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I'm not sure if this is actually done, but you can shift the vertices to be centered at the origin (e.g by subtracting the mean of coordinates from each coordinate for a polygon). The numbers are now close to 0 and will have better precision

Yeah, I thought something similar-- translating to put one vertex at the origin. But at that point, aren't you pretty close to just using the triangles, anyway (since it's a convex polygon)?

Yes, I think you are right.

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