Polyhedron Kernel Computation Using a Geometric Approach

TL;DR

This paper introduces a geometric method for computing the kernel of a polyhedron, offering efficiency improvements over traditional linear programming approaches, especially for generic tessellations and star-shaped detection.

Contribution

It extends a previous geometric approach, optimizing calculations through pre-processing and exact predicates, providing an alternative to algebraic methods for polyhedron kernel computation.

Findings

More efficient than algebraic methods on tessellations

Effective in detecting non-star-shaped polyhedra

Provides detailed implementation and analysis

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 for a polygon has been largely addressed in the literature, fewer methods have been proposed for polyhedra. The most acknowledged solution for the kernel estimation is to solve a linear programming problem. On the contrary, we present a geometric approach that extends our previous method, optimizes it anticipating all calculations in a pre-processing step and introduces the use of geometric exact predicates. Experimental results show that our method is more efficient than the algebraic approach on generic tessellations and in detecting if a polyhedron is not star-shaped. Details on the technical implementation and discussions on pros and cons of the method are also provided.