public static void EigenSolve(Matrix4x4 D, out Vector3 S, out Matrix4x4 V)
{
// D is symmetric
// S is a vector whose elements are eigenvalues
// V is a matrix whose columns are eigenvectors
S = EigenValues(D);
Vector3 V0, V1, V2;
if (S[0] - S[1] > S[1] - S[2])
{
V0 = EigenVector(D, S[0]);
if (S[1] - S[2] < Mathf.Epsilon)
{
V2 = V0.unitOrthogonal();
}
else
{
V2 = EigenVector(D, S[2]); V2 -= V0 * Vector3.Dot(V0, V2); V2 = Vector3.Normalize(V2);
}
V1 = Vector3.Cross(V2, V0);
}
else
{
V2 = EigenVector(D, S[2]);
if (S[0] - S[1] < Mathf.Epsilon)
{
V1 = V2.unitOrthogonal();
}
else
{
V1 = EigenVector(D, S[1]); V1 -= V2 * Vector3.Dot(V2, V1); V1 = Vector3.Normalize(V1);
}
V0 = Vector3.Cross(V1, V2);
}
V = Matrix4x4.identity;
V.SetColumn(0, V0);
V.SetColumn(1, V1);
V.SetColumn(2, V2);
}
public static void EigenSolve(float3x3 D, out float3 S, out float3x3 V)
{
// D is symmetric
// S is a vector whose elements are eigenvalues
// V is a matrix whose columns are eigenvectors
S = EigenValues(D);
float3 V0, V1, V2;
if (S[0] - S[1] > S[1] - S[2])
{
V0 = EigenVector(D, S[0]);
if (S[1] - S[2] < math.FLT_MIN_NORMAL)
{
V2 = V0.unitOrthogonal();
}
else
{
V2 = EigenVector(D, S[2]); V2 -= V0 * math.dot(V0, V2); V2 = math.normalize(V2);
}
V1 = math.cross(V2, V0);
}
else
{
V2 = EigenVector(D, S[2]);
if (S[0] - S[1] < math.FLT_MIN_NORMAL)
{
V1 = V2.unitOrthogonal();
}
else
{
V1 = EigenVector(D, S[1]); V1 -= V2 * math.dot(V2, V1); V1 = math.normalize(V1);
}
V0 = math.cross(V1, V2);
}
V.c0 = V0;
V.c1 = V1;
V.c2 = V2;
}