16 |
|
* 4/3/87 |
17 |
|
*/ |
18 |
|
|
19 |
< |
#include <stdio.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 |
|
|
27 |
< |
#define FTINY 1e-7 |
27 |
> |
#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
28 |
|
|
29 |
– |
#define vertex(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
30 |
– |
|
29 |
|
char vformat[] = "%15.9g %15.9g %15.9g\n"; |
30 |
+ |
char tsargs[] = "4 surf_dx surf_dy surf_dz surf.cal\n"; |
31 |
+ |
char texname[] = "Phong"; |
32 |
|
|
33 |
< |
double funvalue(), dist2(), fdot(), l_hermite(), argument(); |
33 |
> |
int smooth = 0; /* apply smoothing? */ |
34 |
|
|
35 |
+ |
char *modname, *surfname; |
36 |
|
|
37 |
+ |
double funvalue(), l_hermite(), l_bezier(), argument(); |
38 |
+ |
|
39 |
+ |
typedef struct { |
40 |
+ |
FVECT p; /* vertex position */ |
41 |
+ |
FVECT n; /* average normal */ |
42 |
+ |
} POINT; |
43 |
+ |
|
44 |
+ |
|
45 |
|
main(argc, argv) |
46 |
|
int argc; |
47 |
|
char *argv[]; |
48 |
|
{ |
49 |
< |
static double *xyz[4]; |
41 |
< |
double *row0, *row1, *dp; |
42 |
< |
double v1[3], v2[3], vc1[3], vc2[3]; |
43 |
< |
double a1, a2; |
49 |
> |
POINT *row0, *row1, *row2, *rp; |
50 |
|
int i, j, m, n; |
51 |
|
char stmp[256]; |
46 |
– |
double d; |
47 |
– |
register int k; |
52 |
|
|
53 |
|
varset("PI", PI); |
54 |
|
funset("hermite", 5, l_hermite); |
55 |
+ |
funset("bezier", 5, l_bezier); |
56 |
|
|
57 |
|
if (argc < 8) |
58 |
|
goto userror; |
62 |
|
scompile(NULL, argv[++i]); |
63 |
|
else if (!strcmp(argv[i], "-f")) |
64 |
|
fcompile(argv[++i]); |
65 |
+ |
else if (!strcmp(argv[i], "-s")) |
66 |
+ |
smooth++; |
67 |
|
else |
68 |
|
goto userror; |
69 |
|
|
70 |
+ |
modname = argv[1]; |
71 |
+ |
surfname = argv[2]; |
72 |
|
sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
73 |
|
scompile(NULL, stmp); |
74 |
|
sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
80 |
|
if (m <= 0 || n <= 0) |
81 |
|
goto userror; |
82 |
|
|
83 |
< |
row0 = (double *)malloc((n+1)*3*sizeof(double)); |
84 |
< |
row1 = (double *)malloc((n+1)*3*sizeof(double)); |
85 |
< |
if (row0 == NULL || row1 == NULL) { |
83 |
> |
row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
84 |
> |
row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
85 |
> |
row2 = (POINT *)malloc((n+3)*sizeof(POINT)); |
86 |
> |
if (row0 == NULL || row1 == NULL || row2 == NULL) { |
87 |
|
fprintf(stderr, "%s: out of memory\n", argv[0]); |
88 |
|
quit(1); |
89 |
|
} |
90 |
< |
|
90 |
> |
row0++; row1++; row2++; |
91 |
> |
/* print header */ |
92 |
|
printhead(argc, argv); |
93 |
< |
|
94 |
< |
comprow(0.0, row1, n); /* compute zeroeth row */ |
95 |
< |
|
93 |
> |
/* initialize */ |
94 |
> |
comprow(-1.0/m, row0, n); |
95 |
> |
comprow(0.0, row1, n); |
96 |
> |
comprow(1.0/m, row2, n); |
97 |
> |
compnorms(row0, row1, row2, n); |
98 |
> |
/* for each row */ |
99 |
|
for (i = 0; i < m; i++) { |
100 |
|
/* compute next row */ |
101 |
< |
dp = row0; |
101 |
> |
rp = row0; |
102 |
|
row0 = row1; |
103 |
< |
row1 = dp; |
104 |
< |
comprow((double)(i+1)/m, row1, n); |
103 |
> |
row1 = row2; |
104 |
> |
row2 = rp; |
105 |
> |
comprow((double)(i+2)/m, row2, n); |
106 |
> |
compnorms(row0, row1, row2, n); |
107 |
|
|
108 |
|
for (j = 0; j < n; j++) { |
109 |
< |
/* get vertices */ |
110 |
< |
xyz[0] = row0 + 3*j; |
111 |
< |
xyz[1] = row1 + 3*j; |
112 |
< |
xyz[2] = xyz[0] + 3; |
113 |
< |
xyz[3] = xyz[1] + 3; |
114 |
< |
/* rotate vertices */ |
115 |
< |
if (dist2(xyz[0],xyz[3]) < dist2(xyz[1],xyz[2])-FTINY) { |
100 |
< |
dp = xyz[0]; |
101 |
< |
xyz[0] = xyz[1]; |
102 |
< |
xyz[1] = xyz[3]; |
103 |
< |
xyz[3] = xyz[2]; |
104 |
< |
xyz[2] = dp; |
105 |
< |
} |
106 |
< |
/* get normals */ |
107 |
< |
for (k = 0; k < 3; k++) { |
108 |
< |
v1[k] = xyz[1][k] - xyz[0][k]; |
109 |
< |
v2[k] = xyz[2][k] - xyz[0][k]; |
110 |
< |
} |
111 |
< |
fcross(vc1, v1, v2); |
112 |
< |
a1 = fdot(vc1, vc1); |
113 |
< |
for (k = 0; k < 3; k++) { |
114 |
< |
v1[k] = xyz[2][k] - xyz[3][k]; |
115 |
< |
v2[k] = xyz[1][k] - xyz[3][k]; |
116 |
< |
} |
117 |
< |
fcross(vc2, v1, v2); |
118 |
< |
a2 = fdot(vc2, vc2); |
119 |
< |
/* check coplanar */ |
120 |
< |
if (a1 > FTINY*FTINY && a2 > FTINY*FTINY) { |
121 |
< |
d = fdot(vc1, vc2); |
122 |
< |
if (d*d/a1/a2 >= 1.0-FTINY*FTINY) { |
123 |
< |
if (d > 0.0) { /* coplanar */ |
124 |
< |
printf( |
125 |
< |
"\n%s polygon %s.%d.%d\n", |
126 |
< |
argv[1], argv[2], i+1, j+1); |
127 |
< |
printf("0\n0\n12\n"); |
128 |
< |
vertex(xyz[0]); |
129 |
< |
vertex(xyz[1]); |
130 |
< |
vertex(xyz[3]); |
131 |
< |
vertex(xyz[2]); |
132 |
< |
} /* else overlapped */ |
133 |
< |
continue; |
134 |
< |
} /* else bent */ |
135 |
< |
} |
136 |
< |
/* check triangles */ |
137 |
< |
if (a1 > FTINY*FTINY) { |
138 |
< |
printf("\n%s polygon %s.%da%d\n", |
139 |
< |
argv[1], argv[2], i+1, j+1); |
140 |
< |
printf("0\n0\n9\n"); |
141 |
< |
vertex(xyz[0]); |
142 |
< |
vertex(xyz[1]); |
143 |
< |
vertex(xyz[2]); |
144 |
< |
} |
145 |
< |
if (a2 > FTINY*FTINY) { |
146 |
< |
printf("\n%s polygon %s.%db%d\n", |
147 |
< |
argv[1], argv[2], i+1, j+1); |
148 |
< |
printf("0\n0\n9\n"); |
149 |
< |
vertex(xyz[2]); |
150 |
< |
vertex(xyz[1]); |
151 |
< |
vertex(xyz[3]); |
152 |
< |
} |
109 |
> |
/* put polygons */ |
110 |
> |
if ((i+j) & 1) |
111 |
> |
putsquare(&row0[j], &row1[j], |
112 |
> |
&row0[j+1], &row1[j+1]); |
113 |
> |
else |
114 |
> |
putsquare(&row1[j], &row1[j+1], |
115 |
> |
&row0[j], &row0[j+1]); |
116 |
|
} |
117 |
|
} |
118 |
|
|
120 |
|
|
121 |
|
userror: |
122 |
|
fprintf(stderr, "Usage: %s material name ", argv[0]); |
123 |
< |
fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-e expr] [-f file]\n"); |
123 |
> |
fprintf(stderr, "x(s,t) y(s,t) z(s,t) m n [-s][-e expr][-f file]\n"); |
124 |
|
quit(1); |
125 |
|
} |
126 |
|
|
127 |
|
|
128 |
+ |
putsquare(p0, p1, p2, p3) /* put out a square */ |
129 |
+ |
POINT *p0, *p1, *p2, *p3; |
130 |
+ |
{ |
131 |
+ |
static int nout = 0; |
132 |
+ |
FVECT norm[4]; |
133 |
+ |
int axis; |
134 |
+ |
FVECT v1, v2, vc1, vc2; |
135 |
+ |
int ok1, ok2; |
136 |
+ |
/* compute exact normals */ |
137 |
+ |
fvsum(v1, p1->p, p0->p, -1.0); |
138 |
+ |
fvsum(v2, p2->p, p0->p, -1.0); |
139 |
+ |
fcross(vc1, v1, v2); |
140 |
+ |
ok1 = normalize(vc1) != 0.0; |
141 |
+ |
fvsum(v1, p2->p, p3->p, -1.0); |
142 |
+ |
fvsum(v2, p1->p, p3->p, -1.0); |
143 |
+ |
fcross(vc2, v1, v2); |
144 |
+ |
ok2 = normalize(vc2) != 0.0; |
145 |
+ |
if (!(ok1 | ok2)) |
146 |
+ |
return; |
147 |
+ |
/* compute normal interpolation */ |
148 |
+ |
axis = norminterp(norm, p0, p1, p2, p3); |
149 |
+ |
|
150 |
+ |
/* put out quadrilateral? */ |
151 |
+ |
if (ok1 & ok2 && fdot(vc1,vc2) >= 1.0-FTINY*FTINY) { |
152 |
+ |
printf("\n%s ", modname); |
153 |
+ |
if (axis != -1) { |
154 |
+ |
printf("texfunc %s\n", texname); |
155 |
+ |
printf(tsargs); |
156 |
+ |
printf("0\n13\t%d\n", axis); |
157 |
+ |
pvect(norm[0]); |
158 |
+ |
pvect(norm[1]); |
159 |
+ |
pvect(norm[2]); |
160 |
+ |
fvsum(v1, norm[3], vc1, -0.5); |
161 |
+ |
fvsum(v1, v1, vc2, -0.5); |
162 |
+ |
pvect(v1); |
163 |
+ |
printf("\n%s ", texname); |
164 |
+ |
} |
165 |
+ |
printf("polygon %s.%d\n", surfname, ++nout); |
166 |
+ |
printf("0\n0\n12\n"); |
167 |
+ |
pvect(p0->p); |
168 |
+ |
pvect(p1->p); |
169 |
+ |
pvect(p3->p); |
170 |
+ |
pvect(p2->p); |
171 |
+ |
return; |
172 |
+ |
} |
173 |
+ |
/* put out triangles? */ |
174 |
+ |
if (ok1) { |
175 |
+ |
printf("\n%s ", modname); |
176 |
+ |
if (axis != -1) { |
177 |
+ |
printf("texfunc %s\n", texname); |
178 |
+ |
printf(tsargs); |
179 |
+ |
printf("0\n13\t%d\n", axis); |
180 |
+ |
pvect(norm[0]); |
181 |
+ |
pvect(norm[1]); |
182 |
+ |
pvect(norm[2]); |
183 |
+ |
fvsum(v1, norm[3], vc1, -1.0); |
184 |
+ |
pvect(v1); |
185 |
+ |
printf("\n%s ", texname); |
186 |
+ |
} |
187 |
+ |
printf("polygon %s.%d\n", surfname, ++nout); |
188 |
+ |
printf("0\n0\n9\n"); |
189 |
+ |
pvect(p0->p); |
190 |
+ |
pvect(p1->p); |
191 |
+ |
pvect(p2->p); |
192 |
+ |
} |
193 |
+ |
if (ok2) { |
194 |
+ |
printf("\n%s ", modname); |
195 |
+ |
if (axis != -1) { |
196 |
+ |
printf("texfunc %s\n", texname); |
197 |
+ |
printf(tsargs); |
198 |
+ |
printf("0\n13\t%d\n", axis); |
199 |
+ |
pvect(norm[0]); |
200 |
+ |
pvect(norm[1]); |
201 |
+ |
pvect(norm[2]); |
202 |
+ |
fvsum(v2, norm[3], vc2, -1.0); |
203 |
+ |
pvect(v2); |
204 |
+ |
printf("\n%s ", texname); |
205 |
+ |
} |
206 |
+ |
printf("polygon %s.%d\n", surfname, ++nout); |
207 |
+ |
printf("0\n0\n9\n"); |
208 |
+ |
pvect(p2->p); |
209 |
+ |
pvect(p1->p); |
210 |
+ |
pvect(p3->p); |
211 |
+ |
} |
212 |
+ |
} |
213 |
+ |
|
214 |
+ |
|
215 |
|
comprow(s, row, siz) /* compute row of values */ |
216 |
|
double s; |
217 |
< |
register double *row; |
217 |
> |
register POINT *row; |
218 |
|
int siz; |
219 |
|
{ |
220 |
< |
double st[2], step; |
221 |
< |
|
220 |
> |
double st[2]; |
221 |
> |
register int i; |
222 |
> |
/* compute one past each end */ |
223 |
|
st[0] = s; |
224 |
< |
st[1] = 0.0; |
225 |
< |
step = 1.0 / siz; |
224 |
> |
for (i = -1; i <= siz+1; i++) { |
225 |
> |
st[1] = (double)i/siz; |
226 |
> |
row[i].p[0] = funvalue(XNAME, 2, st); |
227 |
> |
row[i].p[1] = funvalue(YNAME, 2, st); |
228 |
> |
row[i].p[2] = funvalue(ZNAME, 2, st); |
229 |
> |
} |
230 |
> |
} |
231 |
> |
|
232 |
> |
|
233 |
> |
compnorms(r0, r1, r2, siz) /* compute row of averaged normals */ |
234 |
> |
register POINT *r0, *r1, *r2; |
235 |
> |
int siz; |
236 |
> |
{ |
237 |
> |
FVECT v1, v2, vc; |
238 |
> |
register int i; |
239 |
> |
|
240 |
> |
if (!smooth) /* not needed if no smoothing */ |
241 |
> |
return; |
242 |
> |
/* compute middle points */ |
243 |
|
while (siz-- >= 0) { |
244 |
< |
*row++ = funvalue(XNAME, 2, st); |
245 |
< |
*row++ = funvalue(YNAME, 2, st); |
246 |
< |
*row++ = funvalue(ZNAME, 2, st); |
247 |
< |
st[1] += step; |
244 |
> |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
245 |
> |
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
246 |
> |
fcross(r1[0].n, v1, v2); |
247 |
> |
fvsum(v1, r0[0].p, r1[0].p, -1.0); |
248 |
> |
fcross(vc, v2, v1); |
249 |
> |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
250 |
> |
fvsum(v2, r1[-1].p, r1[0].p, -1.0); |
251 |
> |
fcross(vc, v1, v2); |
252 |
> |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
253 |
> |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
254 |
> |
fcross(vc, v2, v1); |
255 |
> |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
256 |
> |
normalize(r1[0].n); |
257 |
> |
r0++; r1++; r2++; |
258 |
|
} |
259 |
|
} |
260 |
|
|
261 |
|
|
262 |
+ |
int |
263 |
+ |
norminterp(resmat, p0, p1, p2, p3) /* compute normal interpolation */ |
264 |
+ |
register FVECT resmat[4]; |
265 |
+ |
POINT *p0, *p1, *p2, *p3; |
266 |
+ |
{ |
267 |
+ |
#define u ((ax+1)%3) |
268 |
+ |
#define v ((ax+2)%3) |
269 |
+ |
|
270 |
+ |
register int ax; |
271 |
+ |
double eqnmat[4][4]; |
272 |
+ |
FVECT v1; |
273 |
+ |
register int i, j; |
274 |
+ |
|
275 |
+ |
if (!smooth) /* no interpolation if no smoothing */ |
276 |
+ |
return(-1); |
277 |
+ |
/* find dominant axis */ |
278 |
+ |
VCOPY(v1, p0->n); |
279 |
+ |
fvsum(v1, v1, p1->n, 1.0); |
280 |
+ |
fvsum(v1, v1, p2->n, 1.0); |
281 |
+ |
fvsum(v1, v1, p3->n, 1.0); |
282 |
+ |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
283 |
+ |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
284 |
+ |
/* assign equation matrix */ |
285 |
+ |
eqnmat[0][0] = p0->p[u]*p0->p[v]; |
286 |
+ |
eqnmat[0][1] = p0->p[u]; |
287 |
+ |
eqnmat[0][2] = p0->p[v]; |
288 |
+ |
eqnmat[0][3] = 1.0; |
289 |
+ |
eqnmat[1][0] = p1->p[u]*p1->p[v]; |
290 |
+ |
eqnmat[1][1] = p1->p[u]; |
291 |
+ |
eqnmat[1][2] = p1->p[v]; |
292 |
+ |
eqnmat[1][3] = 1.0; |
293 |
+ |
eqnmat[2][0] = p2->p[u]*p2->p[v]; |
294 |
+ |
eqnmat[2][1] = p2->p[u]; |
295 |
+ |
eqnmat[2][2] = p2->p[v]; |
296 |
+ |
eqnmat[2][3] = 1.0; |
297 |
+ |
eqnmat[3][0] = p3->p[u]*p3->p[v]; |
298 |
+ |
eqnmat[3][1] = p3->p[u]; |
299 |
+ |
eqnmat[3][2] = p3->p[v]; |
300 |
+ |
eqnmat[3][3] = 1.0; |
301 |
+ |
/* invert matrix (solve system) */ |
302 |
+ |
if (!invmat(eqnmat, eqnmat)) |
303 |
+ |
return(-1); /* no solution */ |
304 |
+ |
/* compute result matrix */ |
305 |
+ |
for (j = 0; j < 4; j++) |
306 |
+ |
for (i = 0; i < 3; i++) |
307 |
+ |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
308 |
+ |
eqnmat[j][1]*p1->n[i] + |
309 |
+ |
eqnmat[j][2]*p2->n[i] + |
310 |
+ |
eqnmat[j][3]*p3->n[i]; |
311 |
+ |
return(ax); |
312 |
+ |
|
313 |
+ |
#undef u |
314 |
+ |
#undef v |
315 |
+ |
} |
316 |
+ |
|
317 |
+ |
|
318 |
+ |
/* |
319 |
+ |
* invmat - computes the inverse of mat into inverse. Returns 1 |
320 |
+ |
* if there exists an inverse, 0 otherwise. It uses Gaussian Elimination |
321 |
+ |
* method. |
322 |
+ |
*/ |
323 |
+ |
|
324 |
+ |
invmat(inverse,mat) |
325 |
+ |
double mat[4][4],inverse[4][4]; |
326 |
+ |
{ |
327 |
+ |
#define SWAP(a,b,t) (t=a,a=b,b=t) |
328 |
+ |
|
329 |
+ |
double m4tmp[4][4]; |
330 |
+ |
register int i,j,k; |
331 |
+ |
register double temp; |
332 |
+ |
|
333 |
+ |
bcopy((char *)mat, (char *)m4tmp, sizeof(m4tmp)); |
334 |
+ |
/* set inverse to identity */ |
335 |
+ |
for (i = 0; i < 4; i++) |
336 |
+ |
for (j = 0; j < 4; j++) |
337 |
+ |
inverse[i][j] = i==j ? 1.0 : 0.0; |
338 |
+ |
|
339 |
+ |
for(i = 0; i < 4; i++) { |
340 |
+ |
/* Look for raw with largest pivot and swap raws */ |
341 |
+ |
temp = FTINY; j = -1; |
342 |
+ |
for(k = i; k < 4; k++) |
343 |
+ |
if(ABS(m4tmp[k][i]) > temp) { |
344 |
+ |
temp = ABS(m4tmp[k][i]); |
345 |
+ |
j = k; |
346 |
+ |
} |
347 |
+ |
if(j == -1) /* No replacing raw -> no inverse */ |
348 |
+ |
return(0); |
349 |
+ |
if (j != i) |
350 |
+ |
for(k = 0; k < 4; k++) { |
351 |
+ |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
352 |
+ |
SWAP(inverse[i][k],inverse[j][k],temp); |
353 |
+ |
} |
354 |
+ |
|
355 |
+ |
temp = m4tmp[i][i]; |
356 |
+ |
for(k = 0; k < 4; k++) { |
357 |
+ |
m4tmp[i][k] /= temp; |
358 |
+ |
inverse[i][k] /= temp; |
359 |
+ |
} |
360 |
+ |
for(j = 0; j < 4; j++) { |
361 |
+ |
if(j != i) { |
362 |
+ |
temp = m4tmp[j][i]; |
363 |
+ |
for(k = 0; k < 4; k++) { |
364 |
+ |
m4tmp[j][k] -= m4tmp[i][k]*temp; |
365 |
+ |
inverse[j][k] -= inverse[i][k]*temp; |
366 |
+ |
} |
367 |
+ |
} |
368 |
+ |
} |
369 |
+ |
} |
370 |
+ |
return(1); |
371 |
+ |
|
372 |
+ |
#undef SWAP |
373 |
+ |
} |
374 |
+ |
|
375 |
+ |
|
376 |
|
eputs(msg) |
377 |
|
char *msg; |
378 |
|
{ |
416 |
|
argument(2)*(-2.0*t+3.0)*t*t + |
417 |
|
argument(3)*((t-2.0)*t+1.0)*t + |
418 |
|
argument(4)*(t-1.0)*t*t ); |
419 |
+ |
} |
420 |
+ |
|
421 |
+ |
|
422 |
+ |
double |
423 |
+ |
l_bezier() |
424 |
+ |
{ |
425 |
+ |
double t; |
426 |
+ |
|
427 |
+ |
t = argument(5); |
428 |
+ |
return( argument(1) * (1.+t*(-3.+t*(3.-t))) + |
429 |
+ |
argument(2) * 3.*t*(1.+t*(-2.+t)) + |
430 |
+ |
argument(3) * 3.*t*t*(1.-t) + |
431 |
+ |
argument(4) * t*t*t ); |
432 |
|
} |