标题：Computing Smooth Quasi-geodesic Distance Field (QGDF) with Quadratic Programming
作者：Cao, Luming; Zhao, Junhao; Xu, Jian; Chen, Shuangmin; Liu, Guozhu; Xin, Shiqing; Zhou, Yuanfeng; He, Ying
通讯作者：Xin, Shiqing;Xin, Shiqing
作者机构：[Cao, Luming; Zhao, Junhao; Xin, Shiqing] Shandong Univ, Sch Comp Sci & Technol, Jinan, Peoples R China.; [Xu, Jian] Dalian Univ Technol, Sch Chem E 更多
会议名称：Symposium on Solid and Physical Modeling (SPM) collocated with the Shape Modeling International Conference (SMI)
会议日期：JUN 02-04, 2020
关键词：Smooth geodesic distance field; Quadratic programming; Convex; optimization; Defect-tolerant distances
摘要：Computing geodesic distances on polyhedral surfaces is an important task in digital geometry processing. Speed and accuracy are two commonly-used measurements of evaluating a discrete geodesic algorithm. In applications, such as parametrization and shape analysis, a smooth distance field is often preferred over the exact, non-smooth geodesic distance field. We use the term Quasi-geodesic Distance Field (QGDF) to denote a smooth scalar field that is as close as possible to an exact geodesic distance field. In this paper, we formulate the problem of computing QGDF into a standard quadratic programming (QP) problem which maintains a trade-off between accuracy and smoothness. The proposed QP formulation is also flexible in that it can be naturally extended to point clouds and tetrahedral meshes, and support various user-specified constraints. We demonstrate the effectiveness of QGDF in defect-tolerant distances and symmetry-constrained distances. (C) 2020 Elsevier Ltd. All rights reserved.