/// <summary>
/// Multiplies transformation matrix
/// </summary>
/// <param name="matrix">Matrix to multiply with</param>
/// <returns>Resulting matrix</returns>
public TransformMatrix Multiply(TransformMatrix matrix)
=> new TransformMatrix(
(M11 * matrix.M11) + (M12 * matrix.M21) + (M13 * matrix.M31) + (M14 * matrix.M41),
(M11 * matrix.M12) + (M12 * matrix.M22) + (M13 * matrix.M32) + (M14 * matrix.M42),
(M11 * matrix.M13) + (M12 * matrix.M23) + (M13 * matrix.M33) + (M14 * matrix.M43),
(M11 * matrix.M14) + (M12 * matrix.M24) + (M13 * matrix.M34) + (M14 * matrix.M44),
(M21 * matrix.M11) + (M22 * matrix.M21) + (M23 * matrix.M31) + (M24 * matrix.M41),
(M21 * matrix.M12) + (M22 * matrix.M22) + (M23 * matrix.M32) + (M24 * matrix.M42),
(M21 * matrix.M13) + (M22 * matrix.M23) + (M23 * matrix.M33) + (M24 * matrix.M43),
(M21 * matrix.M14) + (M22 * matrix.M24) + (M23 * matrix.M34) + (M24 * matrix.M44),
(M31 * matrix.M11) + (M32 * matrix.M21) + (M33 * matrix.M31) + (M34 * matrix.M41),
(M31 * matrix.M12) + (M32 * matrix.M22) + (M33 * matrix.M32) + (M34 * matrix.M42),
(M31 * matrix.M13) + (M32 * matrix.M23) + (M33 * matrix.M33) + (M34 * matrix.M43),
(M31 * matrix.M14) + (M32 * matrix.M24) + (M33 * matrix.M34) + (M34 * matrix.M44),
(M41 * matrix.M11) + (M42 * matrix.M21) + (M43 * matrix.M31) + (M44 * matrix.M41),
(M41 * matrix.M12) + (M42 * matrix.M22) + (M43 * matrix.M32) + (M44 * matrix.M42),
(M41 * matrix.M13) + (M42 * matrix.M23) + (M43 * matrix.M33) + (M44 * matrix.M43),
(M41 * matrix.M14) + (M42 * matrix.M24) + (M43 * matrix.M34) + (M44 * matrix.M44));
/// <summary>
/// Create rotation transformation around axis
/// </summary>
/// <param name="axis">Axis to generate rotation about</param>
/// <param name="angle">Angle in radians</param>
/// <param name="point">Anchor point of the rotation</param>
/// <returns>Transformation matrix</returns>
public static TransformMatrix CreateFromRotationAroundAxis(Vector axis, double angle, Point point)
{
var s = Math.Sin(angle);
var c = Math.Cos(angle);
var normVec = axis.Normalize();
var x = normVec.X;
var y = normVec.Y;
var z = normVec.Z;
var xx = x * x;
var yy = y * y;
var zz = z * z;
var xy = x * y;
var xz = x * z;
var yz = y * z;
var matrix = new TransformMatrix(
xx + c * (1.0 - xx), xy - c * xy + s * z, xz - c * xz - s * y, 0.0,
xy - c * xy - s * z, yy + c * (1.0 - yy), yz - c * yz + s * x, 0.0,
xz - c * xz + s * y, yz - c * yz - s * x, zz + c * (1.0 - zz), 0.0,
0.0, 0.0, 0.0, 1.0);
if (Math.Abs(point.X) > double.Epsilon ||
Math.Abs(point.Y) > double.Epsilon ||
Math.Abs(point.Z) > double.Epsilon)
{
var translateMatrix = CreateFromTranslation(point.ToVector());
var translateMatrixInv = CreateFromTranslation(point.ToVector() * -1);
matrix = translateMatrixInv.Multiply(matrix).Multiply(translateMatrix);
}
return(matrix);
}
/// <summary>
/// Transforms this vector with the transformation matrix
/// </summary>
/// <param name="matrix">Transformation matrix</param>
/// <returns>Transformed vector</returns>
public new Vector Transform(TransformMatrix matrix)
=> new Vector(
X * matrix.M11 + Y * matrix.M21 + Z * matrix.M31,
X * matrix.M12 + Y * matrix.M22 + Z * matrix.M32,
X * matrix.M13 + Y * matrix.M23 + Z * matrix.M33);
/// <summary> /// Gets the transformation of this plane relative to the global XYZ /// </summary> /// <param name="plane">Plane</param> /// <returns>Transformation matrix</returns> public static TransformMatrix GetTransformation(this Plane plane) => TransformMatrix.Compose(plane.Direction, plane.Reference, plane.Normal, plane.Point);
