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I recently learned about constructive solid geometry (CSG) which is concerned with defining geometrical shapes (let's assume them to be 3d) from constructors like cubes, spheres, ..., and operations like union, difference, intersection, complement. For simplicity, let's disregard curved surfaces for now and just focus on polyhedra.

There is literature on how to convert a CSG shape into a boundary representation. What I'm looking for is a way to calculate the areas and normal vectors of the boundaries. Is there any theory of CSG primitives that allows for such calculations?

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  • $\begingroup$ Do you want areas and normal vectors for all faces without explicitly constructing them? $\endgroup$ Commented Aug 25 at 16:45
  • $\begingroup$ @HEKTO Not exactly sure what you mean, I guess yes? I mean, defining the shape via CSG already completely determines areas and normal vectors, so the question is whether there is a formalism that performs the computation. $\endgroup$ Commented Sep 5 at 15:34
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    $\begingroup$ A normal way to construct a boundary rep from a CSG is to start from the tree leaves and perform operations with two (union, intersection etc.) or one shape (complement) - then the tree will shrink to a single node. In this case you'll need to calculate faces, which will be probably lost in the next step - for example, they will be swallowed by a union. I thought you wanted to somehow find faces, which will be present in the final shape only - it makes sense, but I don't know how to do that $\endgroup$ Commented Sep 6 at 20:19

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