Polyhedron kernel computation using a geometric approach (English)

Abstract The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel of a polygon has been largely addressed in the literature, fewer methods have been proposed for polyhedra. The most acknowledged solution for kernel estimation is to solve a linear programming problem. We present a geometric approach that extends and optimizes our previous method (Sorgente, 2021). Experimental results show that our method is more efficient than the algebraic approach over polyhedra with a limited number of vertices and faces, making it particularly suitable for the analysis of volumetric tessellations with non-convex elements. The method is also particularly efficient in detecting non-star-shaped polyhedra. Details on the technical implementation, and discussions on the pros and cons of the method, are also provided.

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Highlights • Computation of the kernel of a polyhedron using a geometric approach. • Robust kernel estimation using geometric exact predicates. • An efficient kernel estimation algorithm suitable for volumetric tessellations with non-convex polyhedra.