The Comparison Of Mesh Parameterization Methods Based On Hausdorff Distance

Mesh parameterization studies the 1-1 mapping relationship between mesh in 3-D space and certern parametric field in 2-D space, which is widely used in graph theory, differential geometry, computer graphics, CAGD, digital geometry processing and program designing. Parameterization of triangular meshes is an important research field in computer graphics, and has became a hot research topic in geometry modeling resently. Recently, the research of parametrization of mesh surface have developed dramatically, which made the evaluation of the effect of available parametrization methods increasingly crucial.The purpose of this paper is discussing the comparison of mesh parameterization methods available based on surface reconstruction. This paper analysis several classical parameterization methods of triangular meshes firstly and then reconstructes the original mesh surface using two surfaces of different smooth order for different meshes of parametric field gained from parametrization. The first surface is a Cl rational bezier surface and another is a G1 bezier surface. We gained the reconstructed surfaces based on this two reconstruction methods and then evaluate the effect through Hausdorff distance between the reconstructed surface and original mesh. We also improve the calculation method of Hausdorff distance in Experiments. We adopt an average Hausdorff distance to evaluate the distance between the reconstructed surface and original mesh. This way fully takes the corresponding relationship of every triangular between the reconstructed surface and original mesh into consider, which can evaluate the effect of parameterization methods beter. The experiment results demonstrate that the effect of parametrization methods has relationship with the structure of original mesh.