An efficient mesh fusion method based on reusable Laplace matrix

Abstract

The invention discloses an efficient mesh fusion method based on a reusable Laplace matrix. The method includes: setting the correspondence between the boundary vertices of the source mesh model and the target mesh model, calculating the local transformation from the boundary vertices of the source mesh to the boundary vertices of the corresponding target mesh, using Laplace operator to calculatethe rotation field and the scale factor field, reusing Laplace matrix to reconstruct the geometric coordinates, and so on. In this method, the interpolation problems of geometric fusion, rotating field and scale factor field are transformed into Laplacian (Poisson) equations, and only one Cholesky decomposition and multiple iterations are needed to obtain eight scalar fields, which is two orders of magnitude faster than the traditional geodesic-based interpolation method. This method can not only obtain the results comparable to the traditional Poisson fusion method, but also significantly improve the efficiency and achieve the speed of real-time response.

Description

technical field [0001] The invention relates to the technical field of computer graphics and digital geometry processing, in particular to a grid fusion method based on a reusable Laplacian matrix, so as to realize efficient fusion between grids. Background technique [0002] Mesh fusion is an important problem in the field of computer graphics and digital geometry processing, which is to merge the source mesh with the target mesh to synthesize a new mesh model. There are mainly two existing mainstream methods: reconstruction geometry method and construction transition surface method. The specific content and limitations of these two methods are as follows: reconstruction methods, such as the classic Poisson fusion method, can reconstruct reliable source mesh geometry for fusion boundaries with large differences (shape, size and vertex density), but their The calculation of the rotation field and the scale factor field involves the calculation of the geodesic, which reduces...

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Problems solved by technology

The specific content and limitations of these two methods are as follows: reconstruction methods, such as the classic Poisson fusion method, can reconstruct reliable source mesh geometry for fusion boundaries with large differences (shape, size and vertex density), but their The calculation of the rotation field and the scale factor field involves the calculation of the geodesic, which reduces the efficiency and is difficult to meet the interaction requirements. In order to avoid the time-consuming calculation of the rotation field and the scale factor field, the existing methods often use interactive means to compare the source model and the target grid. Alignment, and then use the less expensive deformation method for geometric reconstruction to achieve fusion. The generalized barycentric coordinate method is used to avoid the solution of equations during the deformation process, which further improves efficiency, but it still cannot meet the needs of real-time interaction.

The method of constructing a transition surface is to construct an implicit surface between the boundary of the source grid and the target grid to achieve smooth splicing. This method can be applied to the fusion of multiple complex boundaries, but the implicit surface (such as radial basis function interpolation) usually It is required to solve the dense matrix equation, and the surface needs to be finally meshed, which is time-consuming, so it is difficult to achieve the interactive response speed

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