#787 – Transforming a Point Using Matrix Multiplication

In WPF, all 2D transformations (e.g. scale, rotate, translate) are done internally using matrix multiplication.

Every point that you want to transform is represented as a 2 x 1 matrix (two rows and one column).  For example:

Assume that you want to transform this point, represented by x and y, into a new point.  We do this by multiplying a 2 x 2 transformation matrix by our original 2 x 1 matrix.  The result is another 2 x 1 matrix, containing our new (transformed) point.

The operation is written as follows, assuming that a, b, c and d represent the four values in our 2 x 2 matrix.  We multiply the 2 x 2 transformation matrix by the original 2 x 1 matrix to get a new 2 x 1 matrix.

(Don’t worry about the values of a, b, c and d for now–we’ll fill them in later).  The actual multiplication is done as follows: