@article{Fu2021, 
author = {Xiao-Ming Fu and Jian-Ping Su and Zheng-Yu Zhao and Qing Fang and Chunyang Ye and Ligang Liu},
title = {Inversion-free geometric mapping construction: A survey},
year = {2021},
journal = {Computational Visual Media},
volume = {7},
number = {3},
pages = {289-318},
keywords = {inversion-free mapping, Jacobian matrix, distortion, first-order methods, second-order methods},
url = {https://www.sciopen.com/article/10.1007/s41095-021-0233-9},
doi = {10.1007/s41095-021-0233-9},
abstract = {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.}
}