Construction Method Of K-2 Ring Mesh Surface Based On Quad Mean Value Coordinates

With the rapid development of economy and technology,the popularization of 3D scanning technology and the wide application of complex geometric objects in Computer Aided Design(CAD),Computer Graphics(CG)and computer animation,research people pay more and more attention to surface modeling technology.At the same time,in the current surface modeling technology,the appearance of singular points is an unavoidable problem.Due to the existence of singular points,the resulting surface may appear"wrinkled"and other phenomena,which seriously affects the quality of the surface.Especially in the process of designing industrial products,if the singularity is not handled properly,the product will fail to meet expectations and become unusable.Therefore,the treatment of singular points becomes an important issue in the surface modeling process.This paper uses a singular point other than the boundary point in the quad mesh as the center point.The mesh composed of K quads containing this vertex is called the K-1 ring mesh at this point,and the vertices of the K-1 ring mesh are regular points with degree equal to 4,the mesh composed of the quad containing the vertices of the K-1 ring is called the K-2 ring mesh of the center point.In order to construct a surface with high continuity at the singular point.We take the K-2 ring at the center point as the control mesh,and propose a simple and flexible surface construction method.First,we give a K-2 ring grid as the control mesh,construct a planar grid with the same topology as it and expand the planar grid into a spatial quadrilateral mesh.At the same time,a global shape factor h is set in this process,which can control the degree of approximation between the surface and the initial control mesh.The smaller the value of h,the closer the generated surface is to the control mesh.Then we sample in the plane grid,calculate the quad mean value coordinates(Quad Mean Value Coordinates,QMVC)of the sampling points about the vertices of the spatial quad mesh,and use the coordinates to generate the surface.Because QMVC is C~?for any point in the spatial quad mesh,so every point on the surface is C~?.The example results show that the algorithm is efficient and have good smoothness.