General Transformations

In general, the math for any transformation, or combination of transformations, looks like:

	newx = A * oldx + B * oldy + C * oldz + D
	newy = E * oldx + F * oldy + G * oldz + H
	newz = I * oldx + J * oldy + K * oldz + L

This can be simplified by treating positions as 4-coordinate vectors, where the last coordinate (w) is usually 1.

The transformation is then a 4x4 matrix that is the vectors are multiplied by.

    | x |     | A B C D |     | x |
    | y |  =  | E F G H |  *  | y |
    | z |     | I J K L |     | z |
    | w |     | M N O P |     | w |