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[Tapadi <>]

Hi,

An easy approximated solution is to discretize both your polygon and your
density function. Then, you can simply integrate the function over the
polygon. This method works for all density functions, even those without
close form integral.

Exact solutions are much more tricky, depending on the nature of your
density function. If its integral is easy to compute over a triangle, then
apply the method you proposed : divide the polygon into triangles, then
compute and sum all integrals.

That's all my ideas, hope it will help!
Best regards,
Hugo Loi
PhD student at Inria - Maverick team



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