标题：Lightweight preprocessing and fast query of geodesic distance via proximity graph
作者：Xin, Shiqing; Wang, Wenping; He, Ying; Zhou, Yuanfeng; Chen, Shuangmin; Tu, Changhe; Shu, Zhenyu
作者机构：[Xin, Shiqing; Zhou, Yuanfeng; Tu, Changhe] Shandong Univ, Sch Comp Sci & Technol, Jinan, Shandong, Peoples R China.; [Wang, Wenping] Univ Hong Kong 更多
会议名称：Symposium on Solid and Physical Modeling (SPM)
会议日期：JUN 11-13, 2018
关键词：Proximity graph; Geodesic distance; Real-time interaction; Exponential; map; Spline curves
摘要：Computing geodesic distance on a mesh surfaces efficiently and accurately is a central task in numerous computer graphics applications. In order to deal with high-resolution mesh surfaces, a lightweight preprocessing is a proper choice to make a balance between query accuracy and speed. In the preprocessing stage, we build a proximity graph g with regard to a set of sample points and keep the exact geodesic distance between any pair of nearby sample points. In the query stage, given two query points s and t, we augment the proximity graph g by adding s and t on-the-fly, and then use the shortest path between s and t on the augmented proximity graph to approximate the exact geodesic path between s and t. We establish an empirical relationship between the number of samples and expected accuracy (measured in relative error), which facilitates fast and accurate query of geodesic distance with a lightweight processing cost. We exhibit the uses of the new approach in two applications real-time computation of discrete exponential map for texture mapping and interactive design of spline curves on surfaces. (C) 2018 Elsevier Ltd. All rights reserved.