Fast Bitmap Rotation and Scaling

The Shear and Transpose Method

The idea of the shear and transpose method of bitmap rotation is to first take a bitmap and compose the shear and transpose functions to produced the desired rotation.

First the bitmap is sheared from:

     a----b
     |    |
     |    |
     c----d

to the given x component of the angle as such:

    a----b
     \    \
 —>   \    \
       c----d

The bitmap is then transposed:

        b
       / \
      /   \
     a     d
      \   /
       \ /
        c

Transformations around the diagonals can be used to increase the range of rotation to the full 360 degrees, however this method requires several passes in order to achieve the final rotation.