27 |
|
|
28 |
|
#define FTINY 1e-7 |
29 |
|
|
30 |
+ |
#define ABS(x) ((x)>=0 ? (x) : -(x)) |
31 |
+ |
|
32 |
|
#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
33 |
|
|
34 |
|
char vformat[] = "%15.9g %15.9g %15.9g\n"; |
39 |
|
|
40 |
|
char *modname, *surfname; |
41 |
|
|
42 |
< |
double funvalue(), l_hermite(), argument(), fabs(); |
42 |
> |
double funvalue(), l_hermite(), argument(); |
43 |
|
|
44 |
|
typedef struct { |
45 |
|
FVECT p; /* vertex position */ |
84 |
|
if (m <= 0 || n <= 0) |
85 |
|
goto userror; |
86 |
|
|
87 |
< |
row0 = (POINT *)malloc((n+1)*sizeof(POINT)); |
88 |
< |
row1 = (POINT *)malloc((n+1)*sizeof(POINT)); |
89 |
< |
row2 = (POINT *)malloc((n+1)*sizeof(POINT)); |
87 |
> |
row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
88 |
> |
row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
89 |
> |
row2 = (POINT *)malloc((n+3)*sizeof(POINT)); |
90 |
|
if (row0 == NULL || row1 == NULL || row2 == NULL) { |
91 |
|
fprintf(stderr, "%s: out of memory\n", argv[0]); |
92 |
|
quit(1); |
93 |
|
} |
94 |
+ |
row0++; row1++; row2++; |
95 |
|
/* print header */ |
96 |
|
printhead(argc, argv); |
97 |
< |
/* compute first two rows */ |
97 |
> |
/* initialize */ |
98 |
> |
comprow(-1.0/m, row0, n); |
99 |
|
comprow(0.0, row1, n); |
100 |
|
comprow(1.0/m, row2, n); |
101 |
< |
compnorms(row1, row1, row2, n); |
101 |
> |
compnorms(row0, row1, row2, n); |
102 |
|
/* for each row */ |
103 |
|
for (i = 0; i < m; i++) { |
104 |
|
/* compute next row */ |
106 |
|
row0 = row1; |
107 |
|
row1 = row2; |
108 |
|
row2 = rp; |
109 |
< |
if (i+2 <= m) { |
110 |
< |
comprow((double)(i+2)/m, row2, n); |
107 |
< |
compnorms(row0, row1, row2, n); |
108 |
< |
} else |
109 |
< |
compnorms(row0, row1, row1, n); |
109 |
> |
comprow((double)(i+2)/m, row2, n); |
110 |
> |
compnorms(row0, row1, row2, n); |
111 |
|
|
112 |
|
for (j = 0; j < n; j++) { |
113 |
|
/* put polygons */ |
221 |
|
register POINT *row; |
222 |
|
int siz; |
223 |
|
{ |
224 |
< |
double st[2], step; |
225 |
< |
|
224 |
> |
double st[2]; |
225 |
> |
register int i; |
226 |
> |
/* compute one past each end */ |
227 |
|
st[0] = s; |
228 |
< |
st[1] = 0.0; |
229 |
< |
step = 1.0 / siz; |
230 |
< |
while (siz-- >= 0) { |
231 |
< |
row->p[0] = funvalue(XNAME, 2, st); |
232 |
< |
row->p[1] = funvalue(YNAME, 2, st); |
231 |
< |
row->p[2] = funvalue(ZNAME, 2, st); |
232 |
< |
row++; |
233 |
< |
st[1] += step; |
228 |
> |
for (i = -1; i <= siz+1; i++) { |
229 |
> |
st[1] = (double)i/siz; |
230 |
> |
row[i].p[0] = funvalue(XNAME, 2, st); |
231 |
> |
row[i].p[1] = funvalue(YNAME, 2, st); |
232 |
> |
row[i].p[2] = funvalue(ZNAME, 2, st); |
233 |
|
} |
234 |
|
} |
235 |
|
|
239 |
|
int siz; |
240 |
|
{ |
241 |
|
FVECT v1, v2, vc; |
242 |
+ |
register int i; |
243 |
|
|
244 |
|
if (!smooth) /* not needed if no smoothing */ |
245 |
|
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++; |
246 |
|
/* compute middle points */ |
247 |
< |
while (--siz > 0) { |
247 |
> |
while (siz-- >= 0) { |
248 |
|
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
249 |
|
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
250 |
|
fcross(r1[0].n, v1, v2); |
260 |
|
normalize(r1[0].n); |
261 |
|
r0++; r1++; r2++; |
262 |
|
} |
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); |
263 |
|
} |
264 |
|
|
265 |
|
|
272 |
|
#define v ((ax+2)%3) |
273 |
|
|
274 |
|
register int ax; |
275 |
< |
double eqnmat[4][4], solmat[4][4]; |
275 |
> |
double eqnmat[4][4]; |
276 |
|
FVECT v1; |
277 |
|
register int i, j; |
278 |
|
|
283 |
|
fvsum(v1, v1, p1->n, 1.0); |
284 |
|
fvsum(v1, v1, p2->n, 1.0); |
285 |
|
fvsum(v1, v1, p3->n, 1.0); |
286 |
< |
ax = fabs(v1[0]) > fabs(v1[1]) ? 0 : 1; |
287 |
< |
ax = fabs(v1[ax]) > fabs(v1[2]) ? ax : 2; |
286 |
> |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
287 |
> |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
288 |
|
/* assign equation matrix */ |
289 |
|
eqnmat[0][0] = p0->p[u]*p0->p[v]; |
290 |
|
eqnmat[0][1] = p0->p[u]; |
303 |
|
eqnmat[3][2] = p3->p[v]; |
304 |
|
eqnmat[3][3] = 1.0; |
305 |
|
/* invert matrix (solve system) */ |
306 |
< |
if (!invmat(solmat, eqnmat)) |
306 |
> |
if (!invmat(eqnmat, eqnmat)) |
307 |
|
return(-1); /* no solution */ |
308 |
|
/* compute result matrix */ |
309 |
|
for (j = 0; j < 4; j++) |
310 |
|
for (i = 0; i < 3; i++) |
311 |
< |
resmat[j][i] = solmat[j][0]*p0->n[i] + |
312 |
< |
solmat[j][1]*p1->n[i] + |
313 |
< |
solmat[j][2]*p2->n[i] + |
314 |
< |
solmat[j][3]*p3->n[i]; |
311 |
> |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
312 |
> |
eqnmat[j][1]*p1->n[i] + |
313 |
> |
eqnmat[j][2]*p2->n[i] + |
314 |
> |
eqnmat[j][3]*p3->n[i]; |
315 |
|
return(ax); |
316 |
|
|
317 |
|
#undef u |
319 |
|
} |
320 |
|
|
321 |
|
|
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 |
– |
|
322 |
|
/* |
323 |
|
* invmat - computes the inverse of mat into inverse. Returns 1 |
324 |
|
* if there exists an inverse, 0 otherwise. It uses Gaussian Elimination |
330 |
|
{ |
331 |
|
#define SWAP(a,b,t) (t=a,a=b,b=t) |
332 |
|
|
333 |
+ |
double m4tmp[4][4]; |
334 |
|
register int i,j,k; |
335 |
|
register double temp; |
336 |
|
|
337 |
< |
setident4(inverse); |
338 |
< |
copymat4(m4tmp, mat); |
337 |
> |
bcopy(mat, m4tmp, sizeof(m4tmp)); |
338 |
> |
/* set inverse to identity */ |
339 |
> |
for (i = 0; i < 4; i++) |
340 |
> |
for (j = 0; j < 4; j++) |
341 |
> |
inverse[i][j] = i==j ? 1.0 : 0.0; |
342 |
|
|
343 |
|
for(i = 0; i < 4; i++) { |
344 |
< |
if(m4tmp[i][i] == 0) { /* Pivot is zero */ |
345 |
< |
/* Look for a raw with pivot != 0 and swap raws */ |
346 |
< |
for(j = i + 1; j < 4; j++) |
347 |
< |
if(m4tmp[j][i] != 0) { |
348 |
< |
for( k = 0; k < 4; k++) { |
349 |
< |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
350 |
< |
SWAP(inverse[i][k],inverse[j][k],temp); |
351 |
< |
} |
352 |
< |
break; |
353 |
< |
} |
354 |
< |
if(j == 4) /* No replacing raw -> no inverse */ |
355 |
< |
return(0); |
356 |
< |
} |
344 |
> |
/* Look for raw with largest pivot and swap raws */ |
345 |
> |
temp = FTINY; j = -1; |
346 |
> |
for(k = i; k < 4; k++) |
347 |
> |
if(ABS(m4tmp[k][i]) > temp) { |
348 |
> |
temp = ABS(m4tmp[k][i]); |
349 |
> |
j = k; |
350 |
> |
} |
351 |
> |
if(j == -1) /* No replacing raw -> no inverse */ |
352 |
> |
return(0); |
353 |
> |
if (j != i) |
354 |
> |
for(k = 0; k < 4; k++) { |
355 |
> |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
356 |
> |
SWAP(inverse[i][k],inverse[j][k],temp); |
357 |
> |
} |
358 |
|
|
359 |
|
temp = m4tmp[i][i]; |
360 |
|
for(k = 0; k < 4; k++) { |
372 |
|
} |
373 |
|
} |
374 |
|
return(1); |
375 |
+ |
|
376 |
|
#undef SWAP |
377 |
|
} |
378 |
|
|