Stretch-Minimizing Volumetric Parameterization

• Published in: Journal of computer science and technology Vol. 30; no. 3; pp. 553 - 564
• Main Author: 金耀 钱归平 赵杰伊 常建 童若锋 张建军
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2015; Springer Nature B.V; Department of Computer Science and Engineering, Zhejiang University, Hangzhou 310027, China%College of New Media, Zhejiang University of Media and Communications, Hangzhou 310018, China%National Centre for Computer Animation, Bournemouth University, Bournemouth, BH12 5BB, U.K
• Subjects: Analysis; Artificial Intelligence; Boundary conditions; Collapse; Computer Science; Data Structures and Information Theory; Deformation; Distortion; Energy; Energy conservation; Energy of formation; Information Systems Applications (incl.Internet); Mapping; Methods; Optimization; Parameterization; Parametrization; Regular Paper; Software Engineering; Solvers; Studies; Theory of Computation; Three dimensional; Tradeoffs; Volumetric analysis; 传统方法; 体积; 参数化; 拉伸; 最小化; 网格节点; 表面参数; 边界条件; stretch-minimizing; foldover-free; volumetric parameterization
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/s11390-015-1545-y

Not many methods for parameterization guarantee bijectivity or local injectivity, which is essential for foldover- free mappings. Stretch-minimizing parameterization which is widely used for surface parameterization, provides foldover-free mappings and is capable of trading off between angle and area distortions. We extend its usage to volumetric parameterization in this paper by deriving a 3D version of stretch-distortion energy and incorporating fixed boundary conditions. Our energy definition includes a naturM barrier term which effectively prevents elements from collapsing and folding over. It saves the effort in other methods of formulating additional energy or constrains to ensure the local injectivity. We propose to minimize the overall energy integrated over the whole mesh with a relaxation-enhanced solver and optimize the energy globally. This is different from the conventional approach of surface parameterization where mesh nodes are optimized individually. Compared with other volumetric parameterizations, method, being foldover-free and offering a good trade-off between our approach bears the advantages of stretch-minimizing angle and volume distortions.