/// <summary>
/// Calculates the inverse matrix using Householder transformations
/// </summary>
public static M22d QrInverse(this M22d mat)
{
var qr = new Matrix <double>((double[])mat, 2, 2);
var diag = qr.QrFactorize();
return((M22d)(qr.QrInverse(diag).Data));
}
/// <summary>
/// Multiplacation of a <see cref="Scale3d"/> with a <see cref="M22d"/>.
/// </summary>
public static M33d Multiply(Scale3d scale, M22d mat)
{
return(new M33d(scale.X * mat.M00,
scale.X * mat.M01,
0,
scale.Y * mat.M10,
scale.Y * mat.M11,
0,
0,
0,
scale.Z));
}
//WARNING: untested
public static Rot2d FromM22d(M22d m)
{
// cos(a) sin(a)
//-sin(a) cos(a)
if (m.M00 >= -1.0 && m.M00 <= 1.0)
{
return(new Rot2d((double)System.Math.Acos(m.M00)));
}
else
{
throw new ArgumentException("Given M22d is not a Rotation-Matrix");
}
}
/// <summary>
/// </summary>
public static M33d operator *(Euclidean3d r3, Rot2d r2)
{
M33d m33 = (M33d)r3;
M22d m22 = (M22d)r2;
return(new M33d(
m33.M00 * m22.M00 + m33.M01 * m22.M10,
m33.M00 * m22.M01 + m33.M01 * m22.M11,
m33.M02,
m33.M10 * m22.M00 + m33.M11 * m22.M10,
m33.M10 * m22.M01 + m33.M11 * m22.M11,
m33.M12,
m33.M20 * m22.M00 + m33.M21 * m22.M10,
m33.M20 * m22.M01 + m33.M21 * m22.M11,
m33.M22
));
}
/// <summary>
/// Returns new array containing transformed points.
/// </summary>
public static V2d[] Transformed(this V2d[] pointArray, M22d m)
{
return(new V2d[pointArray.LongLength].SetByIndexLong(i => m.Transform(pointArray[i])));
}
public static M23d Multiply(M22d m, Euclidean2d r)
{
return(M23d.Multiply(m, (M23d)r));
}
/// <summary>
/// Creates a rigid transformation from a rotation matrix <paramref name="rot"/> and a (subsequent) translation <paramref name="trans"/>.
/// </summary>
public Euclidean2d(M22d rot, V2d trans)
{
Rot = Rot2d.FromM22d(rot);
Trans = trans;
}
public static M22d Multiply(Rot2d rot, M22d mat)
{
return((M22d)rot * mat);
}