/// <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))); } }