Research On Volumetric Parameterization Method Based On Harmonic Mapping

The parameterizations of surface grids and the tetrahedral meshes are key problems in the processing of 3D volume data.The parameterization of surface triangular mesh is the foundation of texture mapping.The parameterization of volume meshes can be used for information reuse,shape matching and analysis,re-meshing and body texture synthesis,which is of great significance to the post-processing of the model.In the process of grid parameterization,the projection will produce flip and distortion.Theoretically,the triangular mesh parameterization is to establish a reversible mapping as much as possible.In this paper,the parameterization is studied with no flip and low twist as the goal.We present a parameterization method of surface based on harmonic mapping.The traditional harmonic mapping parameterization methods may produce triangles with distortions and flips.To solve these problems,we propose a parametric method based on a method of mean-value harmonic mapping.Firstly,the weights of the classical harmonic maps are re-solved by cotangent weights,and then the initial parameterization of the mesh is realized by using the modified harmonic maps.The boundary is kept unchanged.For each interior point in the triangle mesh,we compute the local secondary energy.We adjust the weight of the interior point to achieve the purpose of rearrangement and differentiate the ductility,so that the local energy is the smallest.In this way,this method solves the problem of triangular mesh flapping.A volumetric parameterization algorithm based on spherical harmonic mapping is proposed.Volumetric parameterization has been applied to many fields,and it is quite important to determine the parameter domain.Unit ball is commonly used as target parameter domain,the volumetric parameterization based on the spherical surface is the key issue for many scholars to study.The researchers generally choose the unit ball as the target parameter domain.However,the parameterization of spherical tends to produce distortions of tetrahedral meshes,which seriously affects the effect of body parameterization and its application.Based on the above problems,we propose a parameterization method based on large-scale distortions of spherical harmonic maps.This method combines the volumetric harmonicmapping method and large-scale distorted volume parameterization method.By mapping the generated simple maps to bounded regions,a mapping closest to the original mapping is solved to output the final volume mesh.By comparing the proposed method,it is proved that the method is without distortion approximately.A volumetric parameterization method based on harmonic mapping is studied.The parameterization of volume grids is significantly different from that of surface grids,but it also causes the problems of flipping and distortion.To solve these problems,this paper presents a volumetric parameterization approach based on the bounded-distortion harmonic energy.This is a method that combines the volumetric harmonic mapping and three-dimensional bounded deformation volumetric mapping.Firstly,the parameterization method is improved and the centroid of the grid is re-solved by the median method,then the parameterization can be realized on the target domain.The parameterization of volume mesh is projected to the bounded space in order to find the original mapping of the nearest matrix and control the distortion in a certain range,then the obtained volume mesh is processed to control the distortion produced in the parametric process to a certain extent.Finally,we obtain the low-distortion volume mesh.The experimental results show that the proposed method is featured with short running time and small number of iterations,which ensures the low distortion and non-inversion of the obtained volume grids.