Inversion-free geometric mapping construction: A survey

Computational Visual Media

Chunyang Ye¹  Ligang Liu¹  Xiao-Ming Fu¹  Jian-Ping Su¹  Zheng-Yu Zhao¹  Qing Fang¹ 

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

关键词: inversion-free mapping;    Jacobian matrix;    distortion;    first-order methods;    second-order methods;   

DOI  :  10.1007/s41095-021-0233-9

来源: Springer

【 摘 要 】

A geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

【 授权许可】

CC BY