优化网格以改进计算可见区域的三角扩展算法
Optimizing Mesh to Improve the Triangular Expansion Algorithm for Computing Visibility Regions
AI总结：
本文提出一种优化三角网格的方法，以最小化三角扩展算法中边扩展次数，从而将可见区域查询平均时间提升12%-16%，适用于离线大规模查询场景。
摘要：
本文针对计算可见区域的三角扩展算法（TEA）的查询性能改进问题，通过寻找预处理结构——三角网格的最优实例来实现。TEA在遍历网格时递归地跟踪可见区域，即多边形世界中从查询点可见的所有点的集合。我们证明，测得的查询时间大约与网格遍历过程中三角形边扩展的次数成正比。我们提出了一种新型三角网格，在假设查询点来自已知概率分布的情况下，最小化期望扩展次数。我们设计了一种启发式方法来近似该网格，并在许多类似真实世界环境的具有挑战性的实例上评估了该方法。与参考的约束Delaunay三角剖分相比，所提出的网格将平均查询时间提高了12%-16%。该方法适用于提升需要计算数百万次查询而不考虑预处理时间的离线应用的性能。实现已公开，可复现我们的实验并为社区服务。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
