I'm trying to use OpenCascade's BRepAlgoAPI_Common and BRepAlgoAPI_Fuse as implementations of "intersection" and "union" operations for Constructive Solid Geometry (CSG).
My solids are represented as instances of TopoDS_Shape (although I'm strictly interested in "Solid" values, so mainly TopoDS_Solid and TopoDS_CompSolid)
As far as simple operations on finite shapes goes, this is going pretty well.
However, because CSG operations form a Boolean Algebra, I'm interested in constructing identity values for the two CSG operations.
That is, a value everywhere for which intersection(x, everywhere) == x for all shapes, and a value nowhere for which union(x, nowhere) == x.
The documentation for BRepBuilderAPI_MakeSolid() states that
An empty solid is considered to cover the whole space
As such, I'd expect that I should be able to construct a value for everywhere, (the identity for intersection) by constructing a BRepBuilderAPI_MakeSolid, adding no shells to it, and building the result:
auto everywhere = BRepBuilderAPI_MakeSolid().Shape();
However, if I experiment with this, it actually works as the identity for "union" (nowhere), and if I try and calculate the intersection of an object with everywhere (using BRepAlgoAPI_Common), I get an empty result.
Is it possible for me to construct a shape that will work as an identity for "intersection", and if so how?