Survey on Planar Parameterization of Triangular Meshes

Planar parameterization of triangular meshes is an essential problem of Digital Geometry Processing, especially for texture mapping, remeshing and mesh editing. This paper investigates the latest theoretical and practical results on planar parameterization. Comparisons of several important algorithms on their theoretical basis, complexity, applied environments and numerical implementations are presented in detail. Besides, a new barycentric mapping algorithm is proposed for the planar parameterization of triangular meshes based on convex combinations. Our algorithm is the combination of harmonic mapping and mean-value theorem, so having the priority of conformality, low-distortion and robustness.