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]
matrix.rotate(45 / 180 * PI)
matrix.scale(3, 4)
matrix.translate(50, 100)
matrix.rotate(30 / 180 * PI)
matrix.scale(-2, 4)
now my matrix have values [a, b, c, d, tx, ty]
lets forget about the processes above and imagine that we have only the values a, b, c, d, tx, ty
how can i find total rotation and scale values via a, b, c, d, tx, ty
sorry for my english
Thanks your advance
EDIT
I think it should be an answer somewhere...
i just tried in Flash Builder (AS3) like this
var m:Matrix = new Matrix;
m.rotate(.25 * Math.PI);
m.scale(4, 5);
m.translate(100, 50);
m.rotate(.33 * Math.PI);
m.scale(-3, 2.5);
var shape:Shape = new Shape;
shape.transform.matrix = m;
trace(shape.x, shape.y, shape.scaleX, shape.scaleY, shape.rotation);
and the output is:
x = -23.6
y = 278.8
scaleX = 11.627334873920528
scaleY = -13.54222263865791
rotation = 65.56274134518259 (in degrees)
Not all values of a,b,c,d,tx,ty will yield a valid rotation sequence. I assume the above values are part of a 3x3 homogeneous rotation matrix in 2D
| a b tx |
A = | c d ty |
| 0 0 1 |
which transforms the coordinates [x, y, 1]
into:
[x', y', 1] = A * |x|
|y|
|z|
[dx, dy]=[tx, ty]
sx = sqrt(a² + c²)
and sy = sqrt(b² + d²)
t = atan(c/d)
or t = atan(-b/a)
as also they should be the same.Otherwise you don't have a valid rotation matrix.
The above transformation is expanded to:
x' = tx + sx (x Cos θ - y Sin θ)
y' = ty + sy (x Sin θ + y Cos θ)
when the order is rotation, followed by scale and then translation.