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root/radiance/ray/src/gen/gensurf.c
Revision: 2.16
Committed: Sat Aug 21 11:54:06 2004 UTC (19 years, 7 months ago) by greg
Content type: text/plain
Branch: MAIN
CVS Tags: rad3R7P2, rad3R7P1, rad3R6, rad3R6P1, rad3R8
Changes since 2.15: +5 -42 lines
Log Message:
Eliminated some redundant library calls

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.16 static const char RCSid[] = "$Id: gensurf.c,v 2.15 2004/03/26 21:30:12 schorsch Exp $";
3 greg 1.1 #endif
4 greg 1.2 /*
5 greg 1.1 * 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 greg 2.6 *
15     * 4/16/02 Added conditional vertex output
16 greg 1.1 */
17    
18 greg 2.14 #include "standard.h"
19 schorsch 2.15
20     #include "paths.h"
21 greg 2.16 #include "resolu.h"
22     #include "rterror.h"
23 schorsch 2.13 #include "calcomp.h"
24 greg 1.1
25 greg 2.6 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 greg 1.1
31 greg 1.4 #define ABS(x) ((x)>=0 ? (x) : -(x))
32    
33 greg 2.9 #define ZEROVECT(v) (DOT(v,v) <= FTINY*FTINY)
34    
35 greg 1.3 #define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2])
36 greg 1.1
37     char vformat[] = "%15.9g %15.9g %15.9g\n";
38 greg 1.3 char tsargs[] = "4 surf_dx surf_dy surf_dz surf.cal\n";
39     char texname[] = "Phong";
40 greg 1.1
41 greg 1.3 int smooth = 0; /* apply smoothing? */
42 greg 2.7 int objout = 0; /* output .OBJ format? */
43 greg 1.1
44 greg 1.3 char *modname, *surfname;
45 greg 1.1
46 greg 2.2 /* 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 schorsch 2.11 RREAL *data; /* the data itself, s major sort */
54 greg 2.2 } datarec; /* our recorded data */
55 greg 1.3
56 schorsch 2.13 /* XXX this is redundant with rt/noise3.c, should go to a library */
57 greg 2.2 double l_hermite(), l_bezier(), l_bspline(), l_dataval();
58    
59 greg 1.3 typedef struct {
60 greg 2.7 int valid; /* point is valid (vertex number) */
61 greg 1.3 FVECT p; /* vertex position */
62     FVECT n; /* average normal */
63 schorsch 2.11 RREAL uv[2]; /* (u,v) position */
64 greg 1.3 } POINT;
65    
66    
67 schorsch 2.13 void loaddata(char *file, int m, int n, int pointsize);
68     double l_dataval(char *nam);
69     void putobjrow(POINT *rp, int n);
70     void putsquare(POINT *p0, POINT *p1, POINT *p2, POINT *p3);
71     void comprow(double s, POINT *row, int siz);
72     void compnorms(POINT *r0, POINT *r1, POINT *r2, int siz);
73     int norminterp(FVECT resmat[4], POINT *p0, POINT *p1, POINT *p2, POINT *p3);
74    
75    
76     int
77 greg 1.1 main(argc, argv)
78     int argc;
79     char *argv[];
80     {
81 greg 1.3 POINT *row0, *row1, *row2, *rp;
82 greg 1.1 int i, j, m, n;
83     char stmp[256];
84    
85 greg 1.13 varset("PI", ':', PI);
86 greg 1.14 funset("hermite", 5, ':', l_hermite);
87     funset("bezier", 5, ':', l_bezier);
88     funset("bspline", 5, ':', l_bspline);
89 greg 1.1
90     if (argc < 8)
91     goto userror;
92    
93     for (i = 8; i < argc; i++)
94     if (!strcmp(argv[i], "-e"))
95 greg 1.10 scompile(argv[++i], NULL, 0);
96 greg 1.1 else if (!strcmp(argv[i], "-f"))
97     fcompile(argv[++i]);
98 greg 1.3 else if (!strcmp(argv[i], "-s"))
99     smooth++;
100 greg 2.7 else if (!strcmp(argv[i], "-o"))
101     objout++;
102 greg 1.1 else
103     goto userror;
104    
105 greg 1.3 modname = argv[1];
106     surfname = argv[2];
107 greg 1.1 m = atoi(argv[6]);
108     n = atoi(argv[7]);
109     if (m <= 0 || n <= 0)
110     goto userror;
111 greg 2.2 if (!strcmp(argv[5], "-") || access(argv[5], 4) == 0) { /* file? */
112     funset(ZNAME, 2, ':', l_dataval);
113     if (!strcmp(argv[5],argv[3]) && !strcmp(argv[5],argv[4])) {
114     loaddata(argv[5], m, n, 3);
115     funset(XNAME, 2, ':', l_dataval);
116     funset(YNAME, 2, ':', l_dataval);
117     } else {
118     loaddata(argv[5], m, n, 1);
119     sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]);
120     scompile(stmp, NULL, 0);
121     sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]);
122     scompile(stmp, NULL, 0);
123     }
124     } else {
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     sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]);
130     scompile(stmp, NULL, 0);
131     }
132 greg 1.4 row0 = (POINT *)malloc((n+3)*sizeof(POINT));
133     row1 = (POINT *)malloc((n+3)*sizeof(POINT));
134     row2 = (POINT *)malloc((n+3)*sizeof(POINT));
135 greg 1.3 if (row0 == NULL || row1 == NULL || row2 == NULL) {
136 greg 1.1 fprintf(stderr, "%s: out of memory\n", argv[0]);
137     quit(1);
138     }
139 greg 1.4 row0++; row1++; row2++;
140 greg 1.3 /* print header */
141 greg 2.16 fputs("# ", stdout);
142     printargs(argc, argv, stdout);
143 greg 1.9 eclock = 0;
144 greg 1.4 /* initialize */
145     comprow(-1.0/m, row0, n);
146 greg 1.3 comprow(0.0, row1, n);
147     comprow(1.0/m, row2, n);
148 greg 1.4 compnorms(row0, row1, row2, n);
149 greg 2.8 if (objout) {
150     printf("\nusemtl %s\n\n", modname);
151 greg 2.7 putobjrow(row1, n);
152 greg 2.8 }
153 greg 1.3 /* for each row */
154 greg 1.1 for (i = 0; i < m; i++) {
155     /* compute next row */
156 greg 1.3 rp = row0;
157 greg 1.1 row0 = row1;
158 greg 1.3 row1 = row2;
159     row2 = rp;
160 greg 1.4 comprow((double)(i+2)/m, row2, n);
161     compnorms(row0, row1, row2, n);
162 greg 2.7 if (objout)
163     putobjrow(row1, n);
164 greg 1.1
165     for (j = 0; j < n; j++) {
166 greg 2.6 int orient = (j & 1);
167 greg 1.3 /* put polygons */
168 greg 2.7 if (!(row0[j].valid && row1[j+1].valid))
169 greg 2.6 orient = 1;
170 greg 2.7 else if (!(row1[j].valid && row0[j+1].valid))
171 greg 2.6 orient = 0;
172     if (orient)
173 greg 1.3 putsquare(&row0[j], &row1[j],
174     &row0[j+1], &row1[j+1]);
175     else
176     putsquare(&row1[j], &row1[j+1],
177     &row0[j], &row0[j+1]);
178 greg 1.1 }
179     }
180    
181 schorsch 2.13 return 0;
182 greg 1.1
183     userror:
184     fprintf(stderr, "Usage: %s material name ", argv[0]);
185 greg 1.3 fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-s][-e expr][-f file]\n");
186 schorsch 2.13 return 1;
187 greg 2.2 }
188    
189    
190 schorsch 2.13 void
191     loaddata( /* load point data from file */
192     char *file,
193     int m,
194     int n,
195     int pointsize
196     )
197 greg 2.2 {
198     FILE *fp;
199     char word[64];
200     register int size;
201 schorsch 2.11 register RREAL *dp;
202 greg 2.2
203     datarec.flags = HASBORDER; /* assume border values */
204 greg 2.3 datarec.m = m+1;
205     datarec.n = n+1;
206     size = datarec.m*datarec.n*pointsize;
207 greg 2.2 if (pointsize == 3)
208     datarec.flags |= TRIPLETS;
209 schorsch 2.11 dp = (RREAL *)malloc(size*sizeof(RREAL));
210 greg 2.2 if ((datarec.data = dp) == NULL) {
211     fputs("Out of memory\n", stderr);
212     exit(1);
213     }
214     if (!strcmp(file, "-")) {
215     file = "<stdin>";
216     fp = stdin;
217     } else if ((fp = fopen(file, "r")) == NULL) {
218     fputs(file, stderr);
219     fputs(": cannot open\n", stderr);
220     exit(1);
221     }
222     while (size > 0 && fgetword(word, sizeof(word), fp) != NULL) {
223     if (!isflt(word)) {
224     fprintf(stderr, "%s: garbled data value: %s\n",
225     file, word);
226     exit(1);
227     }
228     *dp++ = atof(word);
229     size--;
230     }
231     if (size == (m+n+1)*pointsize) { /* no border after all */
232 schorsch 2.11 dp = (RREAL *)realloc((void *)datarec.data,
233     m*n*pointsize*sizeof(RREAL));
234 greg 2.2 if (dp != NULL)
235     datarec.data = dp;
236     datarec.flags &= ~HASBORDER;
237 greg 2.3 datarec.m = m;
238     datarec.n = n;
239 greg 2.2 size = 0;
240     }
241 greg 2.3 if (datarec.m < 2 || datarec.n < 2 || size != 0 ||
242     fgetword(word, sizeof(word), fp) != NULL) {
243 greg 2.2 fputs(file, stderr);
244     fputs(": bad number of data points\n", stderr);
245     exit(1);
246     }
247     fclose(fp);
248     }
249    
250    
251     double
252 schorsch 2.13 l_dataval( /* return recorded data value */
253     char *nam
254     )
255 greg 2.2 {
256     double u, v;
257     register int i, j;
258 schorsch 2.11 register RREAL *dp;
259 greg 2.2 double d00, d01, d10, d11;
260     /* compute coordinates */
261     u = argument(1); v = argument(2);
262     if (datarec.flags & HASBORDER) {
263 greg 2.3 i = u *= datarec.m-1;
264     j = v *= datarec.n-1;
265 greg 2.2 } else {
266 greg 2.3 i = u = u*datarec.m - .5;
267     j = v = v*datarec.n - .5;
268 greg 2.2 }
269     if (i < 0) i = 0;
270     else if (i > datarec.m-2) i = datarec.m-2;
271     if (j < 0) j = 0;
272     else if (j > datarec.n-2) j = datarec.n-2;
273     /* compute value */
274     if (datarec.flags & TRIPLETS) {
275 greg 2.3 dp = datarec.data + 3*(j*datarec.m + i);
276     if (nam == ZNAME)
277     dp += 2;
278     else if (nam == YNAME)
279 greg 2.2 dp++;
280     d00 = dp[0]; d01 = dp[3];
281 greg 2.3 dp += 3*datarec.m;
282 greg 2.2 d10 = dp[0]; d11 = dp[3];
283     } else {
284 greg 2.3 dp = datarec.data + j*datarec.m + i;
285 greg 2.2 d00 = dp[0]; d01 = dp[1];
286 greg 2.3 dp += datarec.m;
287 greg 2.2 d10 = dp[0]; d11 = dp[1];
288     }
289     /* bilinear interpolation */
290     return((j+1-v)*((i+1-u)*d00+(u-i)*d01)+(v-j)*((i+1-u)*d10+(u-i)*d11));
291 greg 1.1 }
292    
293    
294 schorsch 2.13 void
295     putobjrow( /* output vertex row to .OBJ */
296     register POINT *rp,
297     int n
298     )
299 greg 2.7 {
300     static int nverts = 0;
301    
302     for ( ; n-- >= 0; rp++) {
303     if (!rp->valid)
304     continue;
305     fputs("v ", stdout);
306 greg 2.9 pvect(rp->p);
307     if (smooth && !ZEROVECT(rp->n))
308 greg 2.7 printf("\tvn %.9g %.9g %.9g\n",
309     rp->n[0], rp->n[1], rp->n[2]);
310     printf("\tvt %.9g %.9g\n", rp->uv[0], rp->uv[1]);
311     rp->valid = ++nverts;
312     }
313     }
314    
315    
316 schorsch 2.13 void
317     putsquare( /* put out a square */
318     POINT *p0,
319     POINT *p1,
320     POINT *p2,
321     POINT *p3
322     )
323 greg 1.3 {
324     static int nout = 0;
325     FVECT norm[4];
326     int axis;
327     FVECT v1, v2, vc1, vc2;
328     int ok1, ok2;
329     /* compute exact normals */
330 greg 2.7 ok1 = (p0->valid && p1->valid && p2->valid);
331 greg 2.6 if (ok1) {
332 greg 2.9 VSUB(v1, p1->p, p0->p);
333     VSUB(v2, p2->p, p0->p);
334 greg 2.6 fcross(vc1, v1, v2);
335     ok1 = (normalize(vc1) != 0.0);
336     }
337 greg 2.7 ok2 = (p1->valid && p2->valid && p3->valid);
338 greg 2.6 if (ok2) {
339 greg 2.9 VSUB(v1, p2->p, p3->p);
340     VSUB(v2, p1->p, p3->p);
341 greg 2.6 fcross(vc2, v1, v2);
342     ok2 = (normalize(vc2) != 0.0);
343     }
344 greg 1.3 if (!(ok1 | ok2))
345     return;
346 greg 2.7 if (objout) { /* output .OBJ faces */
347     int p0n=0, p1n=0, p2n=0, p3n=0;
348     if (smooth) {
349 greg 2.9 if (!ZEROVECT(p0->n))
350     p0n = p0->valid;
351     if (!ZEROVECT(p1->n))
352     p1n = p1->valid;
353     if (!ZEROVECT(p2->n))
354     p2n = p2->valid;
355     if (!ZEROVECT(p3->n))
356     p3n = p3->valid;
357 greg 2.7 }
358     if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
359     printf("f %d/%d/%d %d/%d/%d %d/%d/%d %d/%d/%d\n",
360 greg 2.9 p0->valid, p0->valid, p0n,
361     p1->valid, p1->valid, p1n,
362     p3->valid, p3->valid, p3n,
363     p2->valid, p2->valid, p2n);
364 greg 2.7 return;
365     }
366     if (ok1)
367     printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n",
368 greg 2.9 p0->valid, p0->valid, p0n,
369     p1->valid, p1->valid, p1n,
370     p2->valid, p2->valid, p2n);
371 greg 2.7 if (ok2)
372     printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n",
373 greg 2.9 p2->valid, p2->valid, p2n,
374     p1->valid, p1->valid, p1n,
375     p3->valid, p3->valid, p3n);
376 greg 2.7 return;
377     }
378 greg 1.3 /* compute normal interpolation */
379     axis = norminterp(norm, p0, p1, p2, p3);
380    
381     /* put out quadrilateral? */
382     if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
383     printf("\n%s ", modname);
384     if (axis != -1) {
385     printf("texfunc %s\n", texname);
386     printf(tsargs);
387     printf("0\n13\t%d\n", axis);
388     pvect(norm[0]);
389     pvect(norm[1]);
390     pvect(norm[2]);
391     fvsum(v1, norm[3], vc1, -0.5);
392     fvsum(v1, v1, vc2, -0.5);
393     pvect(v1);
394     printf("\n%s ", texname);
395     }
396     printf("polygon %s.%d\n", surfname, ++nout);
397     printf("0\n0\n12\n");
398     pvect(p0->p);
399     pvect(p1->p);
400     pvect(p3->p);
401     pvect(p2->p);
402     return;
403     }
404     /* put out triangles? */
405     if (ok1) {
406     printf("\n%s ", modname);
407     if (axis != -1) {
408     printf("texfunc %s\n", texname);
409     printf(tsargs);
410     printf("0\n13\t%d\n", axis);
411     pvect(norm[0]);
412     pvect(norm[1]);
413     pvect(norm[2]);
414     fvsum(v1, norm[3], vc1, -1.0);
415     pvect(v1);
416     printf("\n%s ", texname);
417     }
418     printf("polygon %s.%d\n", surfname, ++nout);
419     printf("0\n0\n9\n");
420     pvect(p0->p);
421     pvect(p1->p);
422     pvect(p2->p);
423     }
424     if (ok2) {
425     printf("\n%s ", modname);
426     if (axis != -1) {
427     printf("texfunc %s\n", texname);
428     printf(tsargs);
429     printf("0\n13\t%d\n", axis);
430     pvect(norm[0]);
431     pvect(norm[1]);
432     pvect(norm[2]);
433     fvsum(v2, norm[3], vc2, -1.0);
434     pvect(v2);
435     printf("\n%s ", texname);
436     }
437     printf("polygon %s.%d\n", surfname, ++nout);
438     printf("0\n0\n9\n");
439     pvect(p2->p);
440     pvect(p1->p);
441     pvect(p3->p);
442     }
443     }
444    
445    
446 schorsch 2.13 void
447     comprow( /* compute row of values */
448     double s,
449     register POINT *row,
450     int siz
451     )
452 greg 1.1 {
453 greg 1.4 double st[2];
454 greg 1.8 int end;
455 greg 2.6 int checkvalid;
456 greg 1.4 register int i;
457 greg 1.8
458     if (smooth) {
459     i = -1; /* compute one past each end */
460     end = siz+1;
461     } else {
462     if (s < -FTINY || s > 1.0+FTINY)
463     return;
464     i = 0;
465     end = siz;
466     }
467 greg 1.1 st[0] = s;
468 greg 2.6 checkvalid = (fundefined(VNAME) == 2);
469 greg 1.8 while (i <= end) {
470 greg 1.4 st[1] = (double)i/siz;
471 greg 2.6 if (checkvalid && funvalue(VNAME, 2, st) <= 0.0) {
472     row[i].valid = 0;
473     row[i].p[0] = row[i].p[1] = row[i].p[2] = 0.0;
474 greg 2.7 row[i].uv[0] = row[i].uv[1] = 0.0;
475 greg 2.6 } else {
476     row[i].valid = 1;
477     row[i].p[0] = funvalue(XNAME, 2, st);
478     row[i].p[1] = funvalue(YNAME, 2, st);
479     row[i].p[2] = funvalue(ZNAME, 2, st);
480 greg 2.7 row[i].uv[0] = st[0];
481     row[i].uv[1] = st[1];
482 greg 2.6 }
483 greg 1.8 i++;
484 greg 1.1 }
485 greg 1.3 }
486    
487    
488 schorsch 2.13 void
489     compnorms( /* compute row of averaged normals */
490     register POINT *r0,
491     register POINT *r1,
492     register POINT *r2,
493     int siz
494     )
495 greg 1.3 {
496 greg 1.11 FVECT v1, v2;
497 greg 1.3
498     if (!smooth) /* not needed if no smoothing */
499     return;
500 greg 2.6 /* compute row 1 normals */
501 greg 1.4 while (siz-- >= 0) {
502 greg 2.6 if (!r1[0].valid)
503     continue;
504     if (!r0[0].valid) {
505     if (!r2[0].valid) {
506     r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
507     continue;
508     }
509     fvsum(v1, r2[0].p, r1[0].p, -1.0);
510     } else if (!r2[0].valid)
511     fvsum(v1, r1[0].p, r0[0].p, -1.0);
512     else
513     fvsum(v1, r2[0].p, r0[0].p, -1.0);
514     if (!r1[-1].valid) {
515     if (!r1[1].valid) {
516     r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
517     continue;
518     }
519     fvsum(v2, r1[1].p, r1[0].p, -1.0);
520     } else if (!r1[1].valid)
521     fvsum(v2, r1[0].p, r1[-1].p, -1.0);
522     else
523     fvsum(v2, r1[1].p, r1[-1].p, -1.0);
524 greg 1.3 fcross(r1[0].n, v1, v2);
525     normalize(r1[0].n);
526     r0++; r1++; r2++;
527     }
528     }
529    
530    
531     int
532 schorsch 2.13 norminterp( /* compute normal interpolation */
533     register FVECT resmat[4],
534     POINT *p0,
535     POINT *p1,
536     POINT *p2,
537     POINT *p3
538     )
539 greg 1.3 {
540     #define u ((ax+1)%3)
541     #define v ((ax+2)%3)
542    
543     register int ax;
544 greg 1.12 MAT4 eqnmat;
545 greg 1.3 FVECT v1;
546     register int i, j;
547    
548     if (!smooth) /* no interpolation if no smoothing */
549     return(-1);
550     /* find dominant axis */
551     VCOPY(v1, p0->n);
552     fvsum(v1, v1, p1->n, 1.0);
553     fvsum(v1, v1, p2->n, 1.0);
554     fvsum(v1, v1, p3->n, 1.0);
555 greg 1.4 ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1;
556     ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2;
557 greg 1.3 /* assign equation matrix */
558     eqnmat[0][0] = p0->p[u]*p0->p[v];
559     eqnmat[0][1] = p0->p[u];
560     eqnmat[0][2] = p0->p[v];
561     eqnmat[0][3] = 1.0;
562     eqnmat[1][0] = p1->p[u]*p1->p[v];
563     eqnmat[1][1] = p1->p[u];
564     eqnmat[1][2] = p1->p[v];
565     eqnmat[1][3] = 1.0;
566     eqnmat[2][0] = p2->p[u]*p2->p[v];
567     eqnmat[2][1] = p2->p[u];
568     eqnmat[2][2] = p2->p[v];
569     eqnmat[2][3] = 1.0;
570     eqnmat[3][0] = p3->p[u]*p3->p[v];
571     eqnmat[3][1] = p3->p[u];
572     eqnmat[3][2] = p3->p[v];
573     eqnmat[3][3] = 1.0;
574     /* invert matrix (solve system) */
575 greg 2.5 if (!invmat4(eqnmat, eqnmat))
576 greg 1.3 return(-1); /* no solution */
577     /* compute result matrix */
578     for (j = 0; j < 4; j++)
579     for (i = 0; i < 3; i++)
580 greg 1.4 resmat[j][i] = eqnmat[j][0]*p0->n[i] +
581     eqnmat[j][1]*p1->n[i] +
582     eqnmat[j][2]*p2->n[i] +
583     eqnmat[j][3]*p3->n[i];
584 greg 1.3 return(ax);
585    
586     #undef u
587     #undef v
588 greg 1.1 }
589    
590    
591     double
592 greg 2.12 l_hermite(char *nm)
593 greg 1.1 {
594     double t;
595    
596     t = argument(5);
597     return( argument(1)*((2.0*t-3.0)*t*t+1.0) +
598     argument(2)*(-2.0*t+3.0)*t*t +
599     argument(3)*((t-2.0)*t+1.0)*t +
600     argument(4)*(t-1.0)*t*t );
601 greg 1.6 }
602    
603    
604     double
605 greg 2.12 l_bezier(char *nm)
606 greg 1.6 {
607     double t;
608    
609     t = argument(5);
610     return( argument(1) * (1.+t*(-3.+t*(3.-t))) +
611     argument(2) * 3.*t*(1.+t*(-2.+t)) +
612     argument(3) * 3.*t*t*(1.-t) +
613     argument(4) * t*t*t );
614 greg 1.7 }
615    
616    
617     double
618 greg 2.12 l_bspline(char *nm)
619 greg 1.7 {
620     double t;
621    
622     t = argument(5);
623     return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) +
624     argument(2) * (2./3.+t*t*(-1.+1./2.*t)) +
625     argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) +
626     argument(4) * (1./6.*t*t*t) );
627 greg 1.1 }