Instead of GPU you can also draw the collision test polygons in TCanvas, for example of a TBitmap. You can still draw them on GPU to for the looks but like said, it's propably not fast to read the results from it. And if you draw to GPU they need to be convex.
Overall, unless the polygons consist of hundreds of vertices, the math way will propably be more efficient.
edit: For the math way, if it's ruled that polygon must be convex, then isn't the only scenario such that at least 1 vertex must always be inside other polygon? I recall reading of doing this test with just dot product.
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