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/* Copyright (c) 1989 Regents of the University of California */ |
2 |
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|
1 |
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#ifndef lint |
2 |
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static char SCCSid[] = "$SunId$ LBL"; |
3 |
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#endif |
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|
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/* Copyright (c) 1989 Regents of the University of California */ |
6 |
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|
7 |
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/* |
8 |
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* gensurf.c - program to generate functional surfaces |
9 |
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* |
16 |
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* 4/3/87 |
17 |
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*/ |
18 |
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|
19 |
< |
#include <stdio.h> |
20 |
< |
#include "fvect.h" |
19 |
> |
#include "standard.h" |
20 |
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|
21 |
< |
#define XNAME "X_" /* x function name */ |
22 |
< |
#define YNAME "Y_" /* y function name */ |
23 |
< |
#define ZNAME "Z_" /* z function name */ |
21 |
> |
char XNAME[] = "X`SYS`"; /* x function name */ |
22 |
> |
char YNAME[] = "Y`SYS`"; /* y function name */ |
23 |
> |
char ZNAME[] = "Z`SYS`"; /* z function name */ |
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|
25 |
< |
#define PI 3.14159265358979323846 |
25 |
> |
#define ABS(x) ((x)>=0 ? (x) : -(x)) |
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|
28 |
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#define FTINY 1e-7 |
29 |
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|
27 |
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#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
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|
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char vformat[] = "%15.9g %15.9g %15.9g\n"; |
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|
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char *modname, *surfname; |
36 |
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|
37 |
< |
double funvalue(), l_hermite(), argument(), fabs(); |
37 |
> |
/* recorded data flags */ |
38 |
> |
#define HASBORDER 01 |
39 |
> |
#define TRIPLETS 02 |
40 |
> |
/* a data structure */ |
41 |
> |
struct { |
42 |
> |
int flags; /* data type */ |
43 |
> |
short m, n; /* number of s and t values */ |
44 |
> |
FLOAT *data; /* the data itself, s major sort */ |
45 |
> |
} datarec; /* our recorded data */ |
46 |
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|
47 |
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double l_hermite(), l_bezier(), l_bspline(), l_dataval(); |
48 |
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extern double funvalue(), argument(); |
49 |
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|
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typedef struct { |
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FVECT p; /* vertex position */ |
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FVECT n; /* average normal */ |
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int argc; |
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char *argv[]; |
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{ |
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extern long eclock; |
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POINT *row0, *row1, *row2, *rp; |
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int i, j, m, n; |
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char stmp[256]; |
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|
65 |
< |
varset("PI", PI); |
66 |
< |
funset("hermite", 5, l_hermite); |
65 |
> |
varset("PI", ':', PI); |
66 |
> |
funset("hermite", 5, ':', l_hermite); |
67 |
> |
funset("bezier", 5, ':', l_bezier); |
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funset("bspline", 5, ':', l_bspline); |
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|
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if (argc < 8) |
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goto userror; |
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|
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for (i = 8; i < argc; i++) |
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if (!strcmp(argv[i], "-e")) |
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scompile(NULL, argv[++i]); |
75 |
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scompile(argv[++i], NULL, 0); |
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else if (!strcmp(argv[i], "-f")) |
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fcompile(argv[++i]); |
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else if (!strcmp(argv[i], "-s")) |
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|
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modname = argv[1]; |
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surfname = argv[2]; |
74 |
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sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
75 |
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scompile(NULL, stmp); |
76 |
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sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
77 |
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scompile(NULL, stmp); |
78 |
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sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]); |
79 |
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scompile(NULL, stmp); |
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m = atoi(argv[6]); |
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n = atoi(argv[7]); |
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if (m <= 0 || n <= 0) |
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goto userror; |
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|
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row0 = (POINT *)malloc((n+1)*sizeof(POINT)); |
91 |
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row1 = (POINT *)malloc((n+1)*sizeof(POINT)); |
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row2 = (POINT *)malloc((n+1)*sizeof(POINT)); |
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if (!strcmp(argv[5], "-") || access(argv[5], 4) == 0) { /* file? */ |
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funset(ZNAME, 2, ':', l_dataval); |
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if (!strcmp(argv[5],argv[3]) && !strcmp(argv[5],argv[4])) { |
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loaddata(argv[5], m, n, 3); |
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funset(XNAME, 2, ':', l_dataval); |
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funset(YNAME, 2, ':', l_dataval); |
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} else { |
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loaddata(argv[5], m, n, 1); |
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sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
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scompile(stmp, NULL, 0); |
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sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
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scompile(stmp, NULL, 0); |
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} |
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} else { |
103 |
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sprintf(stmp, "%s(s,t)=%s;", XNAME, argv[3]); |
104 |
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scompile(stmp, NULL, 0); |
105 |
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sprintf(stmp, "%s(s,t)=%s;", YNAME, argv[4]); |
106 |
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scompile(stmp, NULL, 0); |
107 |
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sprintf(stmp, "%s(s,t)=%s;", ZNAME, argv[5]); |
108 |
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scompile(stmp, NULL, 0); |
109 |
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} |
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row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
111 |
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row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
112 |
> |
row2 = (POINT *)malloc((n+3)*sizeof(POINT)); |
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if (row0 == NULL || row1 == NULL || row2 == NULL) { |
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fprintf(stderr, "%s: out of memory\n", argv[0]); |
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quit(1); |
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} |
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row0++; row1++; row2++; |
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/* print header */ |
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printhead(argc, argv); |
120 |
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/* compute first two rows */ |
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eclock = 0; |
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/* initialize */ |
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comprow(-1.0/m, row0, n); |
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comprow(0.0, row1, n); |
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comprow(1.0/m, row2, n); |
125 |
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compnorms(row1, row1, row2, n); |
125 |
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compnorms(row0, row1, row2, n); |
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/* for each row */ |
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for (i = 0; i < m; i++) { |
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/* compute next row */ |
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row0 = row1; |
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row1 = row2; |
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row2 = rp; |
133 |
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if (i+2 <= m) { |
134 |
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comprow((double)(i+2)/m, row2, n); |
107 |
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compnorms(row0, row1, row2, n); |
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} else |
109 |
< |
compnorms(row0, row1, row1, n); |
133 |
> |
comprow((double)(i+2)/m, row2, n); |
134 |
> |
compnorms(row0, row1, row2, n); |
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|
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for (j = 0; j < n; j++) { |
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/* put polygons */ |
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} |
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|
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|
156 |
+ |
loaddata(file, m, n, pointsize) /* load point data from file */ |
157 |
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char *file; |
158 |
+ |
int m, n; |
159 |
+ |
int pointsize; |
160 |
+ |
{ |
161 |
+ |
extern char *fgetword(); |
162 |
+ |
FILE *fp; |
163 |
+ |
char word[64]; |
164 |
+ |
register int size; |
165 |
+ |
register FLOAT *dp; |
166 |
+ |
|
167 |
+ |
datarec.flags = HASBORDER; /* assume border values */ |
168 |
+ |
datarec.m = m+1; |
169 |
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datarec.n = n+1; |
170 |
+ |
size = datarec.m*datarec.n*pointsize; |
171 |
+ |
if (pointsize == 3) |
172 |
+ |
datarec.flags |= TRIPLETS; |
173 |
+ |
dp = (FLOAT *)malloc(size*sizeof(FLOAT)); |
174 |
+ |
if ((datarec.data = dp) == NULL) { |
175 |
+ |
fputs("Out of memory\n", stderr); |
176 |
+ |
exit(1); |
177 |
+ |
} |
178 |
+ |
if (!strcmp(file, "-")) { |
179 |
+ |
file = "<stdin>"; |
180 |
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fp = stdin; |
181 |
+ |
} else if ((fp = fopen(file, "r")) == NULL) { |
182 |
+ |
fputs(file, stderr); |
183 |
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fputs(": cannot open\n", stderr); |
184 |
+ |
exit(1); |
185 |
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} |
186 |
+ |
while (size > 0 && fgetword(word, sizeof(word), fp) != NULL) { |
187 |
+ |
if (!isflt(word)) { |
188 |
+ |
fprintf(stderr, "%s: garbled data value: %s\n", |
189 |
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file, word); |
190 |
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exit(1); |
191 |
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} |
192 |
+ |
*dp++ = atof(word); |
193 |
+ |
size--; |
194 |
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} |
195 |
+ |
if (size == (m+n+1)*pointsize) { /* no border after all */ |
196 |
+ |
dp = (FLOAT *)realloc((char *)datarec.data, |
197 |
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m*n*pointsize*sizeof(FLOAT)); |
198 |
+ |
if (dp != NULL) |
199 |
+ |
datarec.data = dp; |
200 |
+ |
datarec.flags &= ~HASBORDER; |
201 |
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datarec.m = m; |
202 |
+ |
datarec.n = n; |
203 |
+ |
size = 0; |
204 |
+ |
} |
205 |
+ |
if (datarec.m < 2 || datarec.n < 2 || size != 0 || |
206 |
+ |
fgetword(word, sizeof(word), fp) != NULL) { |
207 |
+ |
fputs(file, stderr); |
208 |
+ |
fputs(": bad number of data points\n", stderr); |
209 |
+ |
exit(1); |
210 |
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} |
211 |
+ |
fclose(fp); |
212 |
+ |
} |
213 |
+ |
|
214 |
+ |
|
215 |
+ |
double |
216 |
+ |
l_dataval(nam) /* return recorded data value */ |
217 |
+ |
char *nam; |
218 |
+ |
{ |
219 |
+ |
double u, v; |
220 |
+ |
register int i, j; |
221 |
+ |
register FLOAT *dp; |
222 |
+ |
double d00, d01, d10, d11; |
223 |
+ |
/* compute coordinates */ |
224 |
+ |
u = argument(1); v = argument(2); |
225 |
+ |
if (datarec.flags & HASBORDER) { |
226 |
+ |
i = u *= datarec.m-1; |
227 |
+ |
j = v *= datarec.n-1; |
228 |
+ |
} else { |
229 |
+ |
i = u = u*datarec.m - .5; |
230 |
+ |
j = v = v*datarec.n - .5; |
231 |
+ |
} |
232 |
+ |
if (i < 0) i = 0; |
233 |
+ |
else if (i > datarec.m-2) i = datarec.m-2; |
234 |
+ |
if (j < 0) j = 0; |
235 |
+ |
else if (j > datarec.n-2) j = datarec.n-2; |
236 |
+ |
/* compute value */ |
237 |
+ |
if (datarec.flags & TRIPLETS) { |
238 |
+ |
dp = datarec.data + 3*(j*datarec.m + i); |
239 |
+ |
if (nam == ZNAME) |
240 |
+ |
dp += 2; |
241 |
+ |
else if (nam == YNAME) |
242 |
+ |
dp++; |
243 |
+ |
d00 = dp[0]; d01 = dp[3]; |
244 |
+ |
dp += 3*datarec.m; |
245 |
+ |
d10 = dp[0]; d11 = dp[3]; |
246 |
+ |
} else { |
247 |
+ |
dp = datarec.data + j*datarec.m + i; |
248 |
+ |
d00 = dp[0]; d01 = dp[1]; |
249 |
+ |
dp += datarec.m; |
250 |
+ |
d10 = dp[0]; d11 = dp[1]; |
251 |
+ |
} |
252 |
+ |
/* bilinear interpolation */ |
253 |
+ |
return((j+1-v)*((i+1-u)*d00+(u-i)*d01)+(v-j)*((i+1-u)*d10+(u-i)*d11)); |
254 |
+ |
} |
255 |
+ |
|
256 |
+ |
|
257 |
|
putsquare(p0, p1, p2, p3) /* put out a square */ |
258 |
|
POINT *p0, *p1, *p2, *p3; |
259 |
|
{ |
346 |
|
register POINT *row; |
347 |
|
int siz; |
348 |
|
{ |
349 |
< |
double st[2], step; |
350 |
< |
|
349 |
> |
double st[2]; |
350 |
> |
int end; |
351 |
> |
register int i; |
352 |
> |
|
353 |
> |
if (smooth) { |
354 |
> |
i = -1; /* compute one past each end */ |
355 |
> |
end = siz+1; |
356 |
> |
} else { |
357 |
> |
if (s < -FTINY || s > 1.0+FTINY) |
358 |
> |
return; |
359 |
> |
i = 0; |
360 |
> |
end = siz; |
361 |
> |
} |
362 |
|
st[0] = s; |
363 |
< |
st[1] = 0.0; |
364 |
< |
step = 1.0 / siz; |
365 |
< |
while (siz-- >= 0) { |
366 |
< |
row->p[0] = funvalue(XNAME, 2, st); |
367 |
< |
row->p[1] = funvalue(YNAME, 2, st); |
368 |
< |
row->p[2] = funvalue(ZNAME, 2, st); |
232 |
< |
row++; |
233 |
< |
st[1] += step; |
363 |
> |
while (i <= end) { |
364 |
> |
st[1] = (double)i/siz; |
365 |
> |
row[i].p[0] = funvalue(XNAME, 2, st); |
366 |
> |
row[i].p[1] = funvalue(YNAME, 2, st); |
367 |
> |
row[i].p[2] = funvalue(ZNAME, 2, st); |
368 |
> |
i++; |
369 |
|
} |
370 |
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} |
371 |
|
|
374 |
|
register POINT *r0, *r1, *r2; |
375 |
|
int siz; |
376 |
|
{ |
377 |
< |
FVECT v1, v2, vc; |
377 |
> |
FVECT v1, v2; |
378 |
> |
register int i; |
379 |
|
|
380 |
|
if (!smooth) /* not needed if no smoothing */ |
381 |
|
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++; |
382 |
|
/* compute middle points */ |
383 |
< |
while (--siz > 0) { |
384 |
< |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
385 |
< |
fvsum(v2, r1[1].p, r1[0].p, -1.0); |
383 |
> |
while (siz-- >= 0) { |
384 |
> |
fvsum(v1, r2[0].p, r0[0].p, -1.0); |
385 |
> |
fvsum(v2, r1[1].p, r1[-1].p, -1.0); |
386 |
|
fcross(r1[0].n, v1, v2); |
260 |
– |
fvsum(v1, r0[0].p, r1[0].p, -1.0); |
261 |
– |
fcross(vc, v2, v1); |
262 |
– |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
263 |
– |
fvsum(v2, r1[-1].p, r1[0].p, -1.0); |
264 |
– |
fcross(vc, v1, v2); |
265 |
– |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
266 |
– |
fvsum(v1, r2[0].p, r1[0].p, -1.0); |
267 |
– |
fcross(vc, v2, v1); |
268 |
– |
fvsum(r1[0].n, r1[0].n, vc, 1.0); |
387 |
|
normalize(r1[0].n); |
388 |
|
r0++; r1++; r2++; |
389 |
|
} |
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); |
390 |
|
} |
391 |
|
|
392 |
|
|
399 |
|
#define v ((ax+2)%3) |
400 |
|
|
401 |
|
register int ax; |
402 |
< |
double eqnmat[4][4], solmat[4][4]; |
402 |
> |
MAT4 eqnmat; |
403 |
|
FVECT v1; |
404 |
|
register int i, j; |
405 |
|
|
410 |
|
fvsum(v1, v1, p1->n, 1.0); |
411 |
|
fvsum(v1, v1, p2->n, 1.0); |
412 |
|
fvsum(v1, v1, p3->n, 1.0); |
413 |
< |
ax = fabs(v1[0]) > fabs(v1[1]) ? 0 : 1; |
414 |
< |
ax = fabs(v1[ax]) > fabs(v1[2]) ? ax : 2; |
413 |
> |
ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
414 |
> |
ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
415 |
|
/* assign equation matrix */ |
416 |
|
eqnmat[0][0] = p0->p[u]*p0->p[v]; |
417 |
|
eqnmat[0][1] = p0->p[u]; |
430 |
|
eqnmat[3][2] = p3->p[v]; |
431 |
|
eqnmat[3][3] = 1.0; |
432 |
|
/* invert matrix (solve system) */ |
433 |
< |
if (!invmat(solmat, eqnmat)) |
433 |
> |
if (!invmat(eqnmat, eqnmat)) |
434 |
|
return(-1); /* no solution */ |
435 |
|
/* compute result matrix */ |
436 |
|
for (j = 0; j < 4; j++) |
437 |
|
for (i = 0; i < 3; i++) |
438 |
< |
resmat[j][i] = solmat[j][0]*p0->n[i] + |
439 |
< |
solmat[j][1]*p1->n[i] + |
440 |
< |
solmat[j][2]*p2->n[i] + |
441 |
< |
solmat[j][3]*p3->n[i]; |
438 |
> |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
439 |
> |
eqnmat[j][1]*p1->n[i] + |
440 |
> |
eqnmat[j][2]*p2->n[i] + |
441 |
> |
eqnmat[j][3]*p3->n[i]; |
442 |
|
return(ax); |
443 |
|
|
444 |
|
#undef u |
446 |
|
} |
447 |
|
|
448 |
|
|
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 |
– |
|
449 |
|
/* |
450 |
|
* invmat - computes the inverse of mat into inverse. Returns 1 |
451 |
|
* if there exists an inverse, 0 otherwise. It uses Gaussian Elimination |
453 |
|
*/ |
454 |
|
|
455 |
|
invmat(inverse,mat) |
456 |
< |
double mat[4][4],inverse[4][4]; |
456 |
> |
MAT4 inverse, mat; |
457 |
|
{ |
458 |
|
#define SWAP(a,b,t) (t=a,a=b,b=t) |
459 |
|
|
460 |
+ |
MAT4 m4tmp; |
461 |
|
register int i,j,k; |
462 |
|
register double temp; |
463 |
|
|
370 |
– |
setident4(inverse); |
464 |
|
copymat4(m4tmp, mat); |
465 |
+ |
/* set inverse to identity */ |
466 |
+ |
for (i = 0; i < 4; i++) |
467 |
+ |
for (j = 0; j < 4; j++) |
468 |
+ |
inverse[i][j] = i==j ? 1.0 : 0.0; |
469 |
|
|
470 |
|
for(i = 0; i < 4; i++) { |
471 |
< |
if(m4tmp[i][i] == 0) { /* Pivot is zero */ |
472 |
< |
/* Look for a raw with pivot != 0 and swap raws */ |
473 |
< |
for(j = i + 1; j < 4; j++) |
474 |
< |
if(m4tmp[j][i] != 0) { |
475 |
< |
for( k = 0; k < 4; k++) { |
476 |
< |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
477 |
< |
SWAP(inverse[i][k],inverse[j][k],temp); |
478 |
< |
} |
479 |
< |
break; |
480 |
< |
} |
481 |
< |
if(j == 4) /* No replacing raw -> no inverse */ |
482 |
< |
return(0); |
483 |
< |
} |
471 |
> |
/* Look for row with largest pivot and swap rows */ |
472 |
> |
temp = FTINY; j = -1; |
473 |
> |
for(k = i; k < 4; k++) |
474 |
> |
if(ABS(m4tmp[k][i]) > temp) { |
475 |
> |
temp = ABS(m4tmp[k][i]); |
476 |
> |
j = k; |
477 |
> |
} |
478 |
> |
if(j == -1) /* No replacing row -> no inverse */ |
479 |
> |
return(0); |
480 |
> |
if (j != i) |
481 |
> |
for(k = 0; k < 4; k++) { |
482 |
> |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
483 |
> |
SWAP(inverse[i][k],inverse[j][k],temp); |
484 |
> |
} |
485 |
|
|
486 |
|
temp = m4tmp[i][i]; |
487 |
|
for(k = 0; k < 4; k++) { |
499 |
|
} |
500 |
|
} |
501 |
|
return(1); |
502 |
+ |
|
503 |
|
#undef SWAP |
504 |
|
} |
505 |
|
|
547 |
|
argument(2)*(-2.0*t+3.0)*t*t + |
548 |
|
argument(3)*((t-2.0)*t+1.0)*t + |
549 |
|
argument(4)*(t-1.0)*t*t ); |
550 |
+ |
} |
551 |
+ |
|
552 |
+ |
|
553 |
+ |
double |
554 |
+ |
l_bezier() |
555 |
+ |
{ |
556 |
+ |
double t; |
557 |
+ |
|
558 |
+ |
t = argument(5); |
559 |
+ |
return( argument(1) * (1.+t*(-3.+t*(3.-t))) + |
560 |
+ |
argument(2) * 3.*t*(1.+t*(-2.+t)) + |
561 |
+ |
argument(3) * 3.*t*t*(1.-t) + |
562 |
+ |
argument(4) * t*t*t ); |
563 |
+ |
} |
564 |
+ |
|
565 |
+ |
|
566 |
+ |
double |
567 |
+ |
l_bspline() |
568 |
+ |
{ |
569 |
+ |
double t; |
570 |
+ |
|
571 |
+ |
t = argument(5); |
572 |
+ |
return( argument(1) * (1./6.+t*(-1./2.+t*(1./2.-1./6.*t))) + |
573 |
+ |
argument(2) * (2./3.+t*t*(-1.+1./2.*t)) + |
574 |
+ |
argument(3) * (1./6.+t*(1./2.+t*(1./2.-1./2.*t))) + |
575 |
+ |
argument(4) * (1./6.*t*t*t) ); |
576 |
|
} |