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The goal of this paper is to introduce a new method in computer-aidedgeometry of solid modeling. We put forth a novel algebraic technique toevaluate any variadic expression between polyhedral d-solids (d = 2, 3) withregularized operators of union, intersection, and difference, i.e., any CSGtree. The result is obtained in three steps: first, by computing an independentset of generators for the d-space partition induced by the input; then, byreducing the solid expression to an equivalent logical formula between Booleanterms made by zeros and ones; and, finally, by evaluating this expression usingbitwise operators. This method is implemented in Julia using sparse arrays. Thecomputational evaluation of every possible solid expression, usually denoted asCSG (Constructive Solid Geometry), is reduced to an equivalent logicalexpression of a finite set algebra over the cells of a space partition, andsolved by native bitwise operators.

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays