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But performing that check for a complex polygon with arbitrary number of sides in fragment shader quickly becomes a performance disaster, especially on lower-end GPUs.
Also it turns out that your picking system relied on convex shapes to determine on which building the player clicked. It is actually related to the system which checks if a building the player is trying to place is overlapping with any of the other buildings. So the whole thing needs to be refactored to support concave shapes too. Once you did that you notice the new code is not so fast due to more complex checks, so you add bounding boxes for each shape and first check bounding boxes (cheaper test) before checking polygons.
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