ARdouble arMatrixDet(ARMat *m)
{
if(m->row != m->clm) return 0.0;
return mdet(m->m, m->row, m->row);
}
double matrixDet(Mat m) {
if(m.row != m.clm) {
return 0;
}
return mdet(m.m, m.row, m.row);
}
bool csDIntersect3::Planes (
const csDPlane &p1,
const csDPlane &p2,
const csDPlane &p3,
csDVector3 &isect)
{
//To find the one point that is on all three planes, we need to solve
//the following equation system (we need to find the x, y and z which
//are true for all equations):
// A1*x+B1*y+C1*z+D1=0 //plane1
// A2*x+B2*y+C2*z+D2=0 //plane2
// A3*x+B3*y+C3*z+D3=0 //plane3
//This can be solved according to Cramers rule by looking at the
//determinants of the equation system.
csDMatrix3 mdet (
p1.A (),
p1.B (),
p1.C (),
p2.A (),
p2.B (),
p2.C (),
p3.A (),
p3.B (),
p3.C ());
double det = mdet.Determinant ();
if (det == 0) return false; //some planes are parallel.
csDMatrix3 mx (
-p1.D (),
p1.B (),
p1.C (),
-p2.D (),
p2.B (),
p2.C (),
-p3.D (),
p3.B (),
p3.C ());
double xdet = mx.Determinant ();
csDMatrix3 my (
p1.A (),
-p1.D (),
p1.C (),
p2.A (),
-p2.D (),
p2.C (),
p3.A (),
-p3.D (),
p3.C ());
double ydet = my.Determinant ();
csDMatrix3 mz (
p1.A (),
p1.B (),
-p1.D (),
p2.A (),
p2.B (),
-p2.D (),
p3.A (),
p3.B (),
-p3.D ());
double zdet = mz.Determinant ();
isect.x = xdet / det;
isect.y = ydet / det;
isect.z = zdet / det;
return true;
}