Inversion-free geometric mapping construction:A survey

• 作者: Xiao-Ming Fu Jian-Ping Su Zheng-Yu Zhao Qing Fang Chunyang Ye Ligang Liu
• 来源期刊: 计算可视媒体（英文版）
• 年，卷（期）: 2021,（3）
• 所属期刊栏目: REVIEW ARTICLE
• 页码范围: 289-318
• 页数: 30页
• 语种: 英文

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.