/// <summary>Attempts to invert the given matrix. If the operation succeeds, the inverted matrix is stored in the result parameter.</summary>
/// <param name="matrix">The source matrix.</param>
/// <param name="result">The output matrix.</param>
/// <returns>True if the operation succeeded, False otherwise.</returns>
public static bool Invert <T>(Matrix3X2 <T> matrix, out Matrix3X2 <T> result)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
T det = Scalar.Subtract(Scalar.Multiply(matrix.M11, matrix.M22), Scalar.Multiply(matrix.M21, matrix.M12));
if (!Scalar.GreaterThanOrEqual(Scalar.Abs(det), Scalar <T> .Epsilon))
{
result = new(Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN);
return(false);
}
T invDet = Scalar.Reciprocal(det);
result = default;
result.M11 = Scalar.Multiply(matrix.M22, invDet);
result.M12 = Scalar.Negate(Scalar.Multiply(matrix.M12, invDet));
result.M21 = Scalar.Negate(Scalar.Multiply(matrix.M21, invDet));
result.M22 = Scalar.Multiply(matrix.M11, invDet);
result.M31 = Scalar.Multiply(Scalar.Subtract(Scalar.Multiply(matrix.M21, matrix.M32), Scalar.Multiply(matrix.M31, matrix.M22)), invDet);
result.M32 = Scalar.Multiply(Scalar.Subtract(Scalar.Multiply(matrix.M31, matrix.M12), Scalar.Multiply(matrix.M11, matrix.M32)), invDet);
return(true);
}
public static Plane <T> Normalize <T>(Plane <T> value)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
/*if (Vector.IsHardwareAccelerated)
* {
* T normalLengthSquared = value.Normal.LengthSquared();
* if (MathF.Abs(normalLengthSquared - 1.0f) < NormalizeEpsilon)
* {
* // It already normalized, so we don't need to farther process.
* return value;
* }
* T normalLength = MathF.Sqrt(normalLengthSquared);
* return new Plane(
* value.Normal / normalLength,
* value.D / normalLength);
* }
* else*/
{
T f = Scalar.Add(
Scalar.Add(Scalar.Multiply(value.Normal.X, value.Normal.X),
Scalar.Multiply(value.Normal.Y, value.Normal.Y)),
Scalar.Multiply(value.Normal.Z, value.Normal.Z));
if (!Scalar.GreaterThanOrEqual(Scalar.Abs(Scalar.Subtract(f, Scalar <T> .One)), Scalar.As <float, T>(NormalizeEpsilon)))
{
return(value); // It already normalized, so we don't need to further process.
}
T fInv = Scalar.Reciprocal(Scalar.Sqrt(f));
return(new(
Scalar.Multiply(value.Normal.X, fInv),
Scalar.Multiply(value.Normal.Y, fInv),
Scalar.Multiply(value.Normal.Z, fInv),
Scalar.Multiply(value.Distance, fInv)));
}
}
/// <summary>Attempts to extract the scale, translation, and rotation components from the given scale/rotation/translation matrix.
/// If successful, the out parameters will contained the extracted values.</summary>
/// <param name="matrix">The source matrix.</param>
/// <param name="scale">The scaling component of the transformation matrix.</param>
/// <param name="rotation">The rotation component of the transformation matrix.</param>
/// <returns>True if the source matrix was successfully decomposed; False otherwise.</returns>
public static bool Decompose <T>(Matrix3X3 <T> matrix, out Vector3D <T> scale, out Quaternion <T> rotation)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
bool result = true;
unsafe
{
fixed(Vector3D <T> *scaleBase = &scale)
{
T *pfScales = (T *)scaleBase;
T det;
VectorBasis <T> vectorBasis;
Vector3D <T> ** pVectorBasis = (Vector3D <T> **) & vectorBasis;
Matrix3X3 <T> matTemp = Matrix3X3 <T> .Identity;
CanonicalBasis <T> canonicalBasis = default;
Vector3D <T> * pCanonicalBasis = &canonicalBasis.Row0;
canonicalBasis.Row0 = new Vector3D <T>(Scalar <T> .One, Scalar <T> .Zero, Scalar <T> .Zero);
canonicalBasis.Row1 = new Vector3D <T>(Scalar <T> .Zero, Scalar <T> .One, Scalar <T> .Zero);
canonicalBasis.Row2 = new Vector3D <T>(Scalar <T> .Zero, Scalar <T> .Zero, Scalar <T> .One);
pVectorBasis[0] = &matTemp.Row1;
pVectorBasis[1] = &matTemp.Row2;
pVectorBasis[2] = &matTemp.Row3;
*(pVectorBasis[0]) = new Vector3D <T>(matrix.M11, matrix.M12, matrix.M13);
*(pVectorBasis[1]) = new Vector3D <T>(matrix.M21, matrix.M22, matrix.M23);
*(pVectorBasis[2]) = new Vector3D <T>(matrix.M31, matrix.M32, matrix.M33);
scale.X = pVectorBasis[0]->Length;
scale.Y = pVectorBasis[1]->Length;
scale.Z = pVectorBasis[2]->Length;
uint a, b, c;
#region Ranking
T x = pfScales[0], y = pfScales[1], z = pfScales[2];
if (!Scalar.GreaterThanOrEqual(x, y))
{
if (!Scalar.GreaterThanOrEqual(y, z))
{
a = 2;
b = 1;
c = 0;
}
else
{
a = 1;
if (!Scalar.GreaterThanOrEqual(x, z))
{
b = 2;
c = 0;
}
else
{
b = 0;
c = 2;
}
}
}
else
{
if (!Scalar.GreaterThanOrEqual(x, z))
{
a = 2;
b = 0;
c = 1;
}
else
{
a = 0;
if (!Scalar.GreaterThanOrEqual(y, z))
{
b = 2;
c = 1;
}
else
{
b = 1;
c = 2;
}
}
}
#endregion
if (!Scalar.GreaterThanOrEqual(pfScales[a], Scalar.As <float, T>(DecomposeEpsilon)))
{
*(pVectorBasis[a]) = pCanonicalBasis[a];
}
*pVectorBasis[a] = Vector3D.Normalize(*pVectorBasis[a]);
if (!Scalar.GreaterThanOrEqual(pfScales[b], Scalar.As <float, T>(DecomposeEpsilon)))
{
uint cc;
T fAbsX, fAbsY, fAbsZ;
fAbsX = Scalar.Abs(pVectorBasis[a]->X);
fAbsY = Scalar.Abs(pVectorBasis[a]->Y);
fAbsZ = Scalar.Abs(pVectorBasis[a]->Z);
#region Ranking
if (!Scalar.GreaterThanOrEqual(fAbsX, fAbsY))
{
if (!Scalar.GreaterThanOrEqual(fAbsY, fAbsZ))
{
cc = 0;
}
else
{
if (!Scalar.GreaterThanOrEqual(fAbsX, fAbsZ))
{
cc = 0;
}
else
{
cc = 2;
}
}
}
else
{
if (!Scalar.GreaterThanOrEqual(fAbsX, fAbsZ))
{
cc = 1;
}
else
{
if (!Scalar.GreaterThanOrEqual(fAbsY, fAbsZ))
{
cc = 1;
}
else
{
cc = 2;
}
}
}
#endregion
*pVectorBasis[b] = Vector3D.Cross(*pVectorBasis[a], *(pCanonicalBasis + cc));
}
*pVectorBasis[b] = Vector3D.Normalize(*pVectorBasis[b]);
if (!Scalar.GreaterThanOrEqual(pfScales[c], Scalar.As <float, T>(DecomposeEpsilon)))
{
*pVectorBasis[c] = Vector3D.Cross(*pVectorBasis[a], *pVectorBasis[b]);
}
*pVectorBasis[c] = Vector3D.Normalize(*pVectorBasis[c]);
det = matTemp.GetDeterminant();
// use Kramer's rule to check for handedness of coordinate system
if (!Scalar.GreaterThanOrEqual(det, Scalar <T> .Zero))
{
// switch coordinate system by negating the scale and inverting the basis vector on the x-axis
pfScales[a] = Scalar.Negate(pfScales[a]);
*pVectorBasis[a] = -(*pVectorBasis[a]);
det = Scalar.Negate(det);
}
det = Scalar.Subtract(det, Scalar <T> .One);
det = Scalar.Multiply(det, det);
if (!Scalar.GreaterThanOrEqual(Scalar.As <float, T>(DecomposeEpsilon), det))
{
// Non-SRT matrix encountered
rotation = Quaternion <T> .Identity;
result = false;
}
else
{
// generate the quaternion from the matrix
rotation = Quaternion <T> .CreateFromRotationMatrix(matTemp);
}
}
}
return(result);
}