Inversion-free geometric mapping construction: A survey

Autor: Xiao-Ming Fu, Jian-Ping Su, Zheng-Yu Zhao, Qing Fang, Chunyang Ye, Ligang Liu
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Computational Visual Media, Vol 7, Iss 3, Pp 289-318 (2021)
Druh dokumentu: article
ISSN: 2096-0433
2096-0662
DOI: 10.1007/s41095-021-0233-9
Popis: 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.
Databáze: Directory of Open Access Journals
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