Question

Ive been looking around the net for ages tryin to find how to derive the 2d transformation matices for the above functions. Couldnt find it in my notes for college and it was a past exam question wondering if anybody could help for revision purposes? cheers

Answer 1

A transformation matrix is simply a short-hand for applying a function to the x and y values of a point, independently. In the case of translation, x’ = 1*x + 0*y + dx*1 and y’ = 0*x + 1*y + dy * 1. The matrix representation of these two equations is as follows:

[[ 1  0  dx ] [[ x ]    [[ x' ]
 [ 0  1  dy ]  [ y ]  =  [ y' ]
 [ 0  0  1  ]] [ 1 ]]    [ 1  ]]

The other matrices can be similarly derived–simply determine what x’ and y’ should be, in terms of x, y and 1.