Practical construction of globally injective parameterizations with positional constraints

Computational Visual Media

Research Article

Qi Wang¹  Yuan-Yuan Cheng¹  Ligang Liu¹  Xiao-Ming Fu¹  Wen-Xiang Zhang¹ 

[1] School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, China;

关键词: globally injective parameterization;    constrained parameterization;    bijection;    flip-free;    scaffold mesh;   

DOI  :  10.1007/s41095-022-0269-5

 received in 2021-11-10, accepted in 2022-01-06,  发布年份 2022

来源: Springer

【 摘 要 】

We propose a novel method to compute globally injective parameterizations with arbitrary positional constraints on disk topology meshes. Central to this method is the use of a scaffold mesh that reduces the globally injective constraint to a locally flipfree condition. Hence, given an initial parameterized mesh containing flipped triangles and satisfying the positional constraints, we only need to remove the flips of a overall mesh consisting of the parameterized mesh and the scaffold mesh while always meeting positional constraints. To successfully apply this idea, we develop two key techniques. Firstly, an initialization method is used to generate a valid scaffold mesh and mitigate difficulties in eliminating flips. Secondly, edge-based remeshing is used to optimize the regularity of the scaffold mesh containing flips, thereby improving practical robustness. Compared to state-of-the-art methods, our method is much more robust. We demonstrate the capability and feasibility of our method on a large number of complex meshes.

【 授权许可】

CC BY   
© The Author(s) 2022

【 图 表 】

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