/// <summary> /// Build a transformation taking the standard frame (0,0), (1, 0), (0, 1), and (1, 1) to the points /// p0, p1, p2, and p3. /// </summary> /// <param name="p0">Where (0, 0) is sent</param> /// <param name="p1">Where (1, 0) is sent</param> /// <param name="p2">Where (0, 1) is sent</param> /// <param name="p3">Where (1, 1) is sent</param> /// <returns>The projective transformation effecting the specified mappings</returns> public static ProjectiveTransform2 StandardFrameToPoints(Point p0, Point p1, Point p2, Point p3) { // ProjectiveTransform2 T = new ProjectiveTransform2(); // idea: // Send e1, e2, e3 to p0, p1, p2 by a map K. // Let L be Kinverse. // Then L sends p0, p1, p2 to e1, e2 and e3 . See where p4 goes; call this q. // build projective map P sending e1, e2, e3, and u= (e1+e2+e3) to e1, e2, e3, and q. // then let L = Kinverse; K * P sends e1 to p1; e2 to p2; e3 to p3; and u to q to e4. ProjectiveTransform2 K = new ProjectiveTransform2(); for (int i = 0; i < 3; i++) { K.mat[2, i] = 1.0d; } K.mat[0, 0] = p0.X; K.mat[1, 0] = p0.Y; K.mat[0, 1] = p1.X; K.mat[1, 1] = p1.Y; K.mat[0, 2] = p2.X; K.mat[1, 2] = p2.Y; ProjectiveTransform2 L = new ProjectiveTransform2(); L.mat = LinearTransform2.MatrixInverse(K.mat); double[] v = new double[3]; v[0] = p3.X; v[1] = p3.Y; v[2] = 1.0d; double[] q = new double[3]; for (int i = 0; i < 3; i++) { double tally = 0.0d; for (int j = 0; j < 3; j++) { tally += L.mat[i, j] * v[j]; } q[i] = tally; } double[,] p = new double[3, 3]; for (int i = 0; i < 3; i++) { p[i, i] = q[i]; } ProjectiveTransform2 S = new ProjectiveTransform2(); S.mat = ProjectiveTransform2.MatrixProduct(K.mat, p); return(S); }