computer science - What is a clever bounding box for a 3D monte carlo integration? -


for project, need calculate overlap volume of 2 overlapping ellipsoids in 3d. method isn't problem: i'm picking random points within bounding box , checking whether they're in both ellipsoids simultaneously.

in never-ending quest optimize program in terms of runtime, smaller bounding box advantageous. right now, "box" sphere centered around midpoint between ellipsoids' centers of mass , has diameter corresponding longest ellipsoid axis. arbitrary , i'm overlapping volume contained in sphere, i'd find way optimize entire process.

is there general method optimize bounding volume?

isn't math problem, rather cs problem? seem asking formula defining possible overlap of 2 ellipsoids. intend use formula make code more efficient, sure, not related core question far can tell. if had formula , trying figure out how write code, story. maybe should consider posting https://math.stackexchange.com/

it seems me can redefine question "what formula defining volume overlap possible between 2 ellipsoids in 3d space?", , has no reference computing whatsoever.


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