public static ProjectiveTransform3 operator *(ProjectiveTransform3 T1, ProjectiveTransform3 T2)
{
ProjectiveTransform3 S = new ProjectiveTransform3();
S.mat = MatrixTransform3.MatrixProduct(T1.mat, T2.mat);
return(S);
}
public ProjectiveTransform3 InverseTransform()
{
double[,] m = MatrixInverse(mat);
ProjectiveTransform3 T = new ProjectiveTransform3();
T.mat = mat;
return(T);
}
public static ProjectiveTransform3 PointsToPoints(
Point3D p0, Point3D p1, Point3D p2, Point3D p3, Point3D p4,
Point3D q0, Point3D q1, Point3D q2, Point3D q3, Point3D q4)
{
ProjectiveTransform3 Step1 = StandardFrameToPoints(p0, p1, p2, p3, p4).InverseTransform();
ProjectiveTransform3 Step2 = StandardFrameToPoints(q0, q1, q2, q3, q4);
return(Step2 * Step1);
}
public static ProjectiveTransform3 AxisScale(double xamount, double yamount, double zamount)
{
AffineTransform3 T = AffineTransform3.AxisScale(xamount, yamount, zamount);
ProjectiveTransform3 T2 = new ProjectiveTransform3();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
public static ProjectiveTransform3 Translate(Point3D p, Point3D q)
{
AffineTransform3 T = AffineTransform3.Translate(p, q);
ProjectiveTransform3 T2 = new ProjectiveTransform3();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
public static ProjectiveTransform3 Translate(Vector3D v)
{
AffineTransform3 T = AffineTransform3.Translate(v);
ProjectiveTransform3 T2 = new ProjectiveTransform3();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
public static ProjectiveTransform3 RotateZX(double angle)
{
AffineTransform3 T = AffineTransform3.RotateZX(angle);
ProjectiveTransform3 T2 = new ProjectiveTransform3();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
private static ProjectiveTransform3 StandardFrameToPoints(Point3D p0, Point3D p1, Point3D p2, Point3D p3, Point3D p4)
{
//
ProjectiveTransform3 T = new ProjectiveTransform3();
// idea: send p0, p1, p2, and p3 to e1, e2, e3 and e4 by an linear transformation K of R^3; see where p4 goes; call this q.
// build projective map P sending e1, e2, e3, e4, and u= (e1+e2+e3) to e1, e2, e3, d4, and q.
// then let L = Kinverse; K * P sends e1 to p1; e2 to p2; e3 to p3; e4 to p4, and u to q to e4.
ProjectiveTransform3 K = new ProjectiveTransform3();
for (int i = 0; i < 4; i++)
{
K.mat[3, i] = 1.0d;
}
K.mat[0, 0] = p0.X;
K.mat[1, 0] = p0.Y;
K.mat[2, 0] = p0.Z;
K.mat[0, 1] = p1.X;
K.mat[1, 1] = p1.Y;
K.mat[2, 1] = p1.Z;
K.mat[0, 2] = p2.X;
K.mat[1, 2] = p2.Y;
K.mat[2, 2] = p2.Z;
K.mat[0, 3] = p3.X;
K.mat[1, 3] = p3.Y;
K.mat[2, 3] = p3.Z;
ProjectiveTransform3 L = new ProjectiveTransform3();
L.mat = LinearTransform3.MatrixInverse(K.mat);
double[] v = new double[3];
v[0] = p3.X;
v[1] = p3.Y;
v[2] = p4.Z;
v[3] = 1.0d;
double[] q = new double[4];
for (int i = 0; i < 4; i++)
{
double tally = 0.0d;
for (int j = 0; j < 4; j++)
{
tally += L.mat[i, j] * v[j];
}
q[i] = tally;
}
double[,] p = new double[4, 4];
for (int i = 0; i < 4; i++)
{
p[i, i] = q[i];
}
ProjectiveTransform3 S = new ProjectiveTransform3();
S.mat = ProjectiveTransform3.MatrixProduct(p, K.mat);
return(S);
}
