VectorR3 Matrix3x3::Solve(const VectorR3& u) const // Returns solution
{ // based on Cramer's rule
double sd11 = m22 * m33 - m23 * m32;
double sd21 = m32 * m13 - m12 * m33;
double sd31 = m12 * m23 - m22 * m13;
double sd12 = m31 * m23 - m21 * m33;
double sd22 = m11 * m33 - m31 * m13;
double sd32 = m21 * m13 - m11 * m23;
double sd13 = m21 * m32 - m31 * m22;
double sd23 = m31 * m12 - m11 * m32;
double sd33 = m11 * m22 - m21 * m12;
double detInv = 1.0 / (m11 * sd11 + m12 * sd12 + m13 * sd13);
double rx = (u.x * sd11 + u.y * sd21 + u.z * sd31) * detInv;
double ry = (u.x * sd12 + u.y * sd22 + u.z * sd32) * detInv;
double rz = (u.x * sd13 + u.y * sd23 + u.z * sd33) * detInv;
return (VectorR3(rx, ry, rz));
}
VectorR3 operator *(VectorR3 u, double c) {
return VectorR3(u.X * c, u.Y * c, u.Z * c);
}
VectorR3 operator +(VectorR3 u, VectorR3 v) {
return VectorR3(u.X + v.X, u.Y + v.Y, u.Z + v.Z);
}
VectorR3 operator -(VectorR3 u, VectorR3 v) {
return VectorR3(u.X - v.X, u.Y - v.Y, u.Z - v.Z);
}
VectorR3 VectorR3::CrossProduct(VectorR3 rhs)
{
return VectorR3((Y * rhs.Z) - (Z * rhs.Y), -((X * rhs.Z) - (Z * rhs.X)), (X * rhs.Y) - (Y * rhs.X));
}