extract rotation, scale values from 2d transformation matrix

Question

how can i extract rotation, scale and translation values from 2d transformation matrix? i mean a have a 2d transformation

matrix = [1, 0, 0, 1, 0, 0]

matri         


        

Answer 1

I ran into this problem today and found the easiest solution to transform a point using the matrix. This way, you can extract the translation first, then rotation and scaling.

This only works if x and y are always scaled the same (uniform scaling).

Given your matrix m which has undergone a series of transforms,

var translate:Point;
var rotate:Number;
var scale:Number;

// extract translation
var p:Point = new Point();
translate = m.transformPoint(p);
m.translate( -translate.x, -translate.y);

// extract (uniform) scale
p.x = 1.0;
p.y = 0.0;
p = m.transformPoint(p);
scale = p.length;

// and rotation
rotate = Math.atan2(p.y, p.x);

There you go!