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/* Copyright (c) 1986 Regents of the University of California */ |
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|
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#ifndef lint |
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static char SCCSid[] = "$SunId$ LBL"; |
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#endif |
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|
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/* |
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* mat4.c - routines dealing with 4 X 4 homogeneous transformation matrices. |
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* |
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* 10/19/85 |
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*/ |
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|
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|
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static double m4tmp[4][4]; /* for efficiency */ |
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|
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#ifdef BSD |
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#define copymat4(m4a,m4b) bcopy((char *)m4b,(char *)m4a,sizeof(m4tmp)) |
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#else |
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#define copymat4(m4a,m4b) (void)memcpy((char *)m4a,(char *)m4b,sizeof(m4tmp)) |
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extern char *memcpy(); |
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#endif |
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|
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|
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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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multmat4(m4a, m4b, m4c) /* multiply m4b X m4c and put into m4a */ |
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double m4a[4][4]; |
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register double m4b[4][4], m4c[4][4]; |
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{ |
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register int i, j; |
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|
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for (i = 4; i--; ) |
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for (j = 4; j--; ) |
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m4tmp[i][j] = m4b[i][0]*m4c[0][j] + |
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m4b[i][1]*m4c[1][j] + |
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m4b[i][2]*m4c[2][j] + |
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m4b[i][3]*m4c[3][j]; |
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|
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copymat4(m4a, m4tmp); |
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} |
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|
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|
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multv3(v3a, v3b, m4) /* transform vector v3b by m4 and put into v3a */ |
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double v3a[3]; |
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register double v3b[3]; |
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register double m4[4][4]; |
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{ |
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m4tmp[0][0] = v3b[0]*m4[0][0] + v3b[1]*m4[1][0] + v3b[2]*m4[2][0]; |
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m4tmp[0][1] = v3b[0]*m4[0][1] + v3b[1]*m4[1][1] + v3b[2]*m4[2][1]; |
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m4tmp[0][2] = v3b[0]*m4[0][2] + v3b[1]*m4[1][2] + v3b[2]*m4[2][2]; |
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|
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v3a[0] = m4tmp[0][0]; |
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v3a[1] = m4tmp[0][1]; |
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v3a[2] = m4tmp[0][2]; |
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} |
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|
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|
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multp3(p3a, p3b, m4) /* transform p3b by m4 and put into p3a */ |
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register double p3a[3]; |
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double p3b[3]; |
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register double m4[4][4]; |
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{ |
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multv3(p3a, p3b, m4); /* transform as vector */ |
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p3a[0] += m4[3][0]; /* translate */ |
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p3a[1] += m4[3][1]; |
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p3a[2] += m4[3][2]; |
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} |
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|
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#ifdef INVMAT |
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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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* method with partial pivoting. |
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*/ |
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|
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invmat(inverse,mat) |
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double mat[4][4],inverse[4][4]; |
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{ |
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#define SWAP(a,b,t) (t=a,a=b,b=t) |
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#define ABS(x) (x>=0?x:-(x)) |
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|
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register int i,j,k; |
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register double temp; |
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|
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copymat4(m4tmp, mat); |
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setident(inverse); |
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|
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for(i = 0; i < 4; i++) { |
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/* Look for row with largest pivot and swap rows */ |
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temp = 0; j = -1; |
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for(k = i; k < 4; k++) |
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if(ABS(m4tmp[k][i]) > temp) { |
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temp = ABS(m4tmp[k][i]); |
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j = k; |
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} |
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if(j == -1) /* No replacing row -> no inverse */ |
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return(0); |
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if (j != i) |
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for(k = 0; k < 4; k++) { |
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SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
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SWAP(inverse[i][k],inverse[j][k],temp); |
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} |
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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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m4tmp[i][k] /= temp; |
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inverse[i][k] /= temp; |
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} |
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for(j = 0; j < 4; j++) { |
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if(j != i) { |
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temp = m4tmp[j][i]; |
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for(k = 0; k < 4; k++) { |
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m4tmp[j][k] -= m4tmp[i][k]*temp; |
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inverse[j][k] -= inverse[i][k]*temp; |
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} |
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} |
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} |
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} |
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return(1); |
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|
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#undef ABS |
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#undef SWAP |
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} |
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#endif |
