Inversion-free geometric mapping construction: A survey

Abstract A geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such is required to be inversion-free. Computing inversion-free mappings fundamental task in numerous computer graphics and processing applications, as deformation, texture mapping, mesh generation, others. This usually formulated non-convex, nonlinear, constrained optimization problem. Various methods have been developed solve this As well being inversion-free, different applications various further requirements. We expand the discussion directions (i) problems imposing specific constraints (ii) combinatorial problems. report provides systematic overview of construction, detailed construction methods, including their strengths weaknesses, description open research field.