| 1 |
/* Copyright (c) 1986 Regents of the University of California */ |
| 2 |
|
| 3 |
#ifndef lint |
| 4 |
static char SCCSid[] = "$SunId$ LBL"; |
| 5 |
#endif |
| 6 |
|
| 7 |
/* |
| 8 |
* mat4.c - routines dealing with 4 X 4 homogeneous transformation matrices. |
| 9 |
* |
| 10 |
* 10/19/85 |
| 11 |
*/ |
| 12 |
|
| 13 |
|
| 14 |
static double m4tmp[4][4]; /* for efficiency */ |
| 15 |
|
| 16 |
#define copymat4(m4a,m4b) bcopy((char *)m4b,(char *)m4a,sizeof(m4tmp)) |
| 17 |
|
| 18 |
|
| 19 |
setident4(m4) |
| 20 |
double m4[4][4]; |
| 21 |
{ |
| 22 |
static double ident[4][4] = { |
| 23 |
1.,0.,0.,0., |
| 24 |
0.,1.,0.,0., |
| 25 |
0.,0.,1.,0., |
| 26 |
0.,0.,0.,1., |
| 27 |
}; |
| 28 |
copymat4(m4, ident); |
| 29 |
} |
| 30 |
|
| 31 |
|
| 32 |
multmat4(m4a, m4b, m4c) /* multiply m4b X m4c and put into m4a */ |
| 33 |
double m4a[4][4]; |
| 34 |
register double m4b[4][4], m4c[4][4]; |
| 35 |
{ |
| 36 |
register int i, j; |
| 37 |
|
| 38 |
for (i = 4; i--; ) |
| 39 |
for (j = 4; j--; ) |
| 40 |
m4tmp[i][j] = m4b[i][0]*m4c[0][j] + |
| 41 |
m4b[i][1]*m4c[1][j] + |
| 42 |
m4b[i][2]*m4c[2][j] + |
| 43 |
m4b[i][3]*m4c[3][j]; |
| 44 |
|
| 45 |
copymat4(m4a, m4tmp); |
| 46 |
} |
| 47 |
|
| 48 |
|
| 49 |
multv3(v3a, v3b, m4) /* transform vector v3b by m4 and put into v3a */ |
| 50 |
double v3a[3]; |
| 51 |
register double v3b[3]; |
| 52 |
register double m4[4][4]; |
| 53 |
{ |
| 54 |
m4tmp[0][0] = v3b[0]*m4[0][0] + v3b[1]*m4[1][0] + v3b[2]*m4[2][0]; |
| 55 |
m4tmp[0][1] = v3b[0]*m4[0][1] + v3b[1]*m4[1][1] + v3b[2]*m4[2][1]; |
| 56 |
m4tmp[0][2] = v3b[0]*m4[0][2] + v3b[1]*m4[1][2] + v3b[2]*m4[2][2]; |
| 57 |
|
| 58 |
v3a[0] = m4tmp[0][0]; |
| 59 |
v3a[1] = m4tmp[0][1]; |
| 60 |
v3a[2] = m4tmp[0][2]; |
| 61 |
} |
| 62 |
|
| 63 |
|
| 64 |
multp3(p3a, p3b, m4) /* transform p3b by m4 and put into p3a */ |
| 65 |
register double p3a[3]; |
| 66 |
double p3b[3]; |
| 67 |
register double m4[4][4]; |
| 68 |
{ |
| 69 |
multv3(p3a, p3b, m4); /* transform as vector */ |
| 70 |
p3a[0] += m4[3][0]; /* translate */ |
| 71 |
p3a[1] += m4[3][1]; |
| 72 |
p3a[2] += m4[3][2]; |
| 73 |
} |
| 74 |
|
| 75 |
|
| 76 |
#ifdef INVMAT |
| 77 |
/* |
| 78 |
* invmat - computes the inverse of mat into inverse. Returns 1 |
| 79 |
* if there exists an inverse, 0 otherwise. It uses Gaussian Elimination |
| 80 |
* method with partial pivoting. |
| 81 |
*/ |
| 82 |
|
| 83 |
invmat(inverse,mat) |
| 84 |
double mat[4][4],inverse[4][4]; |
| 85 |
{ |
| 86 |
#define SWAP(a,b,t) (t=a,a=b,b=t) |
| 87 |
#define ABS(x) (x>=0?x:-(x)) |
| 88 |
|
| 89 |
register int i,j,k; |
| 90 |
register double temp; |
| 91 |
|
| 92 |
copymat4(m4tmp, mat); |
| 93 |
setident(inverse); |
| 94 |
|
| 95 |
for(i = 0; i < 4; i++) { |
| 96 |
/* Look for row with largest pivot and swap rows */ |
| 97 |
temp = 0; j = -1; |
| 98 |
for(k = i; k < 4; k++) |
| 99 |
if(ABS(m4tmp[k][i]) > temp) { |
| 100 |
temp = ABS(m4tmp[k][i]); |
| 101 |
j = k; |
| 102 |
} |
| 103 |
if(j == -1) /* No replacing row -> no inverse */ |
| 104 |
return(0); |
| 105 |
if (j != i) |
| 106 |
for(k = 0; k < 4; k++) { |
| 107 |
SWAP(m4tmp[i][k],m4tmp[j][k],temp); |
| 108 |
SWAP(inverse[i][k],inverse[j][k],temp); |
| 109 |
} |
| 110 |
|
| 111 |
temp = m4tmp[i][i]; |
| 112 |
for(k = 0; k < 4; k++) { |
| 113 |
m4tmp[i][k] /= temp; |
| 114 |
inverse[i][k] /= temp; |
| 115 |
} |
| 116 |
for(j = 0; j < 4; j++) { |
| 117 |
if(j != i) { |
| 118 |
temp = m4tmp[j][i]; |
| 119 |
for(k = 0; k < 4; k++) { |
| 120 |
m4tmp[j][k] -= m4tmp[i][k]*temp; |
| 121 |
inverse[j][k] -= inverse[i][k]*temp; |
| 122 |
} |
| 123 |
} |
| 124 |
} |
| 125 |
} |
| 126 |
return(1); |
| 127 |
|
| 128 |
#undef ABS |
| 129 |
#undef SWAP |
| 130 |
} |
| 131 |
#endif |
