Scaling an object with a local scale and a rotation

Question

Hello,

I have an object which has a position, a rotation angle and a scale (x and y). The overall transform matrix is as follows :

QTransform xform;
xform.translate(instance.definition.position.x, instance.definition.position.y);
xform.rotateRadians(instance.definition.rotation);
xform.scale(instance.definition.scale.x, instance.definition.scale.y);

I need to scale this object using a global scale which then modifies the local scale of the object. For example, the object is rotated by 45 degrees, I apply a scale of 1,2, I need to know how this affects the local scale as it should affect both local scale axes.

Thanks.

PS : maybe this is impossible due to being a non affine transformation, I don't know, I didn't find much on Google about this particular problem

UPDATE : I think I need to have at least a 3 col by 2 rows matrix transform to keep enough information, I tried some things in SVG which uses this kind of matrix transform and it seems to work, I will need to update this matrix according to the position and rotation though.

Answer 1

Either scale the object first

or calculate the inverse matrix, apply it to object (that undoes the translation/rotation), scale it and apply the first matrix again.

Answer 2

If you take, say, a rectangle, rotate it so that its edges are no longer parallel to the coordinate axes, then apply a scaling factor to, say, X, it will no longer be a rectangle. It will be a parallelogram, and your data structures will have to accommodate more information than they do now.