public static ProjectiveTransform2 operator *(ProjectiveTransform2 T1, ProjectiveTransform2 T2)
{
ProjectiveTransform2 S = new ProjectiveTransform2();
S.mat = MatrixTransform2.MatrixProduct(T1.mat, T2.mat);
return(S);
}
/// <summary>
/// Return the inverse of this transformation, if it's invertible.
/// <returns>The inverse transform. </returns>
/// </summary>
public ProjectiveTransform2 InverseTransform()
{
double[,] m = MatrixInverse(mat);
ProjectiveTransform2 T = new ProjectiveTransform2();
T.mat = m;
return(T);
}
/// <summary>
/// Construct a scaling transformation of the form (x, y) -> (ax, by)
/// <param name="xamount">The multiplier for x-coordinates.</param>
/// <param name="yamount">The multiplier for y-coordinates.</param>
/// <returns>The scaling transform. </returns>
/// <remarks>Note that if the two scale amounts are equal, the transformation has no effect, when regarded in homogeneous coordinates. </remarks>
/// </summary>
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);
}
/// <summary>
/// Construct a translation that displaces the Point p to the Point q
/// <param name="P">A point that will be translated.</param>
/// <param name="Q">The point where P will end up after translation.</param>
/// <returns>The translation transform. </returns>
/// </summary>
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);
}
/// <summary>
/// Construct a translation that displaces any point by the amount specified by the vector "v"
/// <param name="v">The displacement vector</param>
/// <returns>The translation transform. </returns>
/// </summary>
public static ProjectiveTransform2 Translate(Vector v)
{
AffineTransform2 T = AffineTransform2.Translate(v);
ProjectiveTransform2 T2 = new ProjectiveTransform2();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
/// <summary>
/// Construct a rotation that moves the positive X-axis towards the postive Y-axis by an amount "angle".
/// <param name="angle">The rotation amount, in radians</param>
/// </summary>
public static ProjectiveTransform2 RotateXY(double angle)
{
AffineTransform2 T = AffineTransform2.RotateXY(angle);
ProjectiveTransform2 T2 = new ProjectiveTransform2();
T2.mat = T.mat;
T.mat = null;
return(T2);
}
/// <summary>
/// Build the unique transformation taking four independent points to any four other points.
/// <param name="p0">The 0th point to be moved</param>
/// <param name="p1">The 1st point to be moved</param>
/// <param name="p2">The 2nd point to be moved</param>
/// <param name="p3">The 3rd point to be moved</param>
/// <param name="q0">The point to which p0 will be moved</param>
/// <param name="q1">The point to which p1 will be moved</param>
/// <param name="q2">The point to which p2 will be moved</param>
/// <param name="q3">The point to which p3 will be moved</param>
/// <returns>The projective transform. </returns>
/// </summary>
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);
}
/// <summary>
/// Construct a rotation by amount "angle" around the point "p". The resulting transformation leaves "p" unmoved.
/// <param name="p">The center point for the rotation.</param>
/// <param name="angle">The rotation angle, in radians.</param>
/// <returns>The rotation transform. </returns>
/// </summary>
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);
}
/// <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);
}
private static void testPT()
{
Debug.Print(new ProjectiveTransform2() + "\n should be identity\n");
Vector v1 = new Vector(2, 3); Vector v2 = new Vector(-1, 4);
Point p1 = new Point(1, 5);
Point p2 = new Point(1, 1);
Point p3 = new Point(4, 4);
Point p4 = new Point(2, 5);
Point q1 = new Point(1, 1);
Point q2 = new Point(0, 0);
Point q3 = new Point(1, 2);
Point q4 = new Point(-1, 0);
Point pt = p1 + 0.5 * (p2 - p1);
Point qt = q1 + 0.5 * (q2 - q1);
ProjectiveTransform2 T1 = ProjectiveTransform2.Translate(p1, q1);
Debug.Print("T1:" + T1 * p1 + "\n should be " + q1 + "\n");
ProjectiveTransform2 T3 = ProjectiveTransform2.RotateXY(30 * Math.PI / 180);
LinearTransform2 T4 = LinearTransform2.RotateXY(30 * Math.PI / 180);
Debug.Print("T3,4:" + T3 + "\n should equal " + T4 + "\n");
ProjectiveTransform2 T5 = ProjectiveTransform2.AxisScale(2, -3);
Debug.Print("T5:" + T5 + "\n should be [2 0 ; 0 -3]\n");
ProjectiveTransform2 T6 = ProjectiveTransform2.RotateAboutPoint(p1, 30 * Math.PI / 180);
Debug.Print("T6:" + T6 * p1 + "\n should be " + p1 + "\n");
ProjectiveTransform2 T2 = ProjectiveTransform2.PointsToPoints(p1, p2, p3, p4, q1, q2, q3, q4);
Debug.Print("T2:" + T2 * (p1 + 0.5 * (p2 - p1)) + "\n should be " + (q1 + 0.5 * (q2 - q1)) + "\n");
Debug.Print("T2:" + T2 * p1 + "\n should be " + q1 + "\n");
Debug.Print("T2:" + T2 * p2 + "\n should be " + q2 + "\n");
Debug.Print("T2:" + T2 * p3 + "\n should be " + q3 + "\n");
Debug.Print("T2:" + T2 * p4 + "\n should be " + q4 + "\n");
Debug.Print("InverseTransform:" + T2.InverseTransform() * q4 + "\n should be " + p4 + "\n");
Debug.Print("Composition:" + T2.InverseTransform() * T2 + "\n should be identity\n");
}
