Lightweight preprocessing and fast query of geodesic distance via proximity graph

• Main Authors: Xin, Shiqing, Wang, Wenping, He, Ying, Zhou, Yuanfeng, Chen, Shuangmin, Tu, Changhe, Shu, Zhenyu
• Other Authors: School of Computer Science and Engineering
• Format: Article
• Language: English
• Published: 2019
• Subjects: Proximity Graph; Geodesic Distance; Engineering::Computer science and engineering
• Online Access: https://hdl.handle.net/10356/85378; http://hdl.handle.net/10220/49218
• Institution: Nanyang Technological University

Computing geodesic distance on a mesh surface 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 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 and , we augment the proximity graph by adding and on-the-fly, and then use the shortest path between and on the augmented proximity graph to approximate the exact geodesic path between and . 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.