A Geometric Approach for Computing the Kernel of a Polyhedron

TL;DR

This paper introduces a geometric algorithm for efficiently computing the kernel of a polyhedron, enhancing the analysis of visibility regions compared to traditional linear programming methods.

Contribution

A novel geometric approach for kernel computation in polyhedra, offering improved efficiency over existing linear programming techniques.

Findings

Our method outperforms linear programming in speed for generic tessellations.

The algorithm provides detailed insights into the polyhedron's visibility structure.

Implementation details highlight practical advantages and limitations.

Abstract

We present a geometric algorithm to compute the geometric kernel of a generic polyhedron. The geometric kernel (or simply kernel) is definedas the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has already been largely addressed in the literature, less has been done for polyhedra. Currently, the principal implementation of the kernel estimation is based on the solution of a linear programming problem. We compare against it on several examples, showing that our method is more efficient in analysing the elements of a generic tessellation. Details on the technical implementation and discussions on pros and cons of the method are also provided.