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* 4/3/87 |
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*/ |
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#include <stdio.h> |
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#include "fvect.h" |
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#include "standard.h" |
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#define XNAME "X_" /* x function name */ |
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#define YNAME "Y_" /* y function name */ |
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#define ZNAME "Z_" /* z function name */ |
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#define PI 3.14159265358979323846 |
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#define ABS(x) ((x)>=0 ? (x) : -(x)) |
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#define FTINY 1e-7 |
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|
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#define pvect(p) printf(vformat, (p)[0], (p)[1], (p)[2]) |
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char vformat[] = "%15.9g %15.9g %15.9g\n"; |
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char *modname, *surfname; |
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double funvalue(), l_hermite(), argument(), fabs(); |
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double funvalue(), l_hermite(), l_bezier(), argument(); |
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typedef struct { |
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FVECT p; /* vertex position */ |
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varset("PI", PI); |
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funset("hermite", 5, l_hermite); |
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funset("bezier", 5, l_bezier); |
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if (argc < 8) |
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goto userror; |
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if (m <= 0 || n <= 0) |
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goto userror; |
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row0 = (POINT *)malloc((n+1)*sizeof(POINT)); |
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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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row0 = (POINT *)malloc((n+3)*sizeof(POINT)); |
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row1 = (POINT *)malloc((n+3)*sizeof(POINT)); |
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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); |
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/* compute first two rows */ |
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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); |
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compnorms(row1, row1, row2, n); |
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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; |
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if (i+2 <= m) { |
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comprow((double)(i+2)/m, row2, n); |
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compnorms(row0, row1, row2, n); |
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} else |
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compnorms(row0, row1, row1, n); |
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comprow((double)(i+2)/m, row2, n); |
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compnorms(row0, row1, row2, n); |
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for (j = 0; j < n; j++) { |
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/* put polygons */ |
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register POINT *row; |
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int siz; |
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{ |
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double st[2], step; |
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double st[2]; |
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register int i; |
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/* compute one past each end */ |
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st[0] = s; |
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st[1] = 0.0; |
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step = 1.0 / siz; |
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while (siz-- >= 0) { |
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row->p[0] = funvalue(XNAME, 2, st); |
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row->p[1] = funvalue(YNAME, 2, st); |
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row->p[2] = funvalue(ZNAME, 2, st); |
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row++; |
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st[1] += step; |
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for (i = -1; i <= siz+1; i++) { |
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st[1] = (double)i/siz; |
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row[i].p[0] = funvalue(XNAME, 2, st); |
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row[i].p[1] = funvalue(YNAME, 2, st); |
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row[i].p[2] = funvalue(ZNAME, 2, st); |
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} |
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} |
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int siz; |
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{ |
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FVECT v1, v2, vc; |
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register int i; |
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if (!smooth) /* not needed if no smoothing */ |
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return; |
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/* compute first point */ |
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fvsum(v1, r2[0].p, r1[0].p, -1.0); |
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fvsum(v2, r1[1].p, r1[0].p, -1.0); |
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fcross(r1[0].n, v1, v2); |
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fvsum(v1, r0[0].p, r1[0].p, -1.0); |
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fcross(vc, v2, v1); |
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fvsum(r1[0].n, r1[0].n, vc, 1.0); |
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normalize(r1[0].n); |
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r0++; r1++; r2++; |
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/* compute middle points */ |
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while (--siz > 0) { |
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while (siz-- >= 0) { |
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fvsum(v1, r2[0].p, r1[0].p, -1.0); |
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fvsum(v2, r1[1].p, r1[0].p, -1.0); |
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fcross(r1[0].n, v1, v2); |
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normalize(r1[0].n); |
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r0++; r1++; r2++; |
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} |
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/* compute end point */ |
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fvsum(v1, r0[0].p, r1[0].p, -1.0); |
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fvsum(v2, r1[-1].p, r1[0].p, -1.0); |
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fcross(r1[0].n, v1, v2); |
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fvsum(v1, r2[0].p, r1[0].p, -1.0); |
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fcross(vc, v2, v1); |
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fvsum(r1[0].n, r1[0].n, vc, 1.0); |
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normalize(r1[0].n); |
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} |
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#define v ((ax+2)%3) |
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register int ax; |
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double eqnmat[4][4], solmat[4][4]; |
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double eqnmat[4][4]; |
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FVECT v1; |
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register int i, j; |
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fvsum(v1, v1, p1->n, 1.0); |
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fvsum(v1, v1, p2->n, 1.0); |
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fvsum(v1, v1, p3->n, 1.0); |
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ax = fabs(v1[0]) > fabs(v1[1]) ? 0 : 1; |
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ax = fabs(v1[ax]) > fabs(v1[2]) ? ax : 2; |
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ax = ABS(v1[0]) > ABS(v1[1]) ? 0 : 1; |
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ax = ABS(v1[ax]) > ABS(v1[2]) ? ax : 2; |
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/* assign equation matrix */ |
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eqnmat[0][0] = p0->p[u]*p0->p[v]; |
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eqnmat[0][1] = p0->p[u]; |
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eqnmat[3][2] = p3->p[v]; |
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eqnmat[3][3] = 1.0; |
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/* invert matrix (solve system) */ |
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if (!invmat(solmat, eqnmat)) |
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if (!invmat(eqnmat, eqnmat)) |
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return(-1); /* no solution */ |
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/* compute result matrix */ |
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for (j = 0; j < 4; j++) |
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for (i = 0; i < 3; i++) |
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resmat[j][i] = solmat[j][0]*p0->n[i] + |
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< |
solmat[j][1]*p1->n[i] + |
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< |
solmat[j][2]*p2->n[i] + |
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< |
solmat[j][3]*p3->n[i]; |
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> |
resmat[j][i] = eqnmat[j][0]*p0->n[i] + |
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> |
eqnmat[j][1]*p1->n[i] + |
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eqnmat[j][2]*p2->n[i] + |
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eqnmat[j][3]*p3->n[i]; |
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return(ax); |
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#undef u |
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} |
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static double m4tmp[4][4]; /* for efficiency */ |
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#define copymat4(m4a,m4b) bcopy((char *)m4b,(char *)m4a,sizeof(m4tmp)) |
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setident4(m4) |
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double m4[4][4]; |
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{ |
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static double ident[4][4] = { |
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1.,0.,0.,0., |
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0.,1.,0.,0., |
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0.,0.,1.,0., |
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0.,0.,0.,1., |
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}; |
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copymat4(m4, ident); |
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} |
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|
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/* |
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* invmat - computes the inverse of mat into inverse. Returns 1 |
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* if there exists an inverse, 0 otherwise. It uses Gaussian Elimination |
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{ |
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#define SWAP(a,b,t) (t=a,a=b,b=t) |
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+ |
double m4tmp[4][4]; |
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register int i,j,k; |
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register double temp; |
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< |
setident4(inverse); |
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< |
copymat4(m4tmp, mat); |
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> |
bcopy((char *)mat, (char *)m4tmp, sizeof(m4tmp)); |
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> |
/* set inverse to identity */ |
335 |
> |
for (i = 0; i < 4; i++) |
336 |
> |
for (j = 0; j < 4; j++) |
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> |
inverse[i][j] = i==j ? 1.0 : 0.0; |
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|
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for(i = 0; i < 4; i++) { |
340 |
< |
if(m4tmp[i][i] == 0) { /* Pivot is zero */ |
341 |
< |
/* Look for a raw with pivot != 0 and swap raws */ |
342 |
< |
for(j = i + 1; j < 4; j++) |
343 |
< |
if(m4tmp[j][i] != 0) { |
344 |
< |
for( k = 0; k < 4; k++) { |
345 |
< |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
346 |
< |
SWAP(inverse[i][k],inverse[j][k],temp); |
347 |
< |
} |
348 |
< |
break; |
349 |
< |
} |
350 |
< |
if(j == 4) /* No replacing raw -> no inverse */ |
351 |
< |
return(0); |
352 |
< |
} |
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 |
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} |
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temp = m4tmp[i][i]; |
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for(k = 0; k < 4; k++) { |
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} |
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} |
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return(1); |
371 |
+ |
|
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#undef SWAP |
373 |
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} |
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argument(2)*(-2.0*t+3.0)*t*t + |
417 |
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argument(3)*((t-2.0)*t+1.0)*t + |
418 |
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argument(4)*(t-1.0)*t*t ); |
419 |
+ |
} |
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+ |
|
421 |
+ |
|
422 |
+ |
double |
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+ |
l_bezier() |
424 |
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{ |
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double t; |
426 |
+ |
|
427 |
+ |
t = argument(5); |
428 |
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return( argument(1) * (1.+t*(-3.+t*(3.-t))) + |
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+ |
argument(2) * 3.*t*(1.+t*(-2.+t)) + |
430 |
+ |
argument(3) * 3.*t*t*(1.-t) + |
431 |
+ |
argument(4) * t*t*t ); |
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} |