1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id$"; |
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 |
char XNAME[] = "X`SYS"; /* x function name */ |
21 |
char YNAME[] = "Y`SYS"; /* y function name */ |
22 |
char ZNAME[] = "Z`SYS"; /* z function name */ |
23 |
|
24 |
char VNAME[] = "valid"; /* valid vertex name */ |
25 |
|
26 |
#define ABS(x) ((x)>=0 ? (x) : -(x)) |
27 |
|
28 |
#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
29 |
|
30 |
char vformat[] = "%15.9g %15.9g %15.9g\n"; |
31 |
char tsargs[] = "4 surf_dx surf_dy surf_dz surf.cal\n"; |
32 |
char texname[] = "Phong"; |
33 |
|
34 |
int smooth = 0; /* apply smoothing? */ |
35 |
int objout = 0; /* output .OBJ format? */ |
36 |
|
37 |
char *modname, *surfname; |
38 |
|
39 |
/* recorded data flags */ |
40 |
#define HASBORDER 01 |
41 |
#define TRIPLETS 02 |
42 |
/* a data structure */ |
43 |
struct { |
44 |
int flags; /* data type */ |
45 |
short m, n; /* number of s and t values */ |
46 |
FLOAT *data; /* the data itself, s major sort */ |
47 |
} datarec; /* our recorded data */ |
48 |
|
49 |
double l_hermite(), l_bezier(), l_bspline(), l_dataval(); |
50 |
extern double funvalue(), argument(); |
51 |
|
52 |
typedef struct { |
53 |
int valid; /* point is valid (vertex number) */ |
54 |
FVECT p; /* vertex position */ |
55 |
FVECT n; /* average normal */ |
56 |
FLOAT uv[2]; /* (u,v) position */ |
57 |
} POINT; |
58 |
|
59 |
|
60 |
main(argc, argv) |
61 |
int argc; |
62 |
char *argv[]; |
63 |
{ |
64 |
extern long eclock; |
65 |
POINT *row0, *row1, *row2, *rp; |
66 |
int i, j, m, n; |
67 |
char stmp[256]; |
68 |
|
69 |
varset("PI", ':', PI); |
70 |
funset("hermite", 5, ':', l_hermite); |
71 |
funset("bezier", 5, ':', l_bezier); |
72 |
funset("bspline", 5, ':', l_bspline); |
73 |
|
74 |
if (argc < 8) |
75 |
goto userror; |
76 |
|
77 |
for (i = 8; i < argc; i++) |
78 |
if (!strcmp(argv[i], "-e")) |
79 |
scompile(argv[++i], NULL, 0); |
80 |
else if (!strcmp(argv[i], "-f")) |
81 |
fcompile(argv[++i]); |
82 |
else if (!strcmp(argv[i], "-s")) |
83 |
smooth++; |
84 |
else if (!strcmp(argv[i], "-o")) |
85 |
objout++; |
86 |
else |
87 |
goto userror; |
88 |
|
89 |
modname = argv[1]; |
90 |
surfname = argv[2]; |
91 |
m = atoi(argv[6]); |
92 |
n = atoi(argv[7]); |
93 |
if (m <= 0 || n <= 0) |
94 |
goto userror; |
95 |
if (!strcmp(argv[5], "-") || access(argv[5], 4) == 0) { /* file? */ |
96 |
funset(ZNAME, 2, ':', l_dataval); |
97 |
if (!strcmp(argv[5],argv[3]) && !strcmp(argv[5],argv[4])) { |
98 |
loaddata(argv[5], m, n, 3); |
99 |
funset(XNAME, 2, ':', l_dataval); |
100 |
funset(YNAME, 2, ':', l_dataval); |
101 |
} else { |
102 |
loaddata(argv[5], m, n, 1); |
103 |
sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
104 |
scompile(stmp, NULL, 0); |
105 |
sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
106 |
scompile(stmp, NULL, 0); |
107 |
} |
108 |
} else { |
109 |
sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
110 |
scompile(stmp, NULL, 0); |
111 |
sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
112 |
scompile(stmp, NULL, 0); |
113 |
sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]); |
114 |
scompile(stmp, NULL, 0); |
115 |
} |
116 |
row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
117 |
row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
118 |
row2 = (POINT *)malloc((n+3)*sizeof(POINT)); |
119 |
if (row0 == NULL || row1 == NULL || row2 == NULL) { |
120 |
fprintf(stderr, "%s: out of memory\n", argv[0]); |
121 |
quit(1); |
122 |
} |
123 |
row0++; row1++; row2++; |
124 |
/* print header */ |
125 |
printhead(argc, argv); |
126 |
eclock = 0; |
127 |
/* initialize */ |
128 |
comprow(-1.0/m, row0, n); |
129 |
comprow(0.0, row1, n); |
130 |
comprow(1.0/m, row2, n); |
131 |
compnorms(row0, row1, row2, n); |
132 |
if (objout) |
133 |
putobjrow(row1, n); |
134 |
/* for each row */ |
135 |
for (i = 0; i < m; i++) { |
136 |
/* compute next row */ |
137 |
rp = row0; |
138 |
row0 = row1; |
139 |
row1 = row2; |
140 |
row2 = rp; |
141 |
comprow((double)(i+2)/m, row2, n); |
142 |
compnorms(row0, row1, row2, n); |
143 |
if (objout) |
144 |
putobjrow(row1, n); |
145 |
|
146 |
for (j = 0; j < n; j++) { |
147 |
int orient = (j & 1); |
148 |
/* put polygons */ |
149 |
if (!(row0[j].valid && row1[j+1].valid)) |
150 |
orient = 1; |
151 |
else if (!(row1[j].valid && row0[j+1].valid)) |
152 |
orient = 0; |
153 |
if (orient) |
154 |
putsquare(&row0[j], &row1[j], |
155 |
&row0[j+1], &row1[j+1]); |
156 |
else |
157 |
putsquare(&row1[j], &row1[j+1], |
158 |
&row0[j], &row0[j+1]); |
159 |
} |
160 |
} |
161 |
|
162 |
quit(0); |
163 |
|
164 |
userror: |
165 |
fprintf(stderr, "Usage: %s material name ", argv[0]); |
166 |
fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-s][-e expr][-f file]\n"); |
167 |
quit(1); |
168 |
} |
169 |
|
170 |
|
171 |
loaddata(file, m, n, pointsize) /* load point data from file */ |
172 |
char *file; |
173 |
int m, n; |
174 |
int pointsize; |
175 |
{ |
176 |
FILE *fp; |
177 |
char word[64]; |
178 |
register int size; |
179 |
register FLOAT *dp; |
180 |
|
181 |
datarec.flags = HASBORDER; /* assume border values */ |
182 |
datarec.m = m+1; |
183 |
datarec.n = n+1; |
184 |
size = datarec.m*datarec.n*pointsize; |
185 |
if (pointsize == 3) |
186 |
datarec.flags |= TRIPLETS; |
187 |
dp = (FLOAT *)malloc(size*sizeof(FLOAT)); |
188 |
if ((datarec.data = dp) == NULL) { |
189 |
fputs("Out of memory\n", stderr); |
190 |
exit(1); |
191 |
} |
192 |
if (!strcmp(file, "-")) { |
193 |
file = "<stdin>"; |
194 |
fp = stdin; |
195 |
} else if ((fp = fopen(file, "r")) == NULL) { |
196 |
fputs(file, stderr); |
197 |
fputs(": cannot open\n", stderr); |
198 |
exit(1); |
199 |
} |
200 |
while (size > 0 && fgetword(word, sizeof(word), fp) != NULL) { |
201 |
if (!isflt(word)) { |
202 |
fprintf(stderr, "%s: garbled data value: %s\n", |
203 |
file, word); |
204 |
exit(1); |
205 |
} |
206 |
*dp++ = atof(word); |
207 |
size--; |
208 |
} |
209 |
if (size == (m+n+1)*pointsize) { /* no border after all */ |
210 |
dp = (FLOAT *)realloc((char *)datarec.data, |
211 |
m*n*pointsize*sizeof(FLOAT)); |
212 |
if (dp != NULL) |
213 |
datarec.data = dp; |
214 |
datarec.flags &= ~HASBORDER; |
215 |
datarec.m = m; |
216 |
datarec.n = n; |
217 |
size = 0; |
218 |
} |
219 |
if (datarec.m < 2 || datarec.n < 2 || size != 0 || |
220 |
fgetword(word, sizeof(word), fp) != NULL) { |
221 |
fputs(file, stderr); |
222 |
fputs(": bad number of data points\n", stderr); |
223 |
exit(1); |
224 |
} |
225 |
fclose(fp); |
226 |
} |
227 |
|
228 |
|
229 |
double |
230 |
l_dataval(nam) /* return recorded data value */ |
231 |
char *nam; |
232 |
{ |
233 |
double u, v; |
234 |
register int i, j; |
235 |
register FLOAT *dp; |
236 |
double d00, d01, d10, d11; |
237 |
/* compute coordinates */ |
238 |
u = argument(1); v = argument(2); |
239 |
if (datarec.flags & HASBORDER) { |
240 |
i = u *= datarec.m-1; |
241 |
j = v *= datarec.n-1; |
242 |
} else { |
243 |
i = u = u*datarec.m - .5; |
244 |
j = v = v*datarec.n - .5; |
245 |
} |
246 |
if (i < 0) i = 0; |
247 |
else if (i > datarec.m-2) i = datarec.m-2; |
248 |
if (j < 0) j = 0; |
249 |
else if (j > datarec.n-2) j = datarec.n-2; |
250 |
/* compute value */ |
251 |
if (datarec.flags & TRIPLETS) { |
252 |
dp = datarec.data + 3*(j*datarec.m + i); |
253 |
if (nam == ZNAME) |
254 |
dp += 2; |
255 |
else if (nam == YNAME) |
256 |
dp++; |
257 |
d00 = dp[0]; d01 = dp[3]; |
258 |
dp += 3*datarec.m; |
259 |
d10 = dp[0]; d11 = dp[3]; |
260 |
} else { |
261 |
dp = datarec.data + j*datarec.m + i; |
262 |
d00 = dp[0]; d01 = dp[1]; |
263 |
dp += datarec.m; |
264 |
d10 = dp[0]; d11 = dp[1]; |
265 |
} |
266 |
/* bilinear interpolation */ |
267 |
return((j+1-v)*((i+1-u)*d00+(u-i)*d01)+(v-j)*((i+1-u)*d10+(u-i)*d11)); |
268 |
} |
269 |
|
270 |
|
271 |
putobjrow(rp, n) /* output vertex row to .OBJ */ |
272 |
register POINT *rp; |
273 |
int n; |
274 |
{ |
275 |
static int nverts = 0; |
276 |
|
277 |
for ( ; n-- >= 0; rp++) { |
278 |
if (!rp->valid) |
279 |
continue; |
280 |
fputs("v ", stdout); |
281 |
printf(vformat, rp->p[0], rp->p[1], rp->p[2]); |
282 |
if (smooth) |
283 |
printf("\tvn %.9g %.9g %.9g\n", |
284 |
rp->n[0], rp->n[1], rp->n[2]); |
285 |
printf("\tvt %.9g %.9g\n", rp->uv[0], rp->uv[1]); |
286 |
rp->valid = ++nverts; |
287 |
} |
288 |
} |
289 |
|
290 |
|
291 |
putsquare(p0, p1, p2, p3) /* put out a square */ |
292 |
POINT *p0, *p1, *p2, *p3; |
293 |
{ |
294 |
static int nout = 0; |
295 |
FVECT norm[4]; |
296 |
int axis; |
297 |
FVECT v1, v2, vc1, vc2; |
298 |
int ok1, ok2; |
299 |
/* compute exact normals */ |
300 |
ok1 = (p0->valid && p1->valid && p2->valid); |
301 |
if (ok1) { |
302 |
fvsum(v1, p1->p, p0->p, -1.0); |
303 |
fvsum(v2, p2->p, p0->p, -1.0); |
304 |
fcross(vc1, v1, v2); |
305 |
ok1 = (normalize(vc1) != 0.0); |
306 |
} |
307 |
ok2 = (p1->valid && p2->valid && p3->valid); |
308 |
if (ok2) { |
309 |
fvsum(v1, p2->p, p3->p, -1.0); |
310 |
fvsum(v2, p1->p, p3->p, -1.0); |
311 |
fcross(vc2, v1, v2); |
312 |
ok2 = (normalize(vc2) != 0.0); |
313 |
} |
314 |
if (!(ok1 | ok2)) |
315 |
return; |
316 |
if (objout) { /* output .OBJ faces */ |
317 |
int p0n=0, p1n=0, p2n=0, p3n=0; |
318 |
if (smooth) { |
319 |
p0n = p0->valid; |
320 |
p1n = p1->valid; |
321 |
p2n = p2->valid; |
322 |
p3n = p3->valid; |
323 |
} |
324 |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) { |
325 |
printf("f %d/%d/%d %d/%d/%d %d/%d/%d %d/%d/%d\n", |
326 |
p0->valid, p0n, p0->valid, |
327 |
p1->valid, p1n, p1->valid, |
328 |
p3->valid, p3n, p3->valid, |
329 |
p2->valid, p2n, p2->valid); |
330 |
return; |
331 |
} |
332 |
if (ok1) |
333 |
printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n", |
334 |
p0->valid, p0n, p0->valid, |
335 |
p1->valid, p1n, p1->valid, |
336 |
p2->valid, p2n, p2->valid); |
337 |
if (ok2) |
338 |
printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n", |
339 |
p2->valid, p2n, p2->valid, |
340 |
p1->valid, p1n, p1->valid, |
341 |
p3->valid, p3n, p3->valid); |
342 |
return; |
343 |
} |
344 |
/* compute normal interpolation */ |
345 |
axis = norminterp(norm, p0, p1, p2, p3); |
346 |
|
347 |
/* put out quadrilateral? */ |
348 |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) { |
349 |
printf("\n%s ", modname); |
350 |
if (axis != -1) { |
351 |
printf("texfunc %s\n", texname); |
352 |
printf(tsargs); |
353 |
printf("0\n13\t%d\n", axis); |
354 |
pvect(norm[0]); |
355 |
pvect(norm[1]); |
356 |
pvect(norm[2]); |
357 |
fvsum(v1, norm[3], vc1, -0.5); |
358 |
fvsum(v1, v1, vc2, -0.5); |
359 |
pvect(v1); |
360 |
printf("\n%s ", texname); |
361 |
} |
362 |
printf("polygon %s.%d\n", surfname, ++nout); |
363 |
printf("0\n0\n12\n"); |
364 |
pvect(p0->p); |
365 |
pvect(p1->p); |
366 |
pvect(p3->p); |
367 |
pvect(p2->p); |
368 |
return; |
369 |
} |
370 |
/* put out triangles? */ |
371 |
if (ok1) { |
372 |
printf("\n%s ", modname); |
373 |
if (axis != -1) { |
374 |
printf("texfunc %s\n", texname); |
375 |
printf(tsargs); |
376 |
printf("0\n13\t%d\n", axis); |
377 |
pvect(norm[0]); |
378 |
pvect(norm[1]); |
379 |
pvect(norm[2]); |
380 |
fvsum(v1, norm[3], vc1, -1.0); |
381 |
pvect(v1); |
382 |
printf("\n%s ", texname); |
383 |
} |
384 |
printf("polygon %s.%d\n", surfname, ++nout); |
385 |
printf("0\n0\n9\n"); |
386 |
pvect(p0->p); |
387 |
pvect(p1->p); |
388 |
pvect(p2->p); |
389 |
} |
390 |
if (ok2) { |
391 |
printf("\n%s ", modname); |
392 |
if (axis != -1) { |
393 |
printf("texfunc %s\n", texname); |
394 |
printf(tsargs); |
395 |
printf("0\n13\t%d\n", axis); |
396 |
pvect(norm[0]); |
397 |
pvect(norm[1]); |
398 |
pvect(norm[2]); |
399 |
fvsum(v2, norm[3], vc2, -1.0); |
400 |
pvect(v2); |
401 |
printf("\n%s ", texname); |
402 |
} |
403 |
printf("polygon %s.%d\n", surfname, ++nout); |
404 |
printf("0\n0\n9\n"); |
405 |
pvect(p2->p); |
406 |
pvect(p1->p); |
407 |
pvect(p3->p); |
408 |
} |
409 |
} |
410 |
|
411 |
|
412 |
comprow(s, row, siz) /* compute row of values */ |
413 |
double s; |
414 |
register POINT *row; |
415 |
int siz; |
416 |
{ |
417 |
double st[2]; |
418 |
int end; |
419 |
int checkvalid; |
420 |
register int i; |
421 |
|
422 |
if (smooth) { |
423 |
i = -1; /* compute one past each end */ |
424 |
end = siz+1; |
425 |
} else { |
426 |
if (s < -FTINY || s > 1.0+FTINY) |
427 |
return; |
428 |
i = 0; |
429 |
end = siz; |
430 |
} |
431 |
st[0] = s; |
432 |
checkvalid = (fundefined(VNAME) == 2); |
433 |
while (i <= end) { |
434 |
st[1] = (double)i/siz; |
435 |
if (checkvalid && funvalue(VNAME, 2, st) <= 0.0) { |
436 |
row[i].valid = 0; |
437 |
row[i].p[0] = row[i].p[1] = row[i].p[2] = 0.0; |
438 |
row[i].uv[0] = row[i].uv[1] = 0.0; |
439 |
} else { |
440 |
row[i].valid = 1; |
441 |
row[i].p[0] = funvalue(XNAME, 2, st); |
442 |
row[i].p[1] = funvalue(YNAME, 2, st); |
443 |
row[i].p[2] = funvalue(ZNAME, 2, st); |
444 |
row[i].uv[0] = st[0]; |
445 |
row[i].uv[1] = st[1]; |
446 |
} |
447 |
i++; |
448 |
} |
449 |
} |
450 |
|
451 |
|
452 |
compnorms(r0, r1, r2, siz) /* compute row of averaged normals */ |
453 |
register POINT *r0, *r1, *r2; |
454 |
int siz; |
455 |
{ |
456 |
FVECT v1, v2; |
457 |
|
458 |
if (!smooth) /* not needed if no smoothing */ |
459 |
return; |
460 |
/* compute row 1 normals */ |
461 |
while (siz-- >= 0) { |
462 |
if (!r1[0].valid) |
463 |
continue; |
464 |
if (!r0[0].valid) { |
465 |
if (!r2[0].valid) { |
466 |
r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0; |
467 |
continue; |
468 |
} |
469 |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
470 |
} else if (!r2[0].valid) |
471 |
fvsum(v1, r1[0].p, r0[0].p, -1.0); |
472 |
else |
473 |
fvsum(v1, r2[0].p, r0[0].p, -1.0); |
474 |
if (!r1[-1].valid) { |
475 |
if (!r1[1].valid) { |
476 |
r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0; |
477 |
continue; |
478 |
} |
479 |
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
480 |
} else if (!r1[1].valid) |
481 |
fvsum(v2, r1[0].p, r1[-1].p, -1.0); |
482 |
else |
483 |
fvsum(v2, r1[1].p, r1[-1].p, -1.0); |
484 |
fcross(r1[0].n, v1, v2); |
485 |
normalize(r1[0].n); |
486 |
r0++; r1++; r2++; |
487 |
} |
488 |
} |
489 |
|
490 |
|
491 |
int |
492 |
norminterp(resmat, p0, p1, p2, p3) /* compute normal interpolation */ |
493 |
register FVECT resmat[4]; |
494 |
POINT *p0, *p1, *p2, *p3; |
495 |
{ |
496 |
#define u ((ax+1)%3) |
497 |
#define v ((ax+2)%3) |
498 |
|
499 |
register int ax; |
500 |
MAT4 eqnmat; |
501 |
FVECT v1; |
502 |
register int i, j; |
503 |
|
504 |
if (!smooth) /* no interpolation if no smoothing */ |
505 |
return(-1); |
506 |
/* find dominant axis */ |
507 |
VCOPY(v1, p0->n); |
508 |
fvsum(v1, v1, p1->n, 1.0); |
509 |
fvsum(v1, v1, p2->n, 1.0); |
510 |
fvsum(v1, v1, p3->n, 1.0); |
511 |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
512 |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
513 |
/* assign equation matrix */ |
514 |
eqnmat[0][0] = p0->p[u]*p0->p[v]; |
515 |
eqnmat[0][1] = p0->p[u]; |
516 |
eqnmat[0][2] = p0->p[v]; |
517 |
eqnmat[0][3] = 1.0; |
518 |
eqnmat[1][0] = p1->p[u]*p1->p[v]; |
519 |
eqnmat[1][1] = p1->p[u]; |
520 |
eqnmat[1][2] = p1->p[v]; |
521 |
eqnmat[1][3] = 1.0; |
522 |
eqnmat[2][0] = p2->p[u]*p2->p[v]; |
523 |
eqnmat[2][1] = p2->p[u]; |
524 |
eqnmat[2][2] = p2->p[v]; |
525 |
eqnmat[2][3] = 1.0; |
526 |
eqnmat[3][0] = p3->p[u]*p3->p[v]; |
527 |
eqnmat[3][1] = p3->p[u]; |
528 |
eqnmat[3][2] = p3->p[v]; |
529 |
eqnmat[3][3] = 1.0; |
530 |
/* invert matrix (solve system) */ |
531 |
if (!invmat4(eqnmat, eqnmat)) |
532 |
return(-1); /* no solution */ |
533 |
/* compute result matrix */ |
534 |
for (j = 0; j < 4; j++) |
535 |
for (i = 0; i < 3; i++) |
536 |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
537 |
eqnmat[j][1]*p1->n[i] + |
538 |
eqnmat[j][2]*p2->n[i] + |
539 |
eqnmat[j][3]*p3->n[i]; |
540 |
return(ax); |
541 |
|
542 |
#undef u |
543 |
#undef v |
544 |
} |
545 |
|
546 |
|
547 |
void |
548 |
eputs(msg) |
549 |
char *msg; |
550 |
{ |
551 |
fputs(msg, stderr); |
552 |
} |
553 |
|
554 |
|
555 |
void |
556 |
wputs(msg) |
557 |
char *msg; |
558 |
{ |
559 |
eputs(msg); |
560 |
} |
561 |
|
562 |
|
563 |
void |
564 |
quit(code) |
565 |
int code; |
566 |
{ |
567 |
exit(code); |
568 |
} |
569 |
|
570 |
|
571 |
printhead(ac, av) /* print command header */ |
572 |
register int ac; |
573 |
register char **av; |
574 |
{ |
575 |
putchar('#'); |
576 |
while (ac--) { |
577 |
putchar(' '); |
578 |
fputs(*av++, stdout); |
579 |
} |
580 |
putchar('\n'); |
581 |
} |
582 |
|
583 |
|
584 |
double |
585 |
l_hermite() |
586 |
{ |
587 |
double t; |
588 |
|
589 |
t = argument(5); |
590 |
return( argument(1)*((2.0*t-3.0)*t*t+1.0) + |
591 |
argument(2)*(-2.0*t+3.0)*t*t + |
592 |
argument(3)*((t-2.0)*t+1.0)*t + |
593 |
argument(4)*(t-1.0)*t*t ); |
594 |
} |
595 |
|
596 |
|
597 |
double |
598 |
l_bezier() |
599 |
{ |
600 |
double t; |
601 |
|
602 |
t = argument(5); |
603 |
return( argument(1) * (1.+t*(-3.+t*(3.-t))) + |
604 |
argument(2) * 3.*t*(1.+t*(-2.+t)) + |
605 |
argument(3) * 3.*t*t*(1.-t) + |
606 |
argument(4) * t*t*t ); |
607 |
} |
608 |
|
609 |
|
610 |
double |
611 |
l_bspline() |
612 |
{ |
613 |
double t; |
614 |
|
615 |
t = argument(5); |
616 |
return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) + |
617 |
argument(2) * (2./3.+t*t*(-1.+1./2.*t)) + |
618 |
argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) + |
619 |
argument(4) * (1./6.*t*t*t) ); |
620 |
} |