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

2025-06-04

AI Summary

To address the low query efficiency of the Triangle Expansion Algorithm (TEA) for visibility region computation in polygonal environments, this paper proposes the first query-distribution-aware triangulation paradigm. Unlike conventional constrained Delaunay triangulation, our method explicitly optimizes the triangulation to minimize the expected number of edge expansions during TEA traversal. It integrates probabilistic modeling of query point distribution, heuristic triangulation, and a recursive visibility expansion mechanism to construct a preprocessing mesh tailored to the underlying query statistics. Experimental evaluation on real-world datasets demonstrates an average query speedup of 12–16%, significantly reducing TEA’s traversal redundancy. The approach scales effectively to large-scale offline visibility queries involving up to millions of queries. Our implementation is publicly available.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

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.

Problem

• Optimizing mesh to enhance triangular expansion algorithm efficiency
• Minimizing triangle edge expansions for faster visibility region queries
• Designing heuristic mesh for improved query performance in polygonal worlds

Innovation

• Optimizes triangular mesh for visibility queries
• Minimizes expansions with probability distribution
• Heuristic method improves query times