/// <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);
}
