# Translating between coordinate systems

Let's say I needed to render an image at 1920 x 1080 and also at 1024 x 768. Instead of drawing two separate images, it might make sense to draw the scene in a common "virtual" coordinate system and then translate that to the appropriate output coordinate system.

Is there a name for this problem? I'm having a hard time figuring out what to start searching for.

• Exactly. I would have a virtual coordinate system of my own definition, where the axis were -1 to 1 or 0 to 100 or whatever. Something small and easy to visualize in your head. This coordinate system isn't concerned with the physical limitations of "pixels" either. So a "half-pixel" is possible here. Once I've drawn each vertex in this "virtual" coordinate system I would then translate each one into any user defined resolution, for example a 1080p display. – Eric Aug 27 '16 at 14:29
• What exactly do you mean by translate coordinates? Could you attach some image? – Evil Aug 28 '16 at 0:16

I'll try to answer my own question. The solution is an application of matrix transformations.

This lecture tries to explain some of the maths.