Research And Application Of Surface Parameterization Method Based On Energy Optimization

In recent years,computer graphics has developed rapidly.Among them,grid parameterization,as the basis of grid processing technology,has always been the focus and research hotspot in this field.The triangular mesh parameterization technique is widely used in the fields of texture mapping,visualization analysis and re-meshing.On the basis of the energy optimization method,the following main work is done:Firstly,the classification and application fields of triangular grid parameterization are summarized,and the existing problems are pointed out.The parameterization of triangular mesh is divided into convex combination method,angle flattening method and energy optimization parameterization.At present,more parametric methods are used from local to global.This method has some limitations.It only holds when optimizing a single energy.Whether other energy or compound energy holds still needs to be explored.And in the process of solving,convergence still needs to be deeply analyzed.Secondly,from the point of view of energy,a new global energy equation is established for the combination of deformation energy-elastic potential energy and Dirichlet energy weighting,and a new parameterization method based on energy optimization is proposed.First,the parameterized boundary is fixed;the 3D surface mesh is initially parameterized,and then the elastic potential energy and Dirichlet energy function of the mesh are obtained on the premise of ensuring that the boundary map is invariant.An effective parameterization result is obtained.This method preserves the topological properties of the original mesh more,and is no longer limited to the retention of a certain property(conformal,area-preserving and shape-preserving)of the mesh by a single deformation energy.Through numerical experiments,the parameterization effect is measured by deformation angle and area.Compared with the existing classical parameterization methods,it is concluded that the proposed new parameterization method has better parameterization effect when parameterizing zero deficit grid.The efficiency is higher and the numerical convergence is verified at the same time.Finally,the method proposed in this study is the proposed method,summarizes the programming idea and program design when using Matlab software to solve the energy equation,and gives a simple program.Users only need to input the original grid and run the program to obtain parameterized results,high efficiency and simple calculation.Figure 27;Table 2;Reference 48...