| Mesh parameterization methods are algorithms that map a mesh on 3D space into2 D space.As one of the basic tools of digital geometry processing technology,mesh parametric technology plays an important role in map making,surface mapping,texture map,curve fitting,surface fitting,surface rendering,mesh deformation and other fields.A good grid parameterization method needs to ensure that the parameterized grid has low deformation and no flipping,and has high computational efficiency.For highcurvature meshes,current mesh parameterization methods have achieved good results in producing high-quality parametric meshes.However,existing mesh parameterization methods do not optimize for the secondary objective of mesh quality.For example,to optimize the conformal properties of the grid while maintaining the equidistant properties of the grid.For low-curvature grids,the grid parameterization results generated by the existing parameterization algorithms have little difference in grid quality,but the grid generation efficiency is low,and the ability to restore grid boundaries is poor.In view of the above problems,this thesis proposes two grid parameterization methods,the main work of which is as follows:1.For high curvature mesh,a multi-objective mesh parameterization method(DMA)is proposed in this paper.In this method,Symmetric Dirichlet Energy,MIPS Energy and Area Energy are considered to design the distortion energy function.The main steps include: through the convex combination parameterization method,the initial no-flip parameterized mesh results are quickly constructed;Based on the optimization energy,the parametric mesh is optimized by an imprecise block coordinate descent method.The parameterized mesh generated by this method has better conformal properties,area-preserving properties and isometric properties.2.For low curvature mesh,a optimizing Angle and Length Free Boundary(ALFB)is proposed.This method designs and optimizes the energy function according to the values of the boundary length and the boundary Angle,and uses the optimized Angle and the boundary length to reconstruct the boundary of the parameterized grid.The main steps of ALFB method include: the generation of parameterized mesh boundaries;Border anti-self-cross processing;Calculation of coordinates of points inside the grid.The boundary of the parameterized net generated by this method is more reductive and the deformation of the inner triangle is lower.The grid parameterization efficiency of this method is higher than that of the traditional grid parameterization method. |
