1 |
– |
/* Copyright (c) 1989 Regents of the University of California */ |
2 |
– |
|
1 |
|
#ifndef lint |
2 |
|
static char SCCSid[] = "$SunId$ LBL"; |
3 |
|
#endif |
4 |
|
|
5 |
+ |
/* Copyright (c) 1989 Regents of the University of California */ |
6 |
+ |
|
7 |
|
/* |
8 |
|
* gensurf.c - program to generate functional surfaces |
9 |
|
* |
16 |
|
* 4/3/87 |
17 |
|
*/ |
18 |
|
|
19 |
< |
#include <stdio.h> |
20 |
< |
#include "fvect.h" |
19 |
> |
#include "standard.h" |
20 |
|
|
21 |
|
#define XNAME "X_" /* x function name */ |
22 |
|
#define YNAME "Y_" /* y function name */ |
23 |
|
#define ZNAME "Z_" /* z function name */ |
24 |
|
|
25 |
< |
#define PI 3.14159265358979323846 |
25 |
> |
#define ABS(x) ((x)>=0 ? (x) : -(x)) |
26 |
|
|
28 |
– |
#define FTINY 1e-7 |
29 |
– |
|
27 |
|
#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
28 |
|
|
29 |
|
char vformat[] = "%15.9g %15.9g %15.9g\n"; |
34 |
|
|
35 |
|
char *modname, *surfname; |
36 |
|
|
37 |
< |
double funvalue(), l_hermite(), argument(), fabs(); |
37 |
> |
double funvalue(), l_hermite(), l_bezier(), l_bspline(), argument(); |
38 |
|
|
39 |
|
typedef struct { |
40 |
|
FVECT p; /* vertex position */ |
52 |
|
|
53 |
|
varset("PI", PI); |
54 |
|
funset("hermite", 5, l_hermite); |
55 |
+ |
funset("bezier", 5, l_bezier); |
56 |
+ |
funset("bspline", 5, l_bspline); |
57 |
|
|
58 |
|
if (argc < 8) |
59 |
|
goto userror; |
81 |
|
if (m <= 0 || n <= 0) |
82 |
|
goto userror; |
83 |
|
|
84 |
< |
row0 = (POINT *)malloc((n+1)*sizeof(POINT)); |
85 |
< |
row1 = (POINT *)malloc((n+1)*sizeof(POINT)); |
86 |
< |
row2 = (POINT *)malloc((n+1)*sizeof(POINT)); |
84 |
> |
row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
85 |
> |
row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
86 |
> |
row2 = (POINT *)malloc((n+3)*sizeof(POINT)); |
87 |
|
if (row0 == NULL || row1 == NULL || row2 == NULL) { |
88 |
|
fprintf(stderr, "%s: out of memory\n", argv[0]); |
89 |
|
quit(1); |
90 |
|
} |
91 |
+ |
row0++; row1++; row2++; |
92 |
|
/* print header */ |
93 |
|
printhead(argc, argv); |
94 |
< |
/* compute first two rows */ |
94 |
> |
/* initialize */ |
95 |
> |
comprow(-1.0/m, row0, n); |
96 |
|
comprow(0.0, row1, n); |
97 |
|
comprow(1.0/m, row2, n); |
98 |
< |
compnorms(row1, row1, row2, n); |
98 |
> |
compnorms(row0, row1, row2, n); |
99 |
|
/* for each row */ |
100 |
|
for (i = 0; i < m; i++) { |
101 |
|
/* compute next row */ |
103 |
|
row0 = row1; |
104 |
|
row1 = row2; |
105 |
|
row2 = rp; |
106 |
< |
if (i+2 <= m) { |
107 |
< |
comprow((double)(i+2)/m, row2, n); |
107 |
< |
compnorms(row0, row1, row2, n); |
108 |
< |
} else |
109 |
< |
compnorms(row0, row1, row1, n); |
106 |
> |
comprow((double)(i+2)/m, row2, n); |
107 |
> |
compnorms(row0, row1, row2, n); |
108 |
|
|
109 |
|
for (j = 0; j < n; j++) { |
110 |
|
/* put polygons */ |
218 |
|
register POINT *row; |
219 |
|
int siz; |
220 |
|
{ |
221 |
< |
double st[2], step; |
222 |
< |
|
221 |
> |
double st[2]; |
222 |
> |
int end; |
223 |
> |
register int i; |
224 |
> |
|
225 |
> |
if (smooth) { |
226 |
> |
i = -1; /* compute one past each end */ |
227 |
> |
end = siz+1; |
228 |
> |
} else { |
229 |
> |
if (s < -FTINY || s > 1.0+FTINY) |
230 |
> |
return; |
231 |
> |
i = 0; |
232 |
> |
end = siz; |
233 |
> |
} |
234 |
|
st[0] = s; |
235 |
< |
st[1] = 0.0; |
236 |
< |
step = 1.0 / siz; |
237 |
< |
while (siz-- >= 0) { |
238 |
< |
row->p[0] = funvalue(XNAME, 2, st); |
239 |
< |
row->p[1] = funvalue(YNAME, 2, st); |
240 |
< |
row->p[2] = funvalue(ZNAME, 2, st); |
232 |
< |
row++; |
233 |
< |
st[1] += step; |
235 |
> |
while (i <= end) { |
236 |
> |
st[1] = (double)i/siz; |
237 |
> |
row[i].p[0] = funvalue(XNAME, 2, st); |
238 |
> |
row[i].p[1] = funvalue(YNAME, 2, st); |
239 |
> |
row[i].p[2] = funvalue(ZNAME, 2, st); |
240 |
> |
i++; |
241 |
|
} |
242 |
|
} |
243 |
|
|
247 |
|
int siz; |
248 |
|
{ |
249 |
|
FVECT v1, v2, vc; |
250 |
+ |
register int i; |
251 |
|
|
252 |
|
if (!smooth) /* not needed if no smoothing */ |
253 |
|
return; |
246 |
– |
/* compute first point */ |
247 |
– |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
248 |
– |
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
249 |
– |
fcross(r1[0].n, v1, v2); |
250 |
– |
fvsum(v1, r0[0].p, r1[0].p, -1.0); |
251 |
– |
fcross(vc, v2, v1); |
252 |
– |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
253 |
– |
normalize(r1[0].n); |
254 |
– |
r0++; r1++; r2++; |
254 |
|
/* compute middle points */ |
255 |
< |
while (--siz > 0) { |
255 |
> |
while (siz-- >= 0) { |
256 |
|
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
257 |
|
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
258 |
|
fcross(r1[0].n, v1, v2); |
268 |
|
normalize(r1[0].n); |
269 |
|
r0++; r1++; r2++; |
270 |
|
} |
272 |
– |
/* compute end point */ |
273 |
– |
fvsum(v1, r0[0].p, r1[0].p, -1.0); |
274 |
– |
fvsum(v2, r1[-1].p, r1[0].p, -1.0); |
275 |
– |
fcross(r1[0].n, v1, v2); |
276 |
– |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
277 |
– |
fcross(vc, v2, v1); |
278 |
– |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
279 |
– |
normalize(r1[0].n); |
271 |
|
} |
272 |
|
|
273 |
|
|
280 |
|
#define v ((ax+2)%3) |
281 |
|
|
282 |
|
register int ax; |
283 |
< |
double eqnmat[4][4], solmat[4][4]; |
283 |
> |
double eqnmat[4][4]; |
284 |
|
FVECT v1; |
285 |
|
register int i, j; |
286 |
|
|
291 |
|
fvsum(v1, v1, p1->n, 1.0); |
292 |
|
fvsum(v1, v1, p2->n, 1.0); |
293 |
|
fvsum(v1, v1, p3->n, 1.0); |
294 |
< |
ax = fabs(v1[0]) > fabs(v1[1]) ? 0 : 1; |
295 |
< |
ax = fabs(v1[ax]) > fabs(v1[2]) ? ax : 2; |
294 |
> |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
295 |
> |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
296 |
|
/* assign equation matrix */ |
297 |
|
eqnmat[0][0] = p0->p[u]*p0->p[v]; |
298 |
|
eqnmat[0][1] = p0->p[u]; |
311 |
|
eqnmat[3][2] = p3->p[v]; |
312 |
|
eqnmat[3][3] = 1.0; |
313 |
|
/* invert matrix (solve system) */ |
314 |
< |
if (!invmat(solmat, eqnmat)) |
314 |
> |
if (!invmat(eqnmat, eqnmat)) |
315 |
|
return(-1); /* no solution */ |
316 |
|
/* compute result matrix */ |
317 |
|
for (j = 0; j < 4; j++) |
318 |
|
for (i = 0; i < 3; i++) |
319 |
< |
resmat[j][i] = solmat[j][0]*p0->n[i] + |
320 |
< |
solmat[j][1]*p1->n[i] + |
321 |
< |
solmat[j][2]*p2->n[i] + |
322 |
< |
solmat[j][3]*p3->n[i]; |
319 |
> |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
320 |
> |
eqnmat[j][1]*p1->n[i] + |
321 |
> |
eqnmat[j][2]*p2->n[i] + |
322 |
> |
eqnmat[j][3]*p3->n[i]; |
323 |
|
return(ax); |
324 |
|
|
325 |
|
#undef u |
327 |
|
} |
328 |
|
|
329 |
|
|
339 |
– |
static double m4tmp[4][4]; /* for efficiency */ |
340 |
– |
|
341 |
– |
#define copymat4(m4a,m4b) bcopy((char *)m4b,(char *)m4a,sizeof(m4tmp)) |
342 |
– |
|
343 |
– |
|
344 |
– |
setident4(m4) |
345 |
– |
double m4[4][4]; |
346 |
– |
{ |
347 |
– |
static double ident[4][4] = { |
348 |
– |
1.,0.,0.,0., |
349 |
– |
0.,1.,0.,0., |
350 |
– |
0.,0.,1.,0., |
351 |
– |
0.,0.,0.,1., |
352 |
– |
}; |
353 |
– |
copymat4(m4, ident); |
354 |
– |
} |
355 |
– |
|
330 |
|
/* |
331 |
|
* invmat - computes the inverse of mat into inverse. Returns 1 |
332 |
|
* if there exists an inverse, 0 otherwise. It uses Gaussian Elimination |
338 |
|
{ |
339 |
|
#define SWAP(a,b,t) (t=a,a=b,b=t) |
340 |
|
|
341 |
+ |
double m4tmp[4][4]; |
342 |
|
register int i,j,k; |
343 |
|
register double temp; |
344 |
|
|
345 |
< |
setident4(inverse); |
346 |
< |
copymat4(m4tmp, mat); |
345 |
> |
bcopy((char *)mat, (char *)m4tmp, sizeof(m4tmp)); |
346 |
> |
/* set inverse to identity */ |
347 |
> |
for (i = 0; i < 4; i++) |
348 |
> |
for (j = 0; j < 4; j++) |
349 |
> |
inverse[i][j] = i==j ? 1.0 : 0.0; |
350 |
|
|
351 |
|
for(i = 0; i < 4; i++) { |
352 |
< |
if(m4tmp[i][i] == 0) { /* Pivot is zero */ |
353 |
< |
/* Look for a raw with pivot != 0 and swap raws */ |
354 |
< |
for(j = i + 1; j < 4; j++) |
355 |
< |
if(m4tmp[j][i] != 0) { |
356 |
< |
for( k = 0; k < 4; k++) { |
357 |
< |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
358 |
< |
SWAP(inverse[i][k],inverse[j][k],temp); |
359 |
< |
} |
360 |
< |
break; |
361 |
< |
} |
362 |
< |
if(j == 4) /* No replacing raw -> no inverse */ |
363 |
< |
return(0); |
364 |
< |
} |
352 |
> |
/* Look for raw with largest pivot and swap raws */ |
353 |
> |
temp = FTINY; j = -1; |
354 |
> |
for(k = i; k < 4; k++) |
355 |
> |
if(ABS(m4tmp[k][i]) > temp) { |
356 |
> |
temp = ABS(m4tmp[k][i]); |
357 |
> |
j = k; |
358 |
> |
} |
359 |
> |
if(j == -1) /* No replacing raw -> no inverse */ |
360 |
> |
return(0); |
361 |
> |
if (j != i) |
362 |
> |
for(k = 0; k < 4; k++) { |
363 |
> |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
364 |
> |
SWAP(inverse[i][k],inverse[j][k],temp); |
365 |
> |
} |
366 |
|
|
367 |
|
temp = m4tmp[i][i]; |
368 |
|
for(k = 0; k < 4; k++) { |
380 |
|
} |
381 |
|
} |
382 |
|
return(1); |
383 |
+ |
|
384 |
|
#undef SWAP |
385 |
|
} |
386 |
|
|
428 |
|
argument(2)*(-2.0*t+3.0)*t*t + |
429 |
|
argument(3)*((t-2.0)*t+1.0)*t + |
430 |
|
argument(4)*(t-1.0)*t*t ); |
431 |
+ |
} |
432 |
+ |
|
433 |
+ |
|
434 |
+ |
double |
435 |
+ |
l_bezier() |
436 |
+ |
{ |
437 |
+ |
double t; |
438 |
+ |
|
439 |
+ |
t = argument(5); |
440 |
+ |
return( argument(1) * (1.+t*(-3.+t*(3.-t))) + |
441 |
+ |
argument(2) * 3.*t*(1.+t*(-2.+t)) + |
442 |
+ |
argument(3) * 3.*t*t*(1.-t) + |
443 |
+ |
argument(4) * t*t*t ); |
444 |
+ |
} |
445 |
+ |
|
446 |
+ |
|
447 |
+ |
double |
448 |
+ |
l_bspline() |
449 |
+ |
{ |
450 |
+ |
double t; |
451 |
+ |
|
452 |
+ |
t = argument(5); |
453 |
+ |
return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) + |
454 |
+ |
argument(2) * (2./3.+t*t*(-1.+1./2.*t)) + |
455 |
+ |
argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) + |
456 |
+ |
argument(4) * (1./6.*t*t*t) ); |
457 |
|
} |