测地线路径和距离算法综述
A Survey of Algorithms for Geodesic Paths and Distances
摘要：
弯曲域上的最短路径或测地线的数值计算以及相关联的测地线距离在跨越数字几何处理、科学计算、计算机图形学和计算机视觉的广泛应用中出现。相对于欧几里德距离计算，这些任务由于曲率对最短路径行为的影响以及域的表示本身可能是近似的事实而变得复杂。尽管这个问题的困难，最近的文献已经开发出各种各样的复杂的方法，使快速查询的测地信息，即使在相对较大的模型。本概览审查了计算测地路径和距离的主要方法类别，突出了共同主题和今后改进的机会。
英文摘要：
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and computer vision. Relative to Euclidean distance computation, these tasks are complicated by the influence of curvature on the behavior of shortest paths, as well as the fact that the representation of the domain may itself be approximate. In spite of the difficulty of this problem, recent literature has developed a wide variety of sophisticated methods that enable rapid queries of geodesic information, even on relatively large models. This survey reviews the major categories of approaches to the computation of geodesic paths and distances, highlighting common themes and opportunities for future improvement.
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。
