/// <summary>Get the symmetric inverse of this matrix as a 3-by-3. Returns the zero matrix if singular.</summary>
public void GetSymInverse33(out Matrix33 m)
{
var det = Vector3.Dot(Column1, Vector3.Cross(Column2, Column3));
// ReSharper disable CompareOfFloatsByEqualityOperator
if (det != 0.0f)
// ReSharper restore CompareOfFloatsByEqualityOperator
{
det = 1.0f / det;
}
var a11 = Column1.X;
var a12 = Column2.X;
var a13 = Column3.X;
var a22 = Column2.Y;
var a23 = Column3.Y;
var a33 = Column3.Z;
m.Column1.X = det * (a22 * a33 - a23 * a23);
m.Column1.Y = det * (a13 * a23 - a12 * a33);
m.Column1.Z = det * (a12 * a23 - a13 * a22);
m.Column2.X = m.Column1.Y;
m.Column2.Y = det * (a11 * a33 - a13 * a13);
m.Column2.Z = det * (a13 * a12 - a11 * a23);
m.Column3.X = m.Column1.Z;
m.Column3.Y = m.Column2.Z;
m.Column3.Z = det * (a11 * a22 - a12 * a12);
}
/// <summary>Get the inverse of this matrix as a 2-by-2. Returns the zero matrix if singular.</summary>
public void GetInverse22(out Matrix33 m)
{
var a = Column1.X;
var b = Column2.X;
var c = Column1.Y;
var d = Column2.Y;
var det = a * d - b * c;
// ReSharper disable CompareOfFloatsByEqualityOperator Intentional.
if (det != 0.0f)
// ReSharper restore CompareOfFloatsByEqualityOperator
{
det = 1.0f / det;
}
m.Column1.X = det * d;
m.Column2.X = -det * b;
m.Column1.Z = 0.0f;
m.Column1.Y = -det * c;
m.Column2.Y = det * a;
m.Column2.Z = 0.0f;
m.Column3.X = 0.0f;
m.Column3.Y = 0.0f;
m.Column3.Z = 0.0f;
}
