The Comparison Of Triangular Mesh Parameterization Methods Based On Surface Reconstruction

Surface parameterization is used wided in computer graphics,CAGD and digital geometry processing.Parameterization of triagular meshes becomes a hot research topic in geometry modeling resently,Many researchers present different methods.So evaluate the effect of the different parameterization methods is very important.Visual quality of the mesh is the intuitive criterion of measuring the effect of the parameterization.But many results of different methods is similar with others,and cant not measure the effect directly,so we must define some criterion to measure the effect of the parameterization methods.For this background,this paper presents a method to measure the effect of the parameterization methods of triangular meshes based on surface reconstruction.The main work of this paper are as follows:First analysis several classical parameterization methods of triangular meshes.For different meshes on the plannar field,reconstructed the surface by two methods,and for the different surface by the two reconstruct methods,define different standard to measure the effect of the reconstructed surface.And the effect of the reconstructed surface measure the effect of the parameterization meshods.The first reconstruct method is based on the relationship of the different coordinates and Laplacian matrix,using the geometry information of the triangular mesh and the parameter information of the parametric field to reconstruct a C~0 continnous surface.And evaluate the effect of the methods by the average deviation of the point and area between the primitive mesh and the recontrusted surface.Another method is interpolating the vertices of the triangular mesh by Clough-Tocher(C-T) method,and this surface is a C~1 continnous surface.And evaluate the effect of the methods by the average Hausdorff distant on average triangular patch between the primitive mesh and the recontrusted surface.The effect of the reconstruct result reflect the effect of the parameterization methods.Finally use face mesh and nose mesh implement the parameterization methods above and the reconstruct surface of the Co method,the experiment results demonstrate that,the Harmonic method and the Energy optimizing parameterization method are better than others,and the Uniform method is the worst.