/// <summary>Creates a rotation matrix from the given Quaternion rotation value.</summary>
/// <param name="quaternion">The source Quaternion.</param>
/// <returns>The rotation matrix.</returns>
public static Matrix2X3 <T> CreateFromQuaternion <T>(Quaternion <T> quaternion)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix2X3 <T> result = Matrix2X3 <T> .Identity;
T xx = Scalar.Multiply(quaternion.X, quaternion.X);
T yy = Scalar.Multiply(quaternion.Y, quaternion.Y);
T zz = Scalar.Multiply(quaternion.Z, quaternion.Z);
T xy = Scalar.Multiply(quaternion.X, quaternion.Y);
T wz = Scalar.Multiply(quaternion.Z, quaternion.W);
T xz = Scalar.Multiply(quaternion.Z, quaternion.X);
T wy = Scalar.Multiply(quaternion.Y, quaternion.W);
T yz = Scalar.Multiply(quaternion.Y, quaternion.Z);
T wx = Scalar.Multiply(quaternion.X, quaternion.W);
result.M11 = Scalar.Subtract(Scalar <T> .One, Scalar.Multiply(Scalar <T> .Two, Scalar.Add(yy, zz)));
result.M12 = Scalar.Multiply(Scalar <T> .Two, Scalar.Add(xy, wz));
result.M13 = Scalar.Multiply(Scalar <T> .Two, Scalar.Subtract(xz, wy));
result.M21 = Scalar.Multiply(Scalar <T> .Two, Scalar.Subtract(xy, wz));
result.M22 = Scalar.Subtract(Scalar <T> .One, Scalar.Multiply(Scalar <T> .Two, Scalar.Add(zz, xx)));
result.M23 = Scalar.Multiply(Scalar <T> .Two, Scalar.Add(yz, wx));
return(result);
}
/// <summary>Creates a matrix that rotates around an arbitrary vector.</summary>
/// <param name="axis">The axis to rotate around.</param>
/// <param name="angle">The angle to rotate around the given axis, in radians.</param>
/// <returns>The rotation matrix.</returns>
public static Matrix2X3 <T> CreateFromAxisAngle <T>(Vector3D <T> axis, T angle)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
// a: angle
// x, y, z: unit vector for axis.
//
// Rotation matrix M can compute by using below equation.
//
// T T
// M = uu + (cos a)( I-uu ) + (sin a)S
//
// Where:
//
// u = ( x, y, z )
//
// [ 0 -z y ]
// S = [ z 0 -x ]
// [ -y x 0 ]
//
// [ 1 0 0 ]
// I = [ 0 1 0 ]
// [ 0 0 1 ]
//
//
// [ xx+cosa*(1-xx) yx-cosa*yx-sina*z zx-cosa*xz+sina*y ]
// M = [ xy-cosa*yx+sina*z yy+cosa(1-yy) yz-cosa*yz-sina*x ]
// [ zx-cosa*zx-sina*y zy-cosa*zy+sina*x zz+cosa*(1-zz) ]
//
T x = axis.X, y = axis.Y, z = axis.Z;
T sa = Scalar.Sin(angle), ca = Scalar.Cos(angle);
T xx = Scalar.Multiply(x, x), yy = Scalar.Multiply(y, y), zz = Scalar.Multiply(z, z);
T xy = Scalar.Multiply(x, y), xz = Scalar.Multiply(x, z), yz = Scalar.Multiply(y, z);
Matrix2X3 <T> result = Matrix2X3 <T> .Identity;
result.M11 = Scalar.Add(xx, Scalar.Multiply(ca, Scalar.Subtract(Scalar <T> .One, xx)));
result.M12 = Scalar.Add(Scalar.Subtract(xy, Scalar.Multiply(ca, xy)), Scalar.Multiply(sa, z));
result.M13 = Scalar.Subtract(Scalar.Subtract(xz, Scalar.Multiply(ca, xz)), Scalar.Multiply(sa, y));
result.M21 = Scalar.Subtract(Scalar.Subtract(xy, Scalar.Multiply(ca, xy)), Scalar.Multiply(sa, z));
result.M22 = Scalar.Add(yy, Scalar.Multiply(ca, Scalar.Subtract(Scalar <T> .One, yy)));
result.M23 = Scalar.Add(Scalar.Subtract(yz, Scalar.Multiply(ca, yz)), Scalar.Multiply(sa, x));
return(result);
}
/// <summary>Transforms the given matrix by applying the given Quaternion rotation.</summary>
/// <param name="value">The source matrix to transform.</param>
/// <param name="rotation">The rotation to apply.</param>
/// <returns>The transformed matrix.</returns>
public static Matrix2X3 <T> Transform <T>(Matrix2X3 <T> value, Quaternion <T> rotation)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
// Compute rotation matrix.
T x2 = Scalar.Add(rotation.X, rotation.X);
T y2 = Scalar.Add(rotation.Y, rotation.Y);
T z2 = Scalar.Add(rotation.Z, rotation.Z);
T wx2 = Scalar.Multiply(rotation.W, x2);
T wy2 = Scalar.Multiply(rotation.W, y2);
T wz2 = Scalar.Multiply(rotation.W, z2);
T xx2 = Scalar.Multiply(rotation.X, x2);
T xy2 = Scalar.Multiply(rotation.X, y2);
T xz2 = Scalar.Multiply(rotation.X, z2);
T yy2 = Scalar.Multiply(rotation.Y, y2);
T yz2 = Scalar.Multiply(rotation.Y, z2);
T zz2 = Scalar.Multiply(rotation.Z, z2);
T q11 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, yy2), zz2);
T q21 = Scalar.Subtract(xy2, wz2);
T q31 = Scalar.Add(xz2, wy2);
T q12 = Scalar.Add(xy2, wz2);
T q22 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, xx2), zz2);
T q32 = Scalar.Subtract(yz2, wx2);
T q13 = Scalar.Subtract(xz2, wy2);
T q23 = Scalar.Add(yz2, wx2);
T q33 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, xx2), yy2);
var q1 = new Vector3D <T>(q11, q12, q13);
var q2 = new Vector3D <T>(q21, q22, q23);
var q3 = new Vector3D <T>(q31, q32, q33);
return(new(value.M11 * q1 + value.M12 * q2 + value.M13 * q3, value.M21 *q1 + value.M22 * q2 + value.M23 * q3));
}
public static Matrix2X3 <T> Multiply <T>(Matrix2X3 <T> value1, Matrix3X3 <T> value2)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> value1 * value2;
public static Matrix2X3 <T> Add <T>(Matrix2X3 <T> value1, Matrix2X3 <T> value2)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
return(value1 + value2);
}
/// <summary>Linearly interpolates between the corresponding values of two matrices.</summary>
/// <param name="matrix1">The first source matrix.</param>
/// <param name="matrix2">The second source matrix.</param>
/// <param name="amount">The relative weight of the second source matrix.</param>
/// <returns>The interpolated matrix.</returns>
public static unsafe Matrix2X3 <T> Lerp <T>(Matrix2X3 <T> matrix1, Matrix2X3 <T> matrix2, T amount)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
return(new(Vector3D.Lerp(matrix1.Row1, matrix2.Row2, amount), Vector3D.Lerp(matrix1.Row2, matrix2.Row2, amount)));
}
public static Matrix2X3 <T> Subtract <T>(Matrix2X3 <T> value1, Matrix2X3 <T> value2)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> value1 - value2;
public static Matrix2X3 <T> Negate <T>(Matrix2X3 <T> value)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> - value;
