private void applyTransformationToolStripMenuItem_Click(object sender, EventArgs e)
{
//Matriz A:
// 2x1x2 + 2y1y2
// -2x2y1 + 2y2x1
// 2x1
// 2y1
//Matrix B:
//(2x2**2 + 2y2**2) 0 2x2 2y2
//0 (2x2**2 - 2y2**2) 2y2 -2x2
//2x2 2y2 2 0
//2y2 2x2 0 2
double[][] A = new double[1][];
A[0] = new double[4];
A[0][0] = 0; A[0][1] = 0; A[0][2] = 0; A[0][3] = 0;
Point[] shape1 = Shape1.ToArray();
Point[] shape2 = Shape2.ToArray();
int length = shape1.Length;
for (int i = 0; i < length; i++)
{
double a1 = (2 * shape1[i].X * shape2[i].X) + (2 * shape1[i].Y * shape2[i].Y);
double a2 = ((-2) * shape1[i].Y * shape2[i].X) + (2 * shape1[i].X * shape2[i].Y);
double a3 = (2 * shape1[i].X);
double a4 = (2 * shape1[i].Y);
A[0][0] += a1; A[0][1] += a2; A[0][2] += a3; A[0][3] += a4;
}
double[][] B = new double[4][];
for (int x = 0; x < 4; x++)
{
B[x] = new double[4];
B[x][0] = 0; B[x][1] = 0; B[x][2] = 0; B[x][3] = 0;
}
int length2 = shape2.Length;
for (int i = 0; i < length2; i++)
{
double b1b1 = (2 * shape2[i].X * shape2[i].X) + (2 * shape2[i].Y * shape2[i].Y);
double b1b2 = 0;
double b1b3 = (2 * shape2[i].X);
double b1b4 = (2 * shape2[i].Y);
double b2b1 = 0;
double b2b2 = (2 * shape2[i].X * shape2[i].X) - (2 * shape2[i].Y * shape2[i].Y);
double b2b3 = (2 * shape2[i].Y);
double b2b4 = ((-2) * shape2[i].Y);
double b3b1 = (2 * shape2[i].X);
double b3b2 = (2 * shape2[i].Y);
double b3b3 = 2;
double b3b4 = 0;
double b4b1 = (2 * shape2[i].Y);
double b4b2 = (2 * shape2[i].X);
double b4b3 = 0;
double b4b4 = 2;
B[0][0] += b1b1; B[0][1] += b1b2; B[0][2] += b1b3; B[0][3] += b1b4;
B[1][0] += b2b1; B[1][1] += b2b2; B[1][2] += b2b3; B[1][3] += b2b4;
B[2][0] += b3b1; B[2][1] += b3b2; B[2][2] += b3b3; B[2][3] += b3b4;
B[3][0] += b4b1; B[3][1] += b4b2; B[3][2] += b4b3; B[3][3] += b4b4;
}
//names may be inverted
PCALib.Matrix matrixA = new PCALib.Matrix(A);
PCALib.Matrix matrixB = new PCALib.Matrix(B);
PCALib.Matrix matrixATrans = (PCALib.Matrix)matrixA.Transpose();
PCALib.Matrix matrixBInv = (PCALib.Matrix)matrixB.Inverse;
Debug.Print("Matrix A (Transpose): ");
Debug.Print(matrixATrans.ToString());
Debug.Print("Matrix B: ");
Debug.Print(matrixB.ToString());
PCALib.Matrix matrixTransformationValues = (PCALib.Matrix)matrixBInv.Multiply(matrixATrans);
Debug.Print("Matrix Transformation: ");
Debug.Print(matrixTransformationValues.ToString());
Transformation T2 = new Transformation();
T2.A = matrixTransformationValues[0, 0];
T2.B = matrixTransformationValues[1, 0];
T2.T1 = matrixTransformationValues[2, 0];
T2.T2 = matrixTransformationValues[3, 0];
Shape2 = ApplyTransformation(T2, Shape2);
Pen pRed = new Pen(Brushes.Red, 1);
Pen pBlack = new Pen(Brushes.Black, 1);
Graphics g = panShape2.CreateGraphics();
DisplayShape(Shape1, pRed, g);
DisplayShape(Shape2, pBlack, g);
return;
}
private void applyTransformation2ToolStripMenuItem_Click(object sender, EventArgs e)
{
List <Point> new_shape = new List <Point>();
double[][] A = new double[1][];
A[0] = new double[4];
double[][] B = new double[4][];
for (int x = 0; x < 4; x++)
{
B[x] = new double[4];
}
Point[] shape1 = Shape1.ToArray();
Point[] shape2 = Shape2.ToArray();
int length = shape1.Length;
for (int i = 0; i < length; i++)
{
A[0][0] = (2 * shape1[i].X * shape2[i].X) + (2 * shape1[i].Y * shape2[i].Y);
A[0][1] = ((-2) * shape1[i].Y * shape2[i].X) + (2 * shape1[i].X * shape2[i].Y);
A[0][2] = (2 * shape1[i].X);
A[0][3] = (2 * shape1[i].Y);
B[0][0] = (2 * shape2[i].X * shape2[i].X) + (2 * shape2[i].Y * shape2[i].Y);
B[0][0] = 0;
B[0][0] = (2 * shape2[i].X);
B[0][0] = (2 * shape2[i].Y);
B[1][0] = 0;
B[1][1] = (2 * shape2[i].X * shape2[i].X) - (2 * shape2[i].Y * shape2[i].Y);
B[1][2] = (2 * shape2[i].Y);
B[1][3] = ((-2) * shape2[i].Y);
B[2][0] = (2 * shape2[i].X);
B[2][1] = (2 * shape2[i].Y);
B[2][2] = 2;
B[2][3] = 0;
B[3][0] = (2 * shape2[i].Y);
B[3][1] = (2 * shape2[i].X);
B[3][2] = 0;
B[3][3] = 2;
PCALib.Matrix matrixA = new PCALib.Matrix(A);
PCALib.Matrix matrixB = new PCALib.Matrix(B);
PCALib.Matrix matrixATrans = (PCALib.Matrix)matrixA.Transpose();
PCALib.Matrix matrixBInv = (PCALib.Matrix)matrixB.Inverse;
PCALib.Matrix matrixTransformationValues = (PCALib.Matrix)matrixBInv.Multiply(matrixATrans);
Transformation T2 = new Transformation();
T2.A = matrixTransformationValues[0, 0];
T2.B = matrixTransformationValues[1, 0];
T2.T1 = matrixTransformationValues[2, 0];
T2.T2 = matrixTransformationValues[3, 0];
int X = (int)((T2.A * shape2[i].X) + (T2.B * shape2[i].Y) + T2.T1);
int Y = (int)(((-1) * T2.B * shape2[i].X) + (T2.A * shape2[i].Y) + T2.T2);
shape2[i].X = X;
shape2[i].Y = Y;
Debug.Print("Point " + i + ": " + shape2[i].X + ", " + shape2[i].Y);
new_shape.Add(shape2[i]);
}
Pen pRed = new Pen(Brushes.Red, 1);
Pen pBlack = new Pen(Brushes.Blue, 1);
Graphics g = panShape2.CreateGraphics();
DisplayShape(Shape1, pRed, g);
DisplayShape(new_shape, pBlack, g);
return;
}