The Complex Domain Parameterization Method Based On Subdivision Technology And Boundary Replacement

In isogeometric analysis,in order to meet the requirements of higher accuracy and adapt to the parameterization of complex regions,the research on the parameterization of computational domains has always been in high heat.However,one of the main problems that restrict the parameterized quality of complex planar regions is the self-intersecting problem caused by grid flipping,which has become one of the important standards for measuring the quality of parameterization.This paper focuses on solving the problem of parameterization of complex planar regions,combining the existing Catmull-Clark subdivision technique and the idea of boundary replacement,and exploring a methods that can obtain high quality parameterization effects.For a given planar region surrounded by a B-spline curve,we propose two different planar domain parameterization methods.Through in-depth understanding of the subdivision technique,in the two methods,we use different ideas related to Catmull-Clark subdivision.In the same use of boundary replacement to maintain the boundary,we finally get different parameterization effects,and the validity and robustness of the results are illustrated by our experiments.The main contributions of this paper are as follows:1.In this thesis,we firstly propose a complex domain parameterization method based on subdivision technology and boundary replacement.Our method mainly uses a concept of boundary replacement and combines Catmull-Clark subdivision to achieve a good parameterization on the planar domain composed of curve boundaries.The method firstly converts the curve boundary of a given planar region into a polygonal boundary that can be used to generate a quadrilateral mesh;then the region enclosed by the polygon boundary is decomposed using a polygon convex decomposition method,and then each small region is quadrilaterally divided;finally we maintain the original curve boundary by replacing the boundary control point,and achieve the parameterization of the planar domain on the basis of Catmull-Clark subdivision.The method proposed in this thesis can adapt to the parameterization of complex domain,greatly reducing the generation of flipping meshes in the process of parameterization,and thus giving better results of parameterization and ensuring the validity of the results.2.Then,this paper proposes another domain parameterization meuiod based on interpolation subdivision.This method combines the existing method of.interpolation and approximation of Catmull-Clark subdivision surface.Firstly,it uses boundary transformation and quadrilateral partition to generate quadrilateral mesh.Then it uses a new geometric rule to generate an alternative mesh of the initial mesh for approximation of the subdivision surface in the jfinally.Iterative subdivision of the altermative mesh can generate the limit surface of the initial mesh vertices;then a standard uniform B-spline surface control mesh is generated.The B-spline surface is used to approximate the corresponding Catmull-Clark subdivision surface;finally,the parameterization of the planar region is completed after the boundary is replaced.From the final experimental results,the method exhibits a superior quality of parameterization,except thatth e region boundary is still maintained by the replacement of the boundary vertices,and each part of the planar region gives a high smoothness and robustness.