Calculating where to place one arbitrary 2d shape in another?

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How do I calculate how to fit shape A into shape B? Are there some algorithms I could look up? Neither shape should scale.

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This is pretty close except he doesn't specify what routines he's using: Find maximum area polygon inscribed in larger polygon

The actual use case is fitting a building footprint into an arbitrary area. It's for RTS AI where they need to find a location to place a building.

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