Inversion-free geometric mapping construction: A survey  

作　　者：Xiao-Ming Fu Jian-Ping Su Zheng-Yu Zhao Qing Fang Chunyang Ye Ligang Liu 

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei,China

出　　处：《Computational Visual Media》2021年第3期289-318,共30页计算可视媒体（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.61802359 and 61672482);the USTC Research Funds of the Double FirstClass Initiative(No.YD0010002003)。

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.

关 键 词：inversion-free mapping Jacobian matrix DISTORTION first-order methods second-order methods 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O18[自动化与计算机技术—计算机科学与技术]