internal static HomogenMatrix3 ConvertMatrixToHomogenMatrix3(double[,] matrix)
{
HomogenMatrix3 m = new HomogenMatrix3();
if (matrix != null)
{
try
{
var HomogenMatrix3Type = typeof(HomogenMatrix3);
var HomogenMatrixLine3Type = typeof(HomogenMatrixLine3);
for (int i = 0; i < 3 && i < matrix.GetLength(0); i++)
{
var lineField = HomogenMatrix3Type.GetField("Line" + (i + 1));
if (lineField != null)
{
HomogenMatrixLine3 line = lineField.GetValue(m) as HomogenMatrixLine3;
for (int j = 0; j < 3 && j < matrix.GetLength(1); j++)
{
var colField = HomogenMatrixLine3Type.GetField("Column" + (j + 1));
if (colField != null)
{
colField.SetValue(line, matrix[i, j]);
}
}
}
}
}
catch (System.Exception) { }
}
return m;
}
/// <summary>
/// Applies an affine transformation, given by the transformation matrix to a given rectangle.
/// The resulting bounding box might be larger than the original rectangle if the object is rotated.
/// </summary>
/// <param name="rect">The original bounding rectangle.</param>
/// <param name="homogenMatrix">The transformation matrix.</param>
/// <returns>The bounding box of the transformed rectangle.</returns>
internal static Rectangle TransformBoundingBox(Rectangle rect, HomogenMatrix3 homogenMatrix)
{
// transform all corners
// p1 p2
// ┌────────┐
// │ │
// └────────┘
// p3 p4
Point p1 = Transform(new Point(rect.X, rect.Y), homogenMatrix);
Point p2 = Transform(new Point(rect.X + rect.Width, rect.Y), homogenMatrix);
Point p3 = Transform(new Point(rect.X + rect.Width, rect.Y + rect.Height), homogenMatrix);
Point p4 = Transform(new Point(rect.X, rect.Y + rect.Height), homogenMatrix);
int minX = Math.Min(Math.Min(Math.Min(p1.X, p2.X), p3.X), p4.X);
int maxX = Math.Max(Math.Max(Math.Max(p1.X, p2.X), p3.X), p4.X);
int minY = Math.Min(Math.Min(Math.Min(p1.Y, p2.Y), p3.Y), p4.Y);
int maxY = Math.Max(Math.Max(Math.Max(p1.Y, p2.Y), p3.Y), p4.Y);
return new Rectangle(minX, minY, maxX - minX, maxY - minY);
}
internal static double[,] ConvertHomogenMatrix3ToMatrix(HomogenMatrix3 transformProp)
{
// initialization of a two dimensional array
// matrix [m,n] = array[rows,cols] or array[y,x]
// concatenation of row initializations
// build the standard basis for a transformation matrix
// 1 0 0
// 0 1 0
// 0 0 1
double[,] matrix = new double[,] { { 1.0, 0.0, 0.0 }, { 0.0, 1.0, 0.0 }, { 0.0, 0.0, 1.0 } };
if (transformProp != null)
{
if (transformProp.Line1 != null)
{
matrix[0, 0] = transformProp.Line1.Column1;
matrix[0, 1] = transformProp.Line1.Column2;
matrix[0, 2] = transformProp.Line1.Column3;
}
if (transformProp.Line2 != null)
{
matrix[1, 0] = transformProp.Line2.Column1;
matrix[1, 1] = transformProp.Line2.Column2;
matrix[1, 2] = transformProp.Line2.Column3;
}
if (transformProp.Line3 != null)
{
matrix[2, 0] = transformProp.Line3.Column1;
matrix[2, 1] = transformProp.Line3.Column2;
matrix[2, 2] = transformProp.Line3.Column3;
}
}
return matrix;
}
/// <summary>
/// Applies an affine transformation, given by the transformation matrix to a given coordinate
/// </summary>
/// <param name="pos">The original coordinate.</param>
/// <param name="homogenMatrix">The transformation matrix.</param>
/// <returns>The transformed matrix.</returns>
internal static Point Transform(Point pos, HomogenMatrix3 homogenMatrix)
{
// x' = a11 * x + a12 * y + a13
// y' = a21 * x + a22 * y + a23
// a31 a32 a33 // 3rd line is only to allow matrix inversion, has no additional information, should always be [0, 0, 1]
return new Point(
(int)(homogenMatrix.Line1.Column1 * pos.X + homogenMatrix.Line1.Column2 * pos.Y + homogenMatrix.Line1.Column3),
(int)(homogenMatrix.Line2.Column1 * pos.X + homogenMatrix.Line2.Column2 * pos.Y + homogenMatrix.Line2.Column3)
);
}
