public static LinearTransform2 VectorsToVectors(Vector v1, Vector v2, Vector w1, Vector w2)
{
LinearTransform2 V = new LinearTransform2(v1, v2);
LinearTransform2 W = new LinearTransform2(w1, w2);
return(W * V.InverseTransform());
}
public static LinearTransform2 operator *(LinearTransform2 T1, LinearTransform2 T2)
{
LinearTransform2 S = new LinearTransform2();
S.mat = MatrixProduct(T1.mat, T2.mat);
return(S);
}
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;
*/
}
public LinearTransform2 InverseTransform()
{
double[,] m = MatrixInverse(mat);
LinearTransform2 T = new LinearTransform2();
T.mat = m;
return(T);
}
public static LinearTransform2 RotateXY(double angle)
{
LinearTransform2 T = new LinearTransform2();
T.mat[0, 0] = Math.Cos(angle);
T.mat[1, 1] = T.mat[0, 0];
T.mat[1, 0] = Math.Sin(angle);
T.mat[0, 1] = -T.mat[1, 0];
return(T);
}
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);
}
new private static double[,] MatrixInverse(double[,] mat)
{
double[] translation = new double[3];
translation[0] = mat[0, 2];
translation[1] = mat[1, 2];
translation[2] = 1.0d;
double[,] mm = new double[3, 3];
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
mm[i, j] = mat[i, j];
}
}
mm[2, 2] = 1.0d;
double[,] minv = LinearTransform2.MatrixInverse(mm);
double[] reverseTranslation = new double[3];
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
reverseTranslation[i] -= minv[i, j] * translation[j];
}
}
reverseTranslation[2] = 1.0d;
double[,] res = new double[3, 3];
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
res[i, j] = minv[i, j];
}
res[i, 2] = reverseTranslation[i];
}
res[2, 2] = 1.0d;
return(res);
}