As-Similar-As-Possible Planar Parameterization
保相似的网格参数化

Mesh surface parameterization is an important problem in Digital Geometry Processing,and triangular mesh is the typical form for mesh representation.To solve the problem of planar parameterization for triangular mesh fast,and minimize the distortion of triangles generated in the parameterization simultaneously,a simple as-similar-as-possible planar parameterization method for triangular mesh is presented in this paper.The angles and length ratios between two adjacent edges are globally preserved in a least squares sense after the parameterization,by which the similarity of the corresponding triangles can be satisfied.A linear system is constructed according to the corresponding angle and length ratio of two adjacent edges on the triangular mesh,and the planar parameterization result can be fast obtained by solving the sparse linear system with some initial conditions.Linear constraints can be combined into the linear system in our approach,and the algorithm is of linear complexity.This method has a direct geometric interpretation and can be implemented more easily than other methods.Experimental examples show that good planar parameterization results can be derived from this method,which is a very efficient tool for the applications in Computer Graphics,such as texture mapping.