Transform Texture Space To World Space?

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Still playing around with my idea for a simple lightmapper, and I think I've got most of the texture mapping, and lighting sorted, but I'm struggling to figure out how to convert from Texture Space to World Space.

Does anyone have code, pseudo code or an explanation on how to do this? Language not particularly important, but the more I can avoid mathematical notation and matrices, the better.

I had a look at YAL in the code archives, but can't really make head or tail of what's going on.