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A regularized Boolean set-operation op can be obtained by first taking the interior of the resultant point set of an ordinary Boolean set-operation (Pop Q) and then by taking the closure That is, Pop* Q = closure(interior (Pop Q)). Regularized Boolean set-operations appear in Constructive Solid Geometry (CSG), because regular sets are closed under regularized Boolean set-operations, and because regularization eliminates lower dimensional features, namely isolated vertices and antennas, thus simplifying and restricting the representation to physically meaningful solids.
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