# Screen coordinates to isometric coordinates?

I know this has been discussed here before, but I couldn't find an easy solution for my particular problem. I have a tile system and I'd like to convert screen coordinates into isometric tile coordinates. Here's an image to explain what I need:

As you can see, the coordinates are between 0 and 1. I can't figure out a formula for the conversion though. Can you guys help me?

 tile_x = screen_y - 0.5 + screen_x;

By the way: I would recommend you to use different terminology for screen-coordinates and world-coordinates to avoid mixups. I use x and y for screen coordinates and left-down and right-down for tile coordinates. This saved me from more than one brain-knot. In your example, tile_y would be be left-up and tile_x would be right-up.