/// <summary>
/// Given a point p1 and linearly independent vectors v1 and v2, build the unique transformation taking p1 to q1, v1 to w1, and v2 to w2.
/// <param name="p1">The point to be moved</param>
/// <param name="v1">The first vector</param>
/// <param name="v2">The second vector</param>
/// <param name="q1">The point to which p1 will be moved</param>
/// <param name="w1">The vector to which v1 will be moved</param>
/// <param name="w2">The vector to which v2 will be moved</param>
/// <returns>The affine transform. </returns>
/// </summary>
public static AffineTransform2 PointAndVectorsToPointAndVectors(
Point p1, Vector v1, Vector v2,
Point q1, Vector w1, Vector w2)
{
AffineTransform2 Trans1 = AffineTransform2.Translate(p1, new Point(0, 0));
LinearTransform2 T = LinearTransform2.VectorsToVectors(v1, v2, w1, w2);
AffineTransform2 Trans2 = AffineTransform2.Translate(new Point(0, 0), q1);
AffineTransform2 S = new AffineTransform2();
S.mat = T.Matrix();
return(Trans2 * S * Trans1);
/*
* double[,] linmat = T.Matrix();
* for (int i = 0; i < 2; i++)
* {
* for (int j = 0; j < 2; j++)
* {
* W.mat[i, j] = linmat[i, j];
* }
* }
* return W;
*/
}
private static void testLT()
{
// Results: inverse is broken for LinearTransform; otherwise OK.
Debug.Print(new LinearTransform2() + "\nshould be identity\n");
Vector v1 = new Vector(2, 3); Vector v2 = new Vector(-1, 4);
LinearTransform2 T1 = new LinearTransform2(v1, v2);
Debug.Print(T1 + "\nshould be 2, -1; 3 4.\n");
Debug.Print(T1.Det() + "\n should be 11; " + T1.Trace() + "\nshould be 6\n");
Vector w1 = new Vector(0, 1); Vector w2 = new Vector(1, 1);
LinearTransform2 Tvw = LinearTransform2.VectorsToVectors(v1, v2, w1, w2);
LinearTransform2 T30 = LinearTransform2.RotateXY(30 * Math.PI / 180.0);
LinearTransform2 Ti = T1.InverseTransform();
Debug.Print(T30 + "\nshould be Rot30; lower left = 0.5\n");
Debug.Print(Ti * v1 + "\nshould be e1\n");
Debug.Print(Ti * v2 + "\nshould be e2\n");
Debug.Print(T1 * T1 + "\nshould be [1 -6; 18 13]\n");
Debug.Print(T1 * Ti + "\n should be identity\n");
}