#include "matrix.h"
// remove from sequence 0, 1, 2, 3, two numbers, see following
// example:
// r0 = 1, r1 = 2
// initial sequence:
// 0, 1, 2, 3
// remove number at place r0 (1 for ex):
// 0, 2, 3
// remove number at place r1 (2 for ex):
// 0, 2
// so result for index0(1, 2) is 0
// and for index1(1, 2) is 2
//
// r1\r0 : 0 1 2 3
// ---------------------------
// -- : _123 0_23 01_3 012_
// 0 : _.23 ._23 .1_3 .12_
// 1 : _1.3 0_.3 0._3 0.2_
// 2 : _12. 0_2. 01_. 01._
// ---------------------------
// 0 : 23 23 13 12
// 1 : 13 03 03 02
// 2 : 12 02 01 01
static inline int index0(int r0, int r1)
{ return r1 ? (r0 ? 0 : 1) : (r0 > 1 ? 1 : 2); }
static inline int index1(int r0, int r1)
{ return r1 < 2 ? (r0 < 3 ? 3 : 2) : (r0 > 1 ? 1 : 2); }
static inline int index0(int r)
{ return r ? 1 : 0; }
static inline int index1(int r)
{ return r > 0 ? 1 : 2; }
static inline int index2(int r)
{ return r > 1 ? 2 : 3; }
static inline Real det2(const Matrix4 &m, int r, int c, int rr, int cc) {
const int r0 = index0(r, rr);
const int r1 = index1(r, rr);
const int c0 = index0(c, cc);
const int c1 = index1(c, cc);
return m[r0][c0]*m[r1][c1] - m[r0][c1]*m[r1][c0];
}
static inline Real det3(const Matrix4 &m, int r, int c) {
const int r0 = index0(r);
return m[r0][index0(c)] * det2(m, r, c, 0, 0)
- m[r0][index1(c)] * det2(m, r, c, 0, 1)
+ m[r0][index2(c)] * det2(m, r, c, 0, 2);
}
Real
Matrix4::det() const
{ return m00*det3(*this, 0, 0) - m01*det3(*this, 0, 1) + m02*det3(*this, 0, 2) - m03*det3(*this, 0, 3); }
Matrix4
Matrix4::invert() const {
Vector4 dv(
det3(*this, 0, 0),
-det3(*this, 0, 1),
det3(*this, 0, 2),
-det3(*this, 0, 3) );
Real d = dv.x + dv.y + dv.z + dv.w;
if (fabs(d) <= real_precision)
return zero();
d = 1.0/d;
return Matrix4(
Vector4(dv.x, -det3(*this, 1, 0), det3(*this, 2, 0), -det3(*this, 3, 0))*d,
Vector4(dv.y, det3(*this, 1, 1),-det3(*this, 2, 1), det3(*this, 3, 1))*d,
Vector4(dv.z, -det3(*this, 1, 2), det3(*this, 2, 2), -det3(*this, 3, 2))*d,
Vector4(dv.w, det3(*this, 1, 3),-det3(*this, 2, 3), det3(*this, 3, 3))*d );
}