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 ...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.展开更多
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)。
文摘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.
