AS3: Getting the scale of a Matrix object

Question

Most often, questions are asked about how to scale a DisplayObject, and the answer is usually to use a Matrix.

My question is, how to you GET the scale of a Matrix (

Answer 1

You can get the x and y scales of a matrix even when it's rotated.

Here's the code:

public static function getScaleX(m:Matrix):Number
{
    return Math.sqrt(Math.pow(m.a + m.b, 2));
}

public static function getScaleY(m:Matrix):Number
{
    return Math.sqrt(Math.pow(m.c + m.d, 2));
}

Explanation:

I've found that it's easier to think of A B C D as points that define the x and y axes in the transformed coordinate space. A, B is the position of the first point of the transformed x axis (an identity matrix has these as 1, 0, which will not transform), and C, D is the position of the first point of the transformed y axis (identity values of 0, 1).

If we have a matrix that will scale the x axis by 2 then A, B will be 2, 0. The rest of the points on x axis will be this same distance away from the last (so 2 points away from the last).

If we have a matrix that will rotate 90 degrees clockwise then A, B will be 0, 1 (pointing the x axis along the positive side of the y axis) and C, D will be -1, 0 (pointing the y axis down the negative side of the x axis).

The scale of the x axis is the distance to the first point. In the scenarios that I've mentioned the scale is easy to find. In the previous example A, B is 0, 1 so the scale is 1. If rotation is not on at a 90 degree increment then you can find the length of the line segment from 0, 0 to A, B by using the Pythagorean theorem: sqrt(a^2 + b^2) = c. This is what my code is doing.

Hope this helps someone.