Optimizing Mesh to Improve the Triangular Expansion Algorithm for Computing Visibility Regions

TL;DR

This paper introduces a new triangular mesh optimization that reduces the average query time of the triangular expansion algorithm for visibility region computation, especially beneficial for large-scale offline applications.

Contribution

It proposes a heuristic method to optimize the mesh for minimal expansions, improving query performance by 12-16% over standard triangulations.

Findings

Mean query times reduced by 12-16%

Optimized mesh performs well on real-world-like instances

Approach suitable for large-scale offline querying

Abstract

This paper addresses the problem of improving the query performance of the triangular expansion algorithm (TEA) for computing visibility regions by finding the most advantageous instance of the triangular mesh, the preprocessing structure. The TEA recursively traverses the mesh while keeping track of the visible region, the set of all points visible from a query point in a polygonal world. We show that the measured query time is approximately proportional to the number of triangle edge expansions during the mesh traversal. We propose a new type of triangular mesh that minimizes the expected number of expansions assuming the query points are drawn from a known probability distribution. We design a heuristic method to approximate the mesh and evaluate the approach on many challenging instances that resemble real-world environments. The proposed mesh improves the mean query times by 12-16% compared to the reference constrained Delaunay triangulation. The approach is suitable to boost offline applications that require computing millions of queries without addressing the preprocessing time. The implementation is publicly available to replicate our experiments and serve the community.