public static ProjectiveTransform2 operator *(ProjectiveTransform2 T1, ProjectiveTransform2 T2)
{
ProjectiveTransform2 S = new ProjectiveTransform2();
S.mat = MatrixTransform2.MatrixProduct(T1.mat, T2.mat);
return(S);
}
public ProjectiveTransform2 InverseTransform()
{
double[,] m = MatrixInverse(mat);
ProjectiveTransform2 T = new ProjectiveTransform2();
T.mat = m;
return(T);
}
public static ProjectiveTransform2 PointsToPoints(
Point p0, Point p1, Point p2, Point p3,
Point q0, Point q1, Point q2, Point q3)
{
ProjectiveTransform2 Step1 = StandardFrameToPoints(p0, p1, p2, p3).InverseTransform();
ProjectiveTransform2 Step2 = StandardFrameToPoints(q0, q1, q2, q3);
return(Step2 * Step1);
}
public static ProjectiveTransform2 RotateAboutPoint(Point p, double angle)
{
Point origin = new Point();
ProjectiveTransform2 T1 = Translate(origin - p);
ProjectiveTransform2 T2 = RotateXY(angle);
ProjectiveTransform2 T3 = Translate(p - origin);
return(T3 * T2 * T1);
}
public static ProjectiveTransform2 AxisScale(double xamount, double yamount)
{
AffineTransform2 T = AffineTransform2.AxisScale(xamount, yamount);
ProjectiveTransform2 T2 = new ProjectiveTransform2();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
public static ProjectiveTransform2 Translate(Point p, Point q)
{
AffineTransform2 T = AffineTransform2.Translate(p, q);
ProjectiveTransform2 T2 = new ProjectiveTransform2();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
public static ProjectiveTransform2 Translate(Vector v)
{
AffineTransform2 T = AffineTransform2.Translate(v);
ProjectiveTransform2 T2 = new ProjectiveTransform2();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
public static ProjectiveTransform2 RotateXY(double angle)
{
AffineTransform2 T = AffineTransform2.RotateXY(angle);
ProjectiveTransform2 T2 = new ProjectiveTransform2();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
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);
}