Research On Surface Fitting And Remeshing Method Based On Feature-preserving Topological Directed Graph

Geometric computing is one of the important research directions in the field of computer-aided design and computer graphics,and it is widely used in intelligent medical care,aerospace manufacturing,game entertainment and other industries.In recent years,with the rapid development of computer animation,computer graphics,and computer-aided design and engineering,the fields related to geometric computing are facing more challenges,among which the problems of surface reconstruction and mesh generation are particularly prominent.On the one hand,the algorithms for surface reconstruction of complex models with arbitrary topology usually do not consider the continuity between surfaces,resulting in gaps between adjacent surfaces near the T-junction;on the other hand,meshes generated by fully automatic algorithms often have some elements of poor quality,which will lead to a loss of efficiency and accuracy in the subsequent numerical solution process.The feature-preserving topological directed graph not only contains the important topological information of the input mesh model,but also fully covers the feature edges on the partition boundary,making it suitable for surface reconstruction,remeshing and other fields.Therefore,based on the topological directed graph generation and feature-preserving algorithm,this thesis obtains the feature-preserving topological directed graph,and applies it to the two geometric computing fields of surface fitting and remeshing,effectively solving the above two problems.In conclusion,the main work of this thesis is summarized as follows:1.A non-uniform B-spline surface fitting method based on feature-preserving topological directed graph is proposed.This method first generates a topological directed graph that conforms to the geometric features of the model through speed control,path flipping,feature integration and other feature-preserving algorithms. Then the partitions are extracted and split,and finally the piecewise non-uniform B-spline surface approximation fitting is carried out by duplicate nodes interpolation to obtain the continuous representation of the model and ensure that the adjacent surfaces satisfy C~0 continuity near the T-junction.Experiments show that the fitting deviation of this fitting method is lower than that of the traditional methods.2.A quadrilateral remeshing method based on feature-preserving topological directed graph is proposed.With the help of the related theories of the fenced region,this method first classifies the singularities,and then solves the optimization problem to determine the meta singularities in the fence region.Then,based on particle motion rules and feature-preserving algorithms such as speed control,path flipping, and feature integration,a simpler and feature-preserving topology directed graph is generated.Finally,the pattern-based method is used to generate the sliced quadrilateral meshes on the optimized partition structure,and the final quadrilateral mesh is obtained after splicing and global smoothing.Experiments show that this method can obtain a quadrilateral mesh with a small number of singularities and high quality,which effectively improves the quality of the input mesh.