Tetrahedral Mesh Parameterization For Approximation

Recently years, with the rapid development of computer technology,3-D digital geometricrepresentation methods have been widely used in many fields. In all sorts of industrialapplications, triangular and tetrahedral mesh is a general format of3-D geometry model,therefore, mesh parameterization turns to an important and basic issue in field of digitalgeometry processing and computer graphics. Mesh parameterization has many importantapplications, such as texture mapping, mesh deformation, grid reconstruction, meshcompression and spline fitting, etc. In the3-D space, the problem of mesh parameterizationresults in a one-to-one mapping from a grid mesh to its parametric domain. As for a triangularmesh surface, parametric domain is a two-dimensional plane, and to a tetrahedral mesh, itsparametric domain is a three dimensional space. In the process of parameterization, except thedevelopable surface, all of the grids are impossible to construct a conformal mapping. For thatreason, mesh parameterization process will inevitably lead to some distortion. In fact, studieson triangular mesh parameterization is to construct a reversible mapping as soon as possible,and with distortions as little distortion as possible. This thesis mainly studies the surfacetriangular mesh parameterization and tetrahedral mesh parameterization. The main workincludes:On the basis of classical parameterization method, high curvature models usually produceuneven deformation and tremendous deformation changes in the process of parameterization.In order to solve this problem, this paper proposes a dynamic hybrid energy optimization basedplanar triangular mesh parameterization method. Firstly employ a layered progressive strategyin the surface mesh segmentation, then introduce a layered related dynamic coefficient to theform of mixed energy equation. In this way, in the process of calculating the local optimum, notonly spread globally parameterized deformation, but also reduce global deformation.Compared with some classical parameterization methods through experiments, thisparameterization method has the characteristic of the lower overall deformation.Tetrahedral mesh parameterization method is different from planar parameterization.According to the characteristics of the tetrahedral mesh, this paper proposes solid meshparameters method based on approximation. First of all, the source tetrahedral mesh divides into a stratification based on the intermediate base plane of the grid, and make whole mesh intomultiple layers containing monolayer tetrahedron. Then parameterize each layer boundarysurface respectively. In separating surface, parameterization is introduced into a parametricmethod based on the isothermal domains, effectively avoiding the invalid parameterization.Finally, each layer is divided into local parameter domain by a mapping, all the results aremerged into a unified parameter domain, so as to realize the parameterization of the tetrahedronmodel. This method by using parametric method based on isothermal domain strategy,corresponding to the complex surface of tetrahedral mesh, will get a better performance.