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root/radiance/ray/src/gen/gensurf.c
Revision: 2.14
Committed: Tue Mar 23 15:18:09 2004 UTC (20 years ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.13: +2 -4 lines
Log Message:
Fixed missing declaration for atof()

File Contents

# User Rev Content
1 greg 1.1 #ifndef lint
2 greg 2.14 static const char RCSid[] = "$Id: gensurf.c,v 2.13 2003/11/16 10:29:38 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 2.13 #include "calcomp.h"
20 greg 1.1
21 greg 2.6 char XNAME[] = "X`SYS"; /* x function name */
22     char YNAME[] = "Y`SYS"; /* y function name */
23     char ZNAME[] = "Z`SYS"; /* z function name */
24    
25     char VNAME[] = "valid"; /* valid vertex name */
26 greg 1.1
27 greg 1.4 #define ABS(x) ((x)>=0 ? (x) : -(x))
28    
29 greg 2.9 #define ZEROVECT(v) (DOT(v,v) <= FTINY*FTINY)
30    
31 greg 1.3 #define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2])
32 greg 1.1
33     char vformat[] = "%15.9g %15.9g %15.9g\n";
34 greg 1.3 char tsargs[] = "4 surf_dx surf_dy surf_dz surf.cal\n";
35     char texname[] = "Phong";
36 greg 1.1
37 greg 1.3 int smooth = 0; /* apply smoothing? */
38 greg 2.7 int objout = 0; /* output .OBJ format? */
39 greg 1.1
40 greg 1.3 char *modname, *surfname;
41 greg 1.1
42 greg 2.2 /* recorded data flags */
43     #define HASBORDER 01
44     #define TRIPLETS 02
45     /* a data structure */
46     struct {
47     int flags; /* data type */
48     short m, n; /* number of s and t values */
49 schorsch 2.11 RREAL *data; /* the data itself, s major sort */
50 greg 2.2 } datarec; /* our recorded data */
51 greg 1.3
52 schorsch 2.13 /* XXX this is redundant with rt/noise3.c, should go to a library */
53 greg 2.2 double l_hermite(), l_bezier(), l_bspline(), l_dataval();
54    
55 greg 1.3 typedef struct {
56 greg 2.7 int valid; /* point is valid (vertex number) */
57 greg 1.3 FVECT p; /* vertex position */
58     FVECT n; /* average normal */
59 schorsch 2.11 RREAL uv[2]; /* (u,v) position */
60 greg 1.3 } POINT;
61    
62    
63 schorsch 2.13 void loaddata(char *file, int m, int n, int pointsize);
64     double l_dataval(char *nam);
65     void putobjrow(POINT *rp, int n);
66     void putsquare(POINT *p0, POINT *p1, POINT *p2, POINT *p3);
67     void comprow(double s, POINT *row, int siz);
68     void compnorms(POINT *r0, POINT *r1, POINT *r2, int siz);
69     int norminterp(FVECT resmat[4], POINT *p0, POINT *p1, POINT *p2, POINT *p3);
70     void printhead(int ac, char **av);
71    
72    
73     int
74 greg 1.1 main(argc, argv)
75     int argc;
76     char *argv[];
77     {
78 greg 1.3 POINT *row0, *row1, *row2, *rp;
79 greg 1.1 int i, j, m, n;
80     char stmp[256];
81    
82 greg 1.13 varset("PI", ':', PI);
83 greg 1.14 funset("hermite", 5, ':', l_hermite);
84     funset("bezier", 5, ':', l_bezier);
85     funset("bspline", 5, ':', l_bspline);
86 greg 1.1
87     if (argc < 8)
88     goto userror;
89    
90     for (i = 8; i < argc; i++)
91     if (!strcmp(argv[i], "-e"))
92 greg 1.10 scompile(argv[++i], NULL, 0);
93 greg 1.1 else if (!strcmp(argv[i], "-f"))
94     fcompile(argv[++i]);
95 greg 1.3 else if (!strcmp(argv[i], "-s"))
96     smooth++;
97 greg 2.7 else if (!strcmp(argv[i], "-o"))
98     objout++;
99 greg 1.1 else
100     goto userror;
101    
102 greg 1.3 modname = argv[1];
103     surfname = argv[2];
104 greg 1.1 m = atoi(argv[6]);
105     n = atoi(argv[7]);
106     if (m <= 0 || n <= 0)
107     goto userror;
108 greg 2.2 if (!strcmp(argv[5], "-") || access(argv[5], 4) == 0) { /* file? */
109     funset(ZNAME, 2, ':', l_dataval);
110     if (!strcmp(argv[5],argv[3]) && !strcmp(argv[5],argv[4])) {
111     loaddata(argv[5], m, n, 3);
112     funset(XNAME, 2, ':', l_dataval);
113     funset(YNAME, 2, ':', l_dataval);
114     } else {
115     loaddata(argv[5], m, n, 1);
116     sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]);
117     scompile(stmp, NULL, 0);
118     sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]);
119     scompile(stmp, NULL, 0);
120     }
121     } else {
122     sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]);
123     scompile(stmp, NULL, 0);
124     sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]);
125     scompile(stmp, NULL, 0);
126     sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]);
127     scompile(stmp, NULL, 0);
128     }
129 greg 1.4 row0 = (POINT *)malloc((n+3)*sizeof(POINT));
130     row1 = (POINT *)malloc((n+3)*sizeof(POINT));
131     row2 = (POINT *)malloc((n+3)*sizeof(POINT));
132 greg 1.3 if (row0 == NULL || row1 == NULL || row2 == NULL) {
133 greg 1.1 fprintf(stderr, "%s: out of memory\n", argv[0]);
134     quit(1);
135     }
136 greg 1.4 row0++; row1++; row2++;
137 greg 1.3 /* print header */
138 greg 1.1 printhead(argc, argv);
139 greg 1.9 eclock = 0;
140 greg 1.4 /* initialize */
141     comprow(-1.0/m, row0, n);
142 greg 1.3 comprow(0.0, row1, n);
143     comprow(1.0/m, row2, n);
144 greg 1.4 compnorms(row0, row1, row2, n);
145 greg 2.8 if (objout) {
146     printf("\nusemtl %s\n\n", modname);
147 greg 2.7 putobjrow(row1, n);
148 greg 2.8 }
149 greg 1.3 /* for each row */
150 greg 1.1 for (i = 0; i < m; i++) {
151     /* compute next row */
152 greg 1.3 rp = row0;
153 greg 1.1 row0 = row1;
154 greg 1.3 row1 = row2;
155     row2 = rp;
156 greg 1.4 comprow((double)(i+2)/m, row2, n);
157     compnorms(row0, row1, row2, n);
158 greg 2.7 if (objout)
159     putobjrow(row1, n);
160 greg 1.1
161     for (j = 0; j < n; j++) {
162 greg 2.6 int orient = (j & 1);
163 greg 1.3 /* put polygons */
164 greg 2.7 if (!(row0[j].valid && row1[j+1].valid))
165 greg 2.6 orient = 1;
166 greg 2.7 else if (!(row1[j].valid && row0[j+1].valid))
167 greg 2.6 orient = 0;
168     if (orient)
169 greg 1.3 putsquare(&row0[j], &row1[j],
170     &row0[j+1], &row1[j+1]);
171     else
172     putsquare(&row1[j], &row1[j+1],
173     &row0[j], &row0[j+1]);
174 greg 1.1 }
175     }
176    
177 schorsch 2.13 return 0;
178 greg 1.1
179     userror:
180     fprintf(stderr, "Usage: %s material name ", argv[0]);
181 greg 1.3 fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-s][-e expr][-f file]\n");
182 schorsch 2.13 return 1;
183 greg 2.2 }
184    
185    
186 schorsch 2.13 void
187     loaddata( /* load point data from file */
188     char *file,
189     int m,
190     int n,
191     int pointsize
192     )
193 greg 2.2 {
194     FILE *fp;
195     char word[64];
196     register int size;
197 schorsch 2.11 register RREAL *dp;
198 greg 2.2
199     datarec.flags = HASBORDER; /* assume border values */
200 greg 2.3 datarec.m = m+1;
201     datarec.n = n+1;
202     size = datarec.m*datarec.n*pointsize;
203 greg 2.2 if (pointsize == 3)
204     datarec.flags |= TRIPLETS;
205 schorsch 2.11 dp = (RREAL *)malloc(size*sizeof(RREAL));
206 greg 2.2 if ((datarec.data = dp) == NULL) {
207     fputs("Out of memory\n", stderr);
208     exit(1);
209     }
210     if (!strcmp(file, "-")) {
211     file = "<stdin>";
212     fp = stdin;
213     } else if ((fp = fopen(file, "r")) == NULL) {
214     fputs(file, stderr);
215     fputs(": cannot open\n", stderr);
216     exit(1);
217     }
218     while (size > 0 && fgetword(word, sizeof(word), fp) != NULL) {
219     if (!isflt(word)) {
220     fprintf(stderr, "%s: garbled data value: %s\n",
221     file, word);
222     exit(1);
223     }
224     *dp++ = atof(word);
225     size--;
226     }
227     if (size == (m+n+1)*pointsize) { /* no border after all */
228 schorsch 2.11 dp = (RREAL *)realloc((void *)datarec.data,
229     m*n*pointsize*sizeof(RREAL));
230 greg 2.2 if (dp != NULL)
231     datarec.data = dp;
232     datarec.flags &= ~HASBORDER;
233 greg 2.3 datarec.m = m;
234     datarec.n = n;
235 greg 2.2 size = 0;
236     }
237 greg 2.3 if (datarec.m < 2 || datarec.n < 2 || size != 0 ||
238     fgetword(word, sizeof(word), fp) != NULL) {
239 greg 2.2 fputs(file, stderr);
240     fputs(": bad number of data points\n", stderr);
241     exit(1);
242     }
243     fclose(fp);
244     }
245    
246    
247     double
248 schorsch 2.13 l_dataval( /* return recorded data value */
249     char *nam
250     )
251 greg 2.2 {
252     double u, v;
253     register int i, j;
254 schorsch 2.11 register RREAL *dp;
255 greg 2.2 double d00, d01, d10, d11;
256     /* compute coordinates */
257     u = argument(1); v = argument(2);
258     if (datarec.flags & HASBORDER) {
259 greg 2.3 i = u *= datarec.m-1;
260     j = v *= datarec.n-1;
261 greg 2.2 } else {
262 greg 2.3 i = u = u*datarec.m - .5;
263     j = v = v*datarec.n - .5;
264 greg 2.2 }
265     if (i < 0) i = 0;
266     else if (i > datarec.m-2) i = datarec.m-2;
267     if (j < 0) j = 0;
268     else if (j > datarec.n-2) j = datarec.n-2;
269     /* compute value */
270     if (datarec.flags & TRIPLETS) {
271 greg 2.3 dp = datarec.data + 3*(j*datarec.m + i);
272     if (nam == ZNAME)
273     dp += 2;
274     else if (nam == YNAME)
275 greg 2.2 dp++;
276     d00 = dp[0]; d01 = dp[3];
277 greg 2.3 dp += 3*datarec.m;
278 greg 2.2 d10 = dp[0]; d11 = dp[3];
279     } else {
280 greg 2.3 dp = datarec.data + j*datarec.m + i;
281 greg 2.2 d00 = dp[0]; d01 = dp[1];
282 greg 2.3 dp += datarec.m;
283 greg 2.2 d10 = dp[0]; d11 = dp[1];
284     }
285     /* bilinear interpolation */
286     return((j+1-v)*((i+1-u)*d00+(u-i)*d01)+(v-j)*((i+1-u)*d10+(u-i)*d11));
287 greg 1.1 }
288    
289    
290 schorsch 2.13 void
291     putobjrow( /* output vertex row to .OBJ */
292     register POINT *rp,
293     int n
294     )
295 greg 2.7 {
296     static int nverts = 0;
297    
298     for ( ; n-- >= 0; rp++) {
299     if (!rp->valid)
300     continue;
301     fputs("v ", stdout);
302 greg 2.9 pvect(rp->p);
303     if (smooth && !ZEROVECT(rp->n))
304 greg 2.7 printf("\tvn %.9g %.9g %.9g\n",
305     rp->n[0], rp->n[1], rp->n[2]);
306     printf("\tvt %.9g %.9g\n", rp->uv[0], rp->uv[1]);
307     rp->valid = ++nverts;
308     }
309     }
310    
311    
312 schorsch 2.13 void
313     putsquare( /* put out a square */
314     POINT *p0,
315     POINT *p1,
316     POINT *p2,
317     POINT *p3
318     )
319 greg 1.3 {
320     static int nout = 0;
321     FVECT norm[4];
322     int axis;
323     FVECT v1, v2, vc1, vc2;
324     int ok1, ok2;
325     /* compute exact normals */
326 greg 2.7 ok1 = (p0->valid && p1->valid && p2->valid);
327 greg 2.6 if (ok1) {
328 greg 2.9 VSUB(v1, p1->p, p0->p);
329     VSUB(v2, p2->p, p0->p);
330 greg 2.6 fcross(vc1, v1, v2);
331     ok1 = (normalize(vc1) != 0.0);
332     }
333 greg 2.7 ok2 = (p1->valid && p2->valid && p3->valid);
334 greg 2.6 if (ok2) {
335 greg 2.9 VSUB(v1, p2->p, p3->p);
336     VSUB(v2, p1->p, p3->p);
337 greg 2.6 fcross(vc2, v1, v2);
338     ok2 = (normalize(vc2) != 0.0);
339     }
340 greg 1.3 if (!(ok1 | ok2))
341     return;
342 greg 2.7 if (objout) { /* output .OBJ faces */
343     int p0n=0, p1n=0, p2n=0, p3n=0;
344     if (smooth) {
345 greg 2.9 if (!ZEROVECT(p0->n))
346     p0n = p0->valid;
347     if (!ZEROVECT(p1->n))
348     p1n = p1->valid;
349     if (!ZEROVECT(p2->n))
350     p2n = p2->valid;
351     if (!ZEROVECT(p3->n))
352     p3n = p3->valid;
353 greg 2.7 }
354     if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
355     printf("f %d/%d/%d %d/%d/%d %d/%d/%d %d/%d/%d\n",
356 greg 2.9 p0->valid, p0->valid, p0n,
357     p1->valid, p1->valid, p1n,
358     p3->valid, p3->valid, p3n,
359     p2->valid, p2->valid, p2n);
360 greg 2.7 return;
361     }
362     if (ok1)
363     printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n",
364 greg 2.9 p0->valid, p0->valid, p0n,
365     p1->valid, p1->valid, p1n,
366     p2->valid, p2->valid, p2n);
367 greg 2.7 if (ok2)
368     printf("f %d/%d/%d %d/%d/%d %d/%d/%d\n",
369 greg 2.9 p2->valid, p2->valid, p2n,
370     p1->valid, p1->valid, p1n,
371     p3->valid, p3->valid, p3n);
372 greg 2.7 return;
373     }
374 greg 1.3 /* compute normal interpolation */
375     axis = norminterp(norm, p0, p1, p2, p3);
376    
377     /* put out quadrilateral? */
378     if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) {
379     printf("\n%s ", modname);
380     if (axis != -1) {
381     printf("texfunc %s\n", texname);
382     printf(tsargs);
383     printf("0\n13\t%d\n", axis);
384     pvect(norm[0]);
385     pvect(norm[1]);
386     pvect(norm[2]);
387     fvsum(v1, norm[3], vc1, -0.5);
388     fvsum(v1, v1, vc2, -0.5);
389     pvect(v1);
390     printf("\n%s ", texname);
391     }
392     printf("polygon %s.%d\n", surfname, ++nout);
393     printf("0\n0\n12\n");
394     pvect(p0->p);
395     pvect(p1->p);
396     pvect(p3->p);
397     pvect(p2->p);
398     return;
399     }
400     /* put out triangles? */
401     if (ok1) {
402     printf("\n%s ", modname);
403     if (axis != -1) {
404     printf("texfunc %s\n", texname);
405     printf(tsargs);
406     printf("0\n13\t%d\n", axis);
407     pvect(norm[0]);
408     pvect(norm[1]);
409     pvect(norm[2]);
410     fvsum(v1, norm[3], vc1, -1.0);
411     pvect(v1);
412     printf("\n%s ", texname);
413     }
414     printf("polygon %s.%d\n", surfname, ++nout);
415     printf("0\n0\n9\n");
416     pvect(p0->p);
417     pvect(p1->p);
418     pvect(p2->p);
419     }
420     if (ok2) {
421     printf("\n%s ", modname);
422     if (axis != -1) {
423     printf("texfunc %s\n", texname);
424     printf(tsargs);
425     printf("0\n13\t%d\n", axis);
426     pvect(norm[0]);
427     pvect(norm[1]);
428     pvect(norm[2]);
429     fvsum(v2, norm[3], vc2, -1.0);
430     pvect(v2);
431     printf("\n%s ", texname);
432     }
433     printf("polygon %s.%d\n", surfname, ++nout);
434     printf("0\n0\n9\n");
435     pvect(p2->p);
436     pvect(p1->p);
437     pvect(p3->p);
438     }
439     }
440    
441    
442 schorsch 2.13 void
443     comprow( /* compute row of values */
444     double s,
445     register POINT *row,
446     int siz
447     )
448 greg 1.1 {
449 greg 1.4 double st[2];
450 greg 1.8 int end;
451 greg 2.6 int checkvalid;
452 greg 1.4 register int i;
453 greg 1.8
454     if (smooth) {
455     i = -1; /* compute one past each end */
456     end = siz+1;
457     } else {
458     if (s < -FTINY || s > 1.0+FTINY)
459     return;
460     i = 0;
461     end = siz;
462     }
463 greg 1.1 st[0] = s;
464 greg 2.6 checkvalid = (fundefined(VNAME) == 2);
465 greg 1.8 while (i <= end) {
466 greg 1.4 st[1] = (double)i/siz;
467 greg 2.6 if (checkvalid && funvalue(VNAME, 2, st) <= 0.0) {
468     row[i].valid = 0;
469     row[i].p[0] = row[i].p[1] = row[i].p[2] = 0.0;
470 greg 2.7 row[i].uv[0] = row[i].uv[1] = 0.0;
471 greg 2.6 } else {
472     row[i].valid = 1;
473     row[i].p[0] = funvalue(XNAME, 2, st);
474     row[i].p[1] = funvalue(YNAME, 2, st);
475     row[i].p[2] = funvalue(ZNAME, 2, st);
476 greg 2.7 row[i].uv[0] = st[0];
477     row[i].uv[1] = st[1];
478 greg 2.6 }
479 greg 1.8 i++;
480 greg 1.1 }
481 greg 1.3 }
482    
483    
484 schorsch 2.13 void
485     compnorms( /* compute row of averaged normals */
486     register POINT *r0,
487     register POINT *r1,
488     register POINT *r2,
489     int siz
490     )
491 greg 1.3 {
492 greg 1.11 FVECT v1, v2;
493 greg 1.3
494     if (!smooth) /* not needed if no smoothing */
495     return;
496 greg 2.6 /* compute row 1 normals */
497 greg 1.4 while (siz-- >= 0) {
498 greg 2.6 if (!r1[0].valid)
499     continue;
500     if (!r0[0].valid) {
501     if (!r2[0].valid) {
502     r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
503     continue;
504     }
505     fvsum(v1, r2[0].p, r1[0].p, -1.0);
506     } else if (!r2[0].valid)
507     fvsum(v1, r1[0].p, r0[0].p, -1.0);
508     else
509     fvsum(v1, r2[0].p, r0[0].p, -1.0);
510     if (!r1[-1].valid) {
511     if (!r1[1].valid) {
512     r1[0].n[0] = r1[0].n[1] = r1[0].n[2] = 0.0;
513     continue;
514     }
515     fvsum(v2, r1[1].p, r1[0].p, -1.0);
516     } else if (!r1[1].valid)
517     fvsum(v2, r1[0].p, r1[-1].p, -1.0);
518     else
519     fvsum(v2, r1[1].p, r1[-1].p, -1.0);
520 greg 1.3 fcross(r1[0].n, v1, v2);
521     normalize(r1[0].n);
522     r0++; r1++; r2++;
523     }
524     }
525    
526    
527     int
528 schorsch 2.13 norminterp( /* compute normal interpolation */
529     register FVECT resmat[4],
530     POINT *p0,
531     POINT *p1,
532     POINT *p2,
533     POINT *p3
534     )
535 greg 1.3 {
536     #define u ((ax+1)%3)
537     #define v ((ax+2)%3)
538    
539     register int ax;
540 greg 1.12 MAT4 eqnmat;
541 greg 1.3 FVECT v1;
542     register int i, j;
543    
544     if (!smooth) /* no interpolation if no smoothing */
545     return(-1);
546     /* find dominant axis */
547     VCOPY(v1, p0->n);
548     fvsum(v1, v1, p1->n, 1.0);
549     fvsum(v1, v1, p2->n, 1.0);
550     fvsum(v1, v1, p3->n, 1.0);
551 greg 1.4 ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1;
552     ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2;
553 greg 1.3 /* assign equation matrix */
554     eqnmat[0][0] = p0->p[u]*p0->p[v];
555     eqnmat[0][1] = p0->p[u];
556     eqnmat[0][2] = p0->p[v];
557     eqnmat[0][3] = 1.0;
558     eqnmat[1][0] = p1->p[u]*p1->p[v];
559     eqnmat[1][1] = p1->p[u];
560     eqnmat[1][2] = p1->p[v];
561     eqnmat[1][3] = 1.0;
562     eqnmat[2][0] = p2->p[u]*p2->p[v];
563     eqnmat[2][1] = p2->p[u];
564     eqnmat[2][2] = p2->p[v];
565     eqnmat[2][3] = 1.0;
566     eqnmat[3][0] = p3->p[u]*p3->p[v];
567     eqnmat[3][1] = p3->p[u];
568     eqnmat[3][2] = p3->p[v];
569     eqnmat[3][3] = 1.0;
570     /* invert matrix (solve system) */
571 greg 2.5 if (!invmat4(eqnmat, eqnmat))
572 greg 1.3 return(-1); /* no solution */
573     /* compute result matrix */
574     for (j = 0; j < 4; j++)
575     for (i = 0; i < 3; i++)
576 greg 1.4 resmat[j][i] = eqnmat[j][0]*p0->n[i] +
577     eqnmat[j][1]*p1->n[i] +
578     eqnmat[j][2]*p2->n[i] +
579     eqnmat[j][3]*p3->n[i];
580 greg 1.3 return(ax);
581    
582     #undef u
583     #undef v
584 greg 1.1 }
585    
586    
587 greg 2.6 void
588 greg 1.1 eputs(msg)
589     char *msg;
590     {
591     fputs(msg, stderr);
592     }
593    
594    
595 greg 2.6 void
596 greg 1.1 wputs(msg)
597     char *msg;
598     {
599     eputs(msg);
600     }
601    
602    
603 greg 2.6 void
604 greg 1.1 quit(code)
605 greg 2.4 int code;
606 greg 1.1 {
607     exit(code);
608     }
609    
610    
611 schorsch 2.13 void
612     printhead( /* print command header */
613     register int ac,
614     register char **av
615     )
616 greg 1.1 {
617     putchar('#');
618     while (ac--) {
619     putchar(' ');
620     fputs(*av++, stdout);
621     }
622     putchar('\n');
623     }
624    
625    
626     double
627 greg 2.12 l_hermite(char *nm)
628 greg 1.1 {
629     double t;
630    
631     t = argument(5);
632     return( argument(1)*((2.0*t-3.0)*t*t+1.0) +
633     argument(2)*(-2.0*t+3.0)*t*t +
634     argument(3)*((t-2.0)*t+1.0)*t +
635     argument(4)*(t-1.0)*t*t );
636 greg 1.6 }
637    
638    
639     double
640 greg 2.12 l_bezier(char *nm)
641 greg 1.6 {
642     double t;
643    
644     t = argument(5);
645     return( argument(1) * (1.+t*(-3.+t*(3.-t))) +
646     argument(2) * 3.*t*(1.+t*(-2.+t)) +
647     argument(3) * 3.*t*t*(1.-t) +
648     argument(4) * t*t*t );
649 greg 1.7 }
650    
651    
652     double
653 greg 2.12 l_bspline(char *nm)
654 greg 1.7 {
655     double t;
656    
657     t = argument(5);
658     return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) +
659     argument(2) * (2./3.+t*t*(-1.+1./2.*t)) +
660     argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) +
661     argument(4) * (1./6.*t*t*t) );
662 greg 1.1 }