An affine transformation matrix performs a linear mapping from 2D coordinates to other 2D coordinates that preserves the “straightness” and “parallelness” of lines.

Such a coordinate transformation can be represented by a 3 row by 3 column matrix with an implied last row of [ 0 0 1 ]. This matrix transforms source coordinates (x, y) into destination coordinates (x',y') by considering them to be a column vector and multiplying the coordinate vector by the matrix according to the following process:

[ x ]   [ a  c  tx ] [ x ]   [ a * x + c * y + tx ]
[ y ] = [ b  d  ty ] [ y ] = [ b * x + d * y + ty ]
[ 1 ]   [ 0  0  1  ] [ 1 ]   [         1          ]

Note the locations of b and c.

This class is optimized for speed and minimizes calculations based on its knowledge of the underlying matrix (as opposed to say simply performing matrix multiplication).

Constructors

• Matrix()
• Matrix(a, b, c, d, tx, ty)
• Matrix(values)
• Matrix(matrix)

Properties

• a
• b
• c
• d
• tx
• ty
• values
• translation