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root/radiance/ray/src/gen/gensurf.c
Revision: 2.15
Committed: Fri Mar 26 21:30:12 2004 UTC (20 years ago) by schorsch
Content type: text/plain
Branch: MAIN
Changes since 2.14: +3 -1 lines
Log Message:
Added "paths.h" for access().

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 schorsch 2.15 static const char RCSid[] = "$Id: gensurf.c,v 2.14 2004/03/23 15:18:09 greg 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 schorsch 2.13 #include "calcomp.h"
22 greg 1.1
23 greg 2.6 char XNAME[] = "X`SYS"; /* x function name */
24     char YNAME[] = "Y`SYS"; /* y function name */
25     char ZNAME[] = "Z`SYS"; /* z function name */
26    
27     char VNAME[] = "valid"; /* valid vertex name */
28 greg 1.1
29 greg 1.4 #define ABS(x) ((x)>=0 ? (x) : -(x))
30    
31 greg 2.9 #define ZEROVECT(v) (DOT(v,v) <= FTINY*FTINY)
32    
33 greg 1.3 #define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2])
34 greg 1.1
35     char vformat[] = "%15.9g %15.9g %15.9g\n";
36 greg 1.3 char tsargs[] = "4 surf_dx surf_dy surf_dz surf.cal\n";
37     char texname[] = "Phong";
38 greg 1.1
39 greg 1.3 int smooth = 0; /* apply smoothing? */
40 greg 2.7 int objout = 0; /* output .OBJ format? */
41 greg 1.1
42 greg 1.3 char *modname, *surfname;
43 greg 1.1
44 greg 2.2 /* recorded data flags */
45     #define HASBORDER 01
46     #define TRIPLETS 02
47     /* a data structure */
48     struct {
49     int flags; /* data type */
50     short m, n; /* number of s and t values */
51 schorsch 2.11 RREAL *data; /* the data itself, s major sort */
52 greg 2.2 } datarec; /* our recorded data */
53 greg 1.3
54 schorsch 2.13 /* XXX this is redundant with rt/noise3.c, should go to a library */
55 greg 2.2 double l_hermite(), l_bezier(), l_bspline(), l_dataval();
56    
57 greg 1.3 typedef struct {
58 greg 2.7 int valid; /* point is valid (vertex number) */
59 greg 1.3 FVECT p; /* vertex position */
60     FVECT n; /* average normal */
61 schorsch 2.11 RREAL uv[2]; /* (u,v) position */
62 greg 1.3 } POINT;
63    
64    
65 schorsch 2.13 void loaddata(char *file, int m, int n, int pointsize);
66     double l_dataval(char *nam);
67     void putobjrow(POINT *rp, int n);
68     void putsquare(POINT *p0, POINT *p1, POINT *p2, POINT *p3);
69     void comprow(double s, POINT *row, int siz);
70     void compnorms(POINT *r0, POINT *r1, POINT *r2, int siz);
71     int norminterp(FVECT resmat[4], POINT *p0, POINT *p1, POINT *p2, POINT *p3);
72     void printhead(int ac, char **av);
73    
74    
75     int
76 greg 1.1 main(argc, argv)
77     int argc;
78     char *argv[];
79     {
80 greg 1.3 POINT *row0, *row1, *row2, *rp;
81 greg 1.1 int i, j, m, n;
82     char stmp[256];
83    
84 greg 1.13 varset("PI", ':', PI);
85 greg 1.14 funset("hermite", 5, ':', l_hermite);
86     funset("bezier", 5, ':', l_bezier);
87     funset("bspline", 5, ':', l_bspline);
88 greg 1.1
89     if (argc < 8)
90     goto userror;
91    
92     for (i = 8; i < argc; i++)
93     if (!strcmp(argv[i], "-e"))
94 greg 1.10 scompile(argv[++i], NULL, 0);
95 greg 1.1 else if (!strcmp(argv[i], "-f"))
96     fcompile(argv[++i]);
97 greg 1.3 else if (!strcmp(argv[i], "-s"))
98     smooth++;
99 greg 2.7 else if (!strcmp(argv[i], "-o"))
100     objout++;
101 greg 1.1 else
102     goto userror;
103    
104 greg 1.3 modname = argv[1];
105     surfname = argv[2];
106 greg 1.1 m = atoi(argv[6]);
107     n = atoi(argv[7]);
108     if (m <= 0 || n <= 0)
109     goto userror;
110 greg 2.2 if (!strcmp(argv[5], "-") || access(argv[5], 4) == 0) { /* file? */
111     funset(ZNAME, 2, ':', l_dataval);
112     if (!strcmp(argv[5],argv[3]) && !strcmp(argv[5],argv[4])) {
113     loaddata(argv[5], m, n, 3);
114     funset(XNAME, 2, ':', l_dataval);
115     funset(YNAME, 2, ':', l_dataval);
116     } else {
117     loaddata(argv[5], m, n, 1);
118     sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]);
119     scompile(stmp, NULL, 0);
120     sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]);
121     scompile(stmp, NULL, 0);
122     }
123     } else {
124     sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]);
125     scompile(stmp, NULL, 0);
126     sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]);
127     scompile(stmp, NULL, 0);
128     sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]);
129     scompile(stmp, NULL, 0);
130     }
131 greg 1.4 row0 = (POINT *)malloc((n+3)*sizeof(POINT));
132     row1 = (POINT *)malloc((n+3)*sizeof(POINT));
133     row2 = (POINT *)malloc((n+3)*sizeof(POINT));
134 greg 1.3 if (row0 == NULL || row1 == NULL || row2 == NULL) {
135 greg 1.1 fprintf(stderr, "%s: out of memory\n", argv[0]);
136     quit(1);
137     }
138 greg 1.4 row0++; row1++; row2++;
139 greg 1.3 /* print header */
140 greg 1.1 printhead(argc, argv);
141 greg 1.9 eclock = 0;
142 greg 1.4 /* initialize */
143     comprow(-1.0/m, row0, n);
144 greg 1.3 comprow(0.0, row1, n);
145     comprow(1.0/m, row2, n);
146 greg 1.4 compnorms(row0, row1, row2, n);
147 greg 2.8 if (objout) {
148     printf("\nusemtl %s\n\n", modname);
149 greg 2.7 putobjrow(row1, n);
150 greg 2.8 }
151 greg 1.3 /* for each row */
152 greg 1.1 for (i = 0; i < m; i++) {
153     /* compute next row */
154 greg 1.3 rp = row0;
155 greg 1.1 row0 = row1;
156 greg 1.3 row1 = row2;
157     row2 = rp;
158 greg 1.4 comprow((double)(i+2)/m, row2, n);
159     compnorms(row0, row1, row2, n);
160 greg 2.7 if (objout)
161     putobjrow(row1, n);
162 greg 1.1
163     for (j = 0; j < n; j++) {
164 greg 2.6 int orient = (j & 1);
165 greg 1.3 /* put polygons */
166 greg 2.7 if (!(row0[j].valid && row1[j+1].valid))
167 greg 2.6 orient = 1;
168 greg 2.7 else if (!(row1[j].valid && row0[j+1].valid))
169 greg 2.6 orient = 0;
170     if (orient)
171 greg 1.3 putsquare(&row0[j], &row1[j],
172     &row0[j+1], &row1[j+1]);
173     else
174     putsquare(&row1[j], &row1[j+1],
175     &row0[j], &row0[j+1]);
176 greg 1.1 }
177     }
178    
179 schorsch 2.13 return 0;
180 greg 1.1
181     userror:
182     fprintf(stderr, "Usage: %s material name ", argv[0]);
183 greg 1.3 fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-s][-e expr][-f file]\n");
184 schorsch 2.13 return 1;
185 greg 2.2 }
186    
187    
188 schorsch 2.13 void
189     loaddata( /* load point data from file */
190     char *file,
191     int m,
192     int n,
193     int pointsize
194     )
195 greg 2.2 {
196     FILE *fp;
197     char word[64];
198     register int size;
199 schorsch 2.11 register RREAL *dp;
200 greg 2.2
201     datarec.flags = HASBORDER; /* assume border values */
202 greg 2.3 datarec.m = m+1;
203     datarec.n = n+1;
204     size = datarec.m*datarec.n*pointsize;
205 greg 2.2 if (pointsize == 3)
206     datarec.flags |= TRIPLETS;
207 schorsch 2.11 dp = (RREAL *)malloc(size*sizeof(RREAL));
208 greg 2.2 if ((datarec.data = dp) == NULL) {
209     fputs("Out of memory\n", stderr);
210     exit(1);
211     }
212     if (!strcmp(file, "-")) {
213     file = "<stdin>";
214     fp = stdin;
215     } else if ((fp = fopen(file, "r")) == NULL) {
216     fputs(file, stderr);
217     fputs(": cannot open\n", stderr);
218     exit(1);
219     }
220     while (size > 0 && fgetword(word, sizeof(word), fp) != NULL) {
221     if (!isflt(word)) {
222     fprintf(stderr, "%s: garbled data value: %s\n",
223     file, word);
224     exit(1);
225     }
226     *dp++ = atof(word);
227     size--;
228     }
229     if (size == (m+n+1)*pointsize) { /* no border after all */
230 schorsch 2.11 dp = (RREAL *)realloc((void *)datarec.data,
231     m*n*pointsize*sizeof(RREAL));
232 greg 2.2 if (dp != NULL)
233     datarec.data = dp;
234     datarec.flags &= ~HASBORDER;
235 greg 2.3 datarec.m = m;
236     datarec.n = n;
237 greg 2.2 size = 0;
238     }
239 greg 2.3 if (datarec.m < 2 || datarec.n < 2 || size != 0 ||
240     fgetword(word, sizeof(word), fp) != NULL) {
241 greg 2.2 fputs(file, stderr);
242     fputs(": bad number of data points\n", stderr);
243     exit(1);
244     }
245     fclose(fp);
246     }
247    
248    
249     double
250 schorsch 2.13 l_dataval( /* return recorded data value */
251     char *nam
252     )
253 greg 2.2 {
254     double u, v;
255     register int i, j;
256 schorsch 2.11 register RREAL *dp;
257 greg 2.2 double d00, d01, d10, d11;
258     /* compute coordinates */
259     u = argument(1); v = argument(2);
260     if (datarec.flags & HASBORDER) {
261 greg 2.3 i = u *= datarec.m-1;
262     j = v *= datarec.n-1;
263 greg 2.2 } else {
264 greg 2.3 i = u = u*datarec.m - .5;
265     j = v = v*datarec.n - .5;
266 greg 2.2 }
267     if (i < 0) i = 0;
268     else if (i > datarec.m-2) i = datarec.m-2;
269     if (j < 0) j = 0;
270     else if (j > datarec.n-2) j = datarec.n-2;
271     /* compute value */
272     if (datarec.flags & TRIPLETS) {
273 greg 2.3 dp = datarec.data + 3*(j*datarec.m + i);
274     if (nam == ZNAME)
275     dp += 2;
276     else if (nam == YNAME)
277 greg 2.2 dp++;
278     d00 = dp[0]; d01 = dp[3];
279 greg 2.3 dp += 3*datarec.m;
280 greg 2.2 d10 = dp[0]; d11 = dp[3];
281     } else {
282 greg 2.3 dp = datarec.data + j*datarec.m + i;
283 greg 2.2 d00 = dp[0]; d01 = dp[1];
284 greg 2.3 dp += datarec.m;
285 greg 2.2 d10 = dp[0]; d11 = dp[1];
286     }
287     /* bilinear interpolation */
288     return((j+1-v)*((i+1-u)*d00+(u-i)*d01)+(v-j)*((i+1-u)*d10+(u-i)*d11));
289 greg 1.1 }
290    
291    
292 schorsch 2.13 void
293     putobjrow( /* output vertex row to .OBJ */
294     register POINT *rp,
295     int n
296     )
297 greg 2.7 {
298     static int nverts = 0;
299    
300     for ( ; n-- >= 0; rp++) {
301     if (!rp->valid)
302     continue;
303     fputs("v ", stdout);
304 greg 2.9 pvect(rp->p);
305     if (smooth && !ZEROVECT(rp->n))
306 greg 2.7 printf("\tvn %.9g %.9g %.9g\n",
307     rp->n[0], rp->n[1], rp->n[2]);
308     printf("\tvt %.9g %.9g\n", rp->uv[0], rp->uv[1]);
309     rp->valid = ++nverts;
310     }
311     }
312    
313    
314 schorsch 2.13 void
315     putsquare( /* put out a square */
316     POINT *p0,
317     POINT *p1,
318     POINT *p2,
319     POINT *p3
320     )
321 greg 1.3 {
322     static int nout = 0;
323     FVECT norm[4];
324     int axis;
325     FVECT v1, v2, vc1, vc2;
326     int ok1, ok2;
327     /* compute exact normals */
328 greg 2.7 ok1 = (p0->valid && p1->valid && p2->valid);
329 greg 2.6 if (ok1) {
330 greg 2.9 VSUB(v1, p1->p, p0->p);
331     VSUB(v2, p2->p, p0->p);
332 greg 2.6 fcross(vc1, v1, v2);
333     ok1 = (normalize(vc1) != 0.0);
334     }
335 greg 2.7 ok2 = (p1->valid && p2->valid && p3->valid);
336 greg 2.6 if (ok2) {
337 greg 2.9 VSUB(v1, p2->p, p3->p);
338     VSUB(v2, p1->p, p3->p);
339 greg 2.6 fcross(vc2, v1, v2);
340     ok2 = (normalize(vc2) != 0.0);
341     }
342 greg 1.3 if (!(ok1 | ok2))
343     return;
344 greg 2.7 if (objout) { /* output .OBJ faces */
345     int p0n=0, p1n=0, p2n=0, p3n=0;
346     if (smooth) {
347 greg 2.9 if (!ZEROVECT(p0->n))
348     p0n = p0->valid;
349     if (!ZEROVECT(p1->n))
350     p1n = p1->valid;
351     if (!ZEROVECT(p2->n))
352     p2n = p2->valid;
353     if (!ZEROVECT(p3->n))
354     p3n = p3->valid;
355 greg 2.7 }
356     if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
357     printf("f %d/%d/%d %d/%d/%d %d/%d/%d %d/%d/%d\n",
358 greg 2.9 p0->valid, p0->valid, p0n,
359     p1->valid, p1->valid, p1n,
360     p3->valid, p3->valid, p3n,
361     p2->valid, p2->valid, p2n);
362 greg 2.7 return;
363     }
364     if (ok1)
365     printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n",
366 greg 2.9 p0->valid, p0->valid, p0n,
367     p1->valid, p1->valid, p1n,
368     p2->valid, p2->valid, p2n);
369 greg 2.7 if (ok2)
370     printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n",
371 greg 2.9 p2->valid, p2->valid, p2n,
372     p1->valid, p1->valid, p1n,
373     p3->valid, p3->valid, p3n);
374 greg 2.7 return;
375     }
376 greg 1.3 /* compute normal interpolation */
377     axis = norminterp(norm, p0, p1, p2, p3);
378    
379     /* put out quadrilateral? */
380     if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
381     printf("\n%s ", modname);
382     if (axis != -1) {
383     printf("texfunc %s\n", texname);
384     printf(tsargs);
385     printf("0\n13\t%d\n", axis);
386     pvect(norm[0]);
387     pvect(norm[1]);
388     pvect(norm[2]);
389     fvsum(v1, norm[3], vc1, -0.5);
390     fvsum(v1, v1, vc2, -0.5);
391     pvect(v1);
392     printf("\n%s ", texname);
393     }
394     printf("polygon %s.%d\n", surfname, ++nout);
395     printf("0\n0\n12\n");
396     pvect(p0->p);
397     pvect(p1->p);
398     pvect(p3->p);
399     pvect(p2->p);
400     return;
401     }
402     /* put out triangles? */
403     if (ok1) {
404     printf("\n%s ", modname);
405     if (axis != -1) {
406     printf("texfunc %s\n", texname);
407     printf(tsargs);
408     printf("0\n13\t%d\n", axis);
409     pvect(norm[0]);
410     pvect(norm[1]);
411     pvect(norm[2]);
412     fvsum(v1, norm[3], vc1, -1.0);
413     pvect(v1);
414     printf("\n%s ", texname);
415     }
416     printf("polygon %s.%d\n", surfname, ++nout);
417     printf("0\n0\n9\n");
418     pvect(p0->p);
419     pvect(p1->p);
420     pvect(p2->p);
421     }
422     if (ok2) {
423     printf("\n%s ", modname);
424     if (axis != -1) {
425     printf("texfunc %s\n", texname);
426     printf(tsargs);
427     printf("0\n13\t%d\n", axis);
428     pvect(norm[0]);
429     pvect(norm[1]);
430     pvect(norm[2]);
431     fvsum(v2, norm[3], vc2, -1.0);
432     pvect(v2);
433     printf("\n%s ", texname);
434     }
435     printf("polygon %s.%d\n", surfname, ++nout);
436     printf("0\n0\n9\n");
437     pvect(p2->p);
438     pvect(p1->p);
439     pvect(p3->p);
440     }
441     }
442    
443    
444 schorsch 2.13 void
445     comprow( /* compute row of values */
446     double s,
447     register POINT *row,
448     int siz
449     )
450 greg 1.1 {
451 greg 1.4 double st[2];
452 greg 1.8 int end;
453 greg 2.6 int checkvalid;
454 greg 1.4 register int i;
455 greg 1.8
456     if (smooth) {
457     i = -1; /* compute one past each end */
458     end = siz+1;
459     } else {
460     if (s < -FTINY || s > 1.0+FTINY)
461     return;
462     i = 0;
463     end = siz;
464     }
465 greg 1.1 st[0] = s;
466 greg 2.6 checkvalid = (fundefined(VNAME) == 2);
467 greg 1.8 while (i <= end) {
468 greg 1.4 st[1] = (double)i/siz;
469 greg 2.6 if (checkvalid && funvalue(VNAME, 2, st) <= 0.0) {
470     row[i].valid = 0;
471     row[i].p[0] = row[i].p[1] = row[i].p[2] = 0.0;
472 greg 2.7 row[i].uv[0] = row[i].uv[1] = 0.0;
473 greg 2.6 } else {
474     row[i].valid = 1;
475     row[i].p[0] = funvalue(XNAME, 2, st);
476     row[i].p[1] = funvalue(YNAME, 2, st);
477     row[i].p[2] = funvalue(ZNAME, 2, st);
478 greg 2.7 row[i].uv[0] = st[0];
479     row[i].uv[1] = st[1];
480 greg 2.6 }
481 greg 1.8 i++;
482 greg 1.1 }
483 greg 1.3 }
484    
485    
486 schorsch 2.13 void
487     compnorms( /* compute row of averaged normals */
488     register POINT *r0,
489     register POINT *r1,
490     register POINT *r2,
491     int siz
492     )
493 greg 1.3 {
494 greg 1.11 FVECT v1, v2;
495 greg 1.3
496     if (!smooth) /* not needed if no smoothing */
497     return;
498 greg 2.6 /* compute row 1 normals */
499 greg 1.4 while (siz-- >= 0) {
500 greg 2.6 if (!r1[0].valid)
501     continue;
502     if (!r0[0].valid) {
503     if (!r2[0].valid) {
504     r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
505     continue;
506     }
507     fvsum(v1, r2[0].p, r1[0].p, -1.0);
508     } else if (!r2[0].valid)
509     fvsum(v1, r1[0].p, r0[0].p, -1.0);
510     else
511     fvsum(v1, r2[0].p, r0[0].p, -1.0);
512     if (!r1[-1].valid) {
513     if (!r1[1].valid) {
514     r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
515     continue;
516     }
517     fvsum(v2, r1[1].p, r1[0].p, -1.0);
518     } else if (!r1[1].valid)
519     fvsum(v2, r1[0].p, r1[-1].p, -1.0);
520     else
521     fvsum(v2, r1[1].p, r1[-1].p, -1.0);
522 greg 1.3 fcross(r1[0].n, v1, v2);
523     normalize(r1[0].n);
524     r0++; r1++; r2++;
525     }
526     }
527    
528    
529     int
530 schorsch 2.13 norminterp( /* compute normal interpolation */
531     register FVECT resmat[4],
532     POINT *p0,
533     POINT *p1,
534     POINT *p2,
535     POINT *p3
536     )
537 greg 1.3 {
538     #define u ((ax+1)%3)
539     #define v ((ax+2)%3)
540    
541     register int ax;
542 greg 1.12 MAT4 eqnmat;
543 greg 1.3 FVECT v1;
544     register int i, j;
545    
546     if (!smooth) /* no interpolation if no smoothing */
547     return(-1);
548     /* find dominant axis */
549     VCOPY(v1, p0->n);
550     fvsum(v1, v1, p1->n, 1.0);
551     fvsum(v1, v1, p2->n, 1.0);
552     fvsum(v1, v1, p3->n, 1.0);
553 greg 1.4 ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1;
554     ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2;
555 greg 1.3 /* assign equation matrix */
556     eqnmat[0][0] = p0->p[u]*p0->p[v];
557     eqnmat[0][1] = p0->p[u];
558     eqnmat[0][2] = p0->p[v];
559     eqnmat[0][3] = 1.0;
560     eqnmat[1][0] = p1->p[u]*p1->p[v];
561     eqnmat[1][1] = p1->p[u];
562     eqnmat[1][2] = p1->p[v];
563     eqnmat[1][3] = 1.0;
564     eqnmat[2][0] = p2->p[u]*p2->p[v];
565     eqnmat[2][1] = p2->p[u];
566     eqnmat[2][2] = p2->p[v];
567     eqnmat[2][3] = 1.0;
568     eqnmat[3][0] = p3->p[u]*p3->p[v];
569     eqnmat[3][1] = p3->p[u];
570     eqnmat[3][2] = p3->p[v];
571     eqnmat[3][3] = 1.0;
572     /* invert matrix (solve system) */
573 greg 2.5 if (!invmat4(eqnmat, eqnmat))
574 greg 1.3 return(-1); /* no solution */
575     /* compute result matrix */
576     for (j = 0; j < 4; j++)
577     for (i = 0; i < 3; i++)
578 greg 1.4 resmat[j][i] = eqnmat[j][0]*p0->n[i] +
579     eqnmat[j][1]*p1->n[i] +
580     eqnmat[j][2]*p2->n[i] +
581     eqnmat[j][3]*p3->n[i];
582 greg 1.3 return(ax);
583    
584     #undef u
585     #undef v
586 greg 1.1 }
587    
588    
589 greg 2.6 void
590 greg 1.1 eputs(msg)
591     char *msg;
592     {
593     fputs(msg, stderr);
594     }
595    
596    
597 greg 2.6 void
598 greg 1.1 wputs(msg)
599     char *msg;
600     {
601     eputs(msg);
602     }
603    
604    
605 greg 2.6 void
606 greg 1.1 quit(code)
607 greg 2.4 int code;
608 greg 1.1 {
609     exit(code);
610     }
611    
612    
613 schorsch 2.13 void
614     printhead( /* print command header */
615     register int ac,
616     register char **av
617     )
618 greg 1.1 {
619     putchar('#');
620     while (ac--) {
621     putchar(' ');
622     fputs(*av++, stdout);
623     }
624     putchar('\n');
625     }
626    
627    
628     double
629 greg 2.12 l_hermite(char *nm)
630 greg 1.1 {
631     double t;
632    
633     t = argument(5);
634     return( argument(1)*((2.0*t-3.0)*t*t+1.0) +
635     argument(2)*(-2.0*t+3.0)*t*t +
636     argument(3)*((t-2.0)*t+1.0)*t +
637     argument(4)*(t-1.0)*t*t );
638 greg 1.6 }
639    
640    
641     double
642 greg 2.12 l_bezier(char *nm)
643 greg 1.6 {
644     double t;
645    
646     t = argument(5);
647     return( argument(1) * (1.+t*(-3.+t*(3.-t))) +
648     argument(2) * 3.*t*(1.+t*(-2.+t)) +
649     argument(3) * 3.*t*t*(1.-t) +
650     argument(4) * t*t*t );
651 greg 1.7 }
652    
653    
654     double
655 greg 2.12 l_bspline(char *nm)
656 greg 1.7 {
657     double t;
658    
659     t = argument(5);
660     return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) +
661     argument(2) * (2./3.+t*t*(-1.+1./2.*t)) +
662     argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) +
663     argument(4) * (1./6.*t*t*t) );
664 greg 1.1 }