/// <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"); }