Research On Surface Modeling And Isometry Based On Catmull-Clark Subdivision

People are no longer satisfied with simple,intuitive feelings about products,and are moving toward richness and complexity.It is precisely because of this demand that it has promoted the rapid development of reverse engineering and its processing technology.The parametric surfaces that were well known in the past have already had a profound research.In recent years,many domestic and foreign researchers have turned their attention to the relatively novel field of subdivision surfaces.The main reason is that compared to parametric surfaces,subdivision surfaces have the advantage of arbitrary topology and overall continuity for more complex surface representations,which in turn promotes their use in games,animation,medicine,and multi-resolution analysis.There is a wider range of application prospects.The subdivision loop subdivision of triangular mesh has been relatively mature research and development,and this article will mainly focus on the subdivision of the quadrilateral mesh.Find out the advantages of Catmull-Clark subdivision and Loop subdivision comparison for quadrilateral mesh subdivision.The Catmull-Clark subdivision was further studied on the basis of the previous Loop subdivision mode research,especially the solution of the problem on the engineering surface,combined with the current popular reverse engineering technology,with the reverse engineering as the background.The application of Catmull-Clark subdivision surface in processing is the research direction,mainly researching the following contents:· Firstly,the overall situation and process of reverse engineering are outlined,and the method is introduced in detail.Combined with the relevant knowledge of subdivision surfaces,the feasibility and prospect of the combination of the two are analyzed.· Summing up the knowledge of surface subdivision,starting from different methods of subdividing surfaces,introduce some common subdivision methods such as Loop subdivision,Catmull-Clark subdivision,and Doo-Sabin subdivision.Focus on the comparison of these methods and find the similarities and differences between the methods.And summarize why this article will focus on Catmull-Clark analysis· Further introduction and research on the knowledge of Catmull-Clark subdivision limit subdivision surfaces and their normal vectors.Also refer to the existing Loop subdivision algorithm based on vertex flatness adaptive subdivision algorithm applied to Catmull.-In the Clark subdivision,and comparing with the traditional method,whether it can smoothly solve the problem that subdivision surfaces have too fast surface mesh growth rate due to continuous subdivision process.· Compare the two methods of traditional Catmull-Clark subdivision surface,find the differences between the two methods,and summarize the deficiencies of the two methods,combined with the Loop subdivision surface based on the weighted asymptotic difference,etc.Based on the distance method,an isometric approximation of Catmull-Clark subdivision surface based on weighted asymptotic difference is proposed.This method is applied to the program to obtain the equidistant effect map.Weights,and do error analysis.· Catmull-Clark Adaptive Segmentation Algorithm and Catmull-Clark Isometric Algorithm for Weighted Asymptotic Differences are used to perform a complete process experiment.This method is directly applied to the actual product using a laboratory 3D printer to verify the feasibility of the algorithm.