Question

I’m using XNA but it doesn’t matter too much for this example. So let’s say I have a sprite. I then apply a scaling matrix before anything. Is the scaling matrix applied scaling the local axis of the sprite or just moving the points down? In other words, is applying a scaling matrix of 0.5f in the world space to my sprite at the world origin scaling down the local axis of the sprite or just all the points that make up that sprite by half?

The same kind of applies to a translation and then scaling. In my head, I picture a translation matrix of 30,30 as moving the sprite’s local origin to 30,30 and as a result, the sprite’s local axis to 30,30. Then, scaling by 0.5f would scale back the local axis but I don’t see why the origin of the sprite would now be at 15,15.

This confusion compounds the fact that is you perform a translation of 1 to the right on the x-axis in the world, you are now moving based on the scale which you applied (so you would only move .5 in the world). This leads me to believe that the scale is applied to the object’s own axis.

Btw, if you guys talk about the origin in your followups, could you state which origin you are referring to?

Thanks

Answer 1

Normally a sprite is defined by it’s vertices (points). Applying a scaling matrix to a sprite will transform the vertices (points) of the sprite.

A scale matrix always assumes (0, 0) is the origin of the scale transform. So if you scale a sprite centered at (30, 30) all points will stretch away from the (0, 0) point. If it helps, imagine the sprite as a small dot on a circle around the (0, 0) point with that entire circle being scaled.

If you want to scale a sprite at (30, 30) from the center of the sprite, you have to translate the center of the sprite to (0, 0) first, then translate the sprite back out to (30, 30) after the scale has been performed.

So that would be:

   Translate(-30, -30)
   Scale(0.5)
   Translate(30, 30)