/// <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);
}
/// <summary>Creates a spherical billboard that rotates around a specified object position.</summary>
/// <param name="objectPosition">Position of the object the billboard will rotate around.</param>
/// <param name="cameraPosition">Position of the camera.</param>
/// <param name="cameraUpVector">The up vector of the camera.</param>
/// <param name="cameraForwardVector">The forward vector of the camera.</param>
/// <returns>The created billboard matrix</returns>
public static Matrix2X3 <T> CreateBillboard <T>(Vector3D <T> objectPosition, Vector3D <T> cameraPosition, Vector3D <T> cameraUpVector, Vector3D <T> cameraForwardVector)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Vector3D <T> zaxis = objectPosition - cameraPosition;
var norm = zaxis.LengthSquared;
if (!Scalar.GreaterThanOrEqual(norm, Scalar.As <float, T>(BillboardEpsilon)))
{
zaxis = -cameraForwardVector;
}
else
{
zaxis = Vector3D.Multiply(zaxis, Scalar.Reciprocal(Scalar.Sqrt(norm)));
}
Vector3D <T> xaxis = Vector3D.Normalize(Vector3D.Cross(cameraUpVector, zaxis));
Vector3D <T> yaxis = Vector3D.Cross(zaxis, xaxis);
return(new(xaxis, yaxis));
}
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)));
}
}