |
st[1] = (double)i/siz; |
| 475 |
if (checkvalid && funvalue(VNAME, 2, st) <= 0.0) { |
| 476 |
row[i].valid = 0; |
| 477 |
row[i].p[0] = row[i].p[1] = row[i].p[2] = 0.0; |
| 478 |
row[i].uv[0] = row[i].uv[1] = 0.0; |
| 479 |
} else { |
| 480 |
row[i].valid = 1; |
| 481 |
row[i].p[0] = funvalue(XNAME, 2, st); |
| 482 |
row[i].p[1] = funvalue(YNAME, 2, st); |
| 483 |
row[i].p[2] = funvalue(ZNAME, 2, st); |
| 484 |
row[i].uv[0] = st[0]; |
| 485 |
row[i].uv[1] = st[1]; |
| 486 |
} |
| 487 |
i++; |
| 488 |
} |
| 489 |
} |
| 490 |
|
| 491 |
|
| 492 |
void |
| 493 |
compnorms( /* compute row of averaged normals */ |
| 494 |
POINT *r0, |
| 495 |
POINT *r1, |
| 496 |
POINT *r2, |
| 497 |
int siz |
| 498 |
) |
| 499 |
{ |
| 500 |
FVECT v1, v2; |
| 501 |
|
| 502 |
if (!smooth) /* not needed if no smoothing */ |
| 503 |
return; |
| 504 |
/* compute row 1 normals */ |
| 505 |
while (siz-- >= 0) { |
| 506 |
if (!r1[0].valid) |
| 507 |
continue; |
| 508 |
if (!r0[0].valid) { |
| 509 |
if (!r2[0].valid) { |
| 510 |
r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0; |
| 511 |
continue; |
| 512 |
} |
| 513 |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
| 514 |
} else if (!r2[0].valid) |
| 515 |
fvsum(v1, r1[0].p, r0[0].p, -1.0); |
| 516 |
else |
| 517 |
fvsum(v1, r2[0].p, r0[0].p, -1.0); |
| 518 |
if (!r1[-1].valid) { |
| 519 |
if (!r1[1].valid) { |
| 520 |
r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0; |
| 521 |
continue; |
| 522 |
} |
| 523 |
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
| 524 |
} else if (!r1[1].valid) |
| 525 |
fvsum(v2, r1[0].p, r1[-1].p, -1.0); |
| 526 |
else |
| 527 |
fvsum(v2, r1[1].p, r1[-1].p, -1.0); |
| 528 |
fcross(r1[0].n, v1, v2); |
| 529 |
normalize(r1[0].n); |
| 530 |
r0++; r1++; r2++; |
| 531 |
} |
| 532 |
} |
| 533 |
|
| 534 |
|
| 535 |
int |
| 536 |
norminterp( /* compute normal interpolation */ |
| 537 |
FVECT resmat[4], |
| 538 |
POINT *p0, |
| 539 |
POINT *p1, |
| 540 |
POINT *p2, |
| 541 |
POINT *p3 |
| 542 |
) |
| 543 |
{ |
| 544 |
#define u ((ax+1)%3) |
| 545 |
#define v ((ax+2)%3) |
| 546 |
|
| 547 |
int ax; |
| 548 |
MAT4 eqnmat; |
| 549 |
FVECT v1; |
| 550 |
int i, j; |
| 551 |
|
| 552 |
if (!smooth) /* no interpolation if no smoothing */ |
| 553 |
return(-1); |
| 554 |
/* find dominant axis */ |
| 555 |
VCOPY(v1, p0->n); |
| 556 |
fvsum(v1, v1, p1->n, 1.0); |
| 557 |
fvsum(v1, v1, p2->n, 1.0); |
| 558 |
fvsum(v1, v1, p3->n, 1.0); |
| 559 |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
| 560 |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
| 561 |
/* assign equation matrix */ |
| 562 |
eqnmat[0][0] = p0->p[u]*p0->p[v]; |
| 563 |
eqnmat[0][1] = p0->p[u]; |
| 564 |
eqnmat[0][2] = p0->p[v]; |
| 565 |
eqnmat[0][3] = 1.0; |
| 566 |
eqnmat[1][0] = p1->p[u]*p1->p[v]; |
| 567 |
eqnmat[1][1] = p1->p[u]; |
| 568 |
eqnmat[1][2] = p1->p[v]; |
| 569 |
eqnmat[1][3] = 1.0; |
| 570 |
eqnmat[2][0] = p2->p[u]*p2->p[v]; |
| 571 |
eqnmat[2][1] = p2->p[u]; |
| 572 |
eqnmat[2][2] = p2->p[v]; |
| 573 |
eqnmat[2][3] = 1.0; |
| 574 |
eqnmat[3][0] = p3->p[u]*p3->p[v]; |
| 575 |
eqnmat[3][1] = p3->p[u]; |
| 576 |
eqnmat[3][2] = p3->p[v]; |
| 577 |
eqnmat[3][3] = 1.0; |
| 578 |
/* invert matrix (solve system) */ |
| 579 |
if (!invmat4(eqnmat, eqnmat)) |
| 580 |
return(-1); /* no solution */ |
| 581 |
/* compute result matrix */ |
| 582 |
for (j = 0; j < 4; j++) |
| 583 |
for (i = 0; i < 3; i++) |
| 584 |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
| 585 |
eqnmat[j][1]*p1->n[i] + |
| 586 |
eqnmat[j][2]*p2->n[i] + |
| 587 |
eqnmat[j][3]*p3->n[i]; |
| 588 |
return(ax); |
| 589 |
|
| 590 |
#undef u |
| 591 |
#undef v |
| 592 |
} |
| 593 |
|
| 594 |
|
| 595 |
double |
| 596 |
l_hermite(char *nm) |
| 597 |
{ |
| 598 |
double t; |
| 599 |
|
| 600 |
t = argument(5); |
| 601 |
return( argument(1)*((2.0*t-3.0)*t*t+1.0) + |
| 602 |
argument(2)*(-2.0*t+3.0)*t*t + |
| 603 |
argument(3)*((t-2.0)*t+1.0)*t + |
| 604 |
argument(4)*(t-1.0)*t*t ); |
| 605 |
} |
| 606 |
|
| 607 |
|
| 608 |
double |
| 609 |
l_bezier(char *nm) |
| 610 |
{ |
| 611 |
double t; |
| 612 |
|
| 613 |
t = argument(5); |
| 614 |
return( argument(1) * (1.+t*(-3.+t*(3.-t))) + |
| 615 |
argument(2) * 3.*t*(1.+t*(-2.+t)) + |
| 616 |
argument(3) * 3.*t*t*(1.-t) + |
| 617 |
argument(4) * t*t*t ); |
| 618 |
} |
| 619 |
|
| 620 |
|
| 621 |
double |
| 622 |
l_bspline(char *nm) |
| 623 |
{ |
| 624 |
double t; |
| 625 |
|
| 626 |
t = argument(5); |
| 627 |
return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) + |
| 628 |
argument(2) * (2./3.+t*t*(-1.+1./2.*t)) + |
| 629 |
argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) + |
| 630 |
argument(4) * (1./6.*t*t*t) ); |
| 631 |
} |
