Research On Catmul-Clark Subdivision Surface Patching Method Based On Coons Modeling

The manufacturing technology of complex surface-like parts has been widely used in the fields of aviation,aerospace,energy,and national defense,and is an important strategic guarantee of national security and great power status.In the process of CNC machining of complex surface class parts,surface filling(also known as surface filling)technology is often required to solve problems such as machining model data repair and tool offset model interference processing.Currently,subdivision surface modeling methods are widely used in film and television,animation and other fields.Compared with the NURBS modeling method,the subdivision surface modeling method is more suitable for the design and manufacturing of complex surface models.The Coons modeling method is based on the data information of the four boundaries to build the surface model,which makes Coons surface can be used as a tool for surface filling.There are no reports in the literature on Catmull-Clark subdivision surface surfacing using Coons modeling.Therefore,in order to solve the problems of subdivision surface machining model data repair and tool offset model interference processing,this paper researches and develops the Coons modeling method and conducts a study on the Catmull-Clark subdivision surface patching method based on Coons modeling.The main research contents of the whole paper are as follows.(1)The construction of Catmull-Clark subdivision surface machining model is based on the control of mesh topology characteristics of Catmull-Clark subdivision surface,and then the cell array is studied to realize the piecewise representation of Catmull-Clark subdivision surface,calculate the position and normal direction of limit vertices,construct the limit mesh representation machining model,and then calculate the Gaussian curvature,It provides a theoretical basis for the method and technology of using Coons surface to fill the non-interference Catmull-Clark subdivision surface and fill the loophole after interpolation.(2)The basic principle and modeling method of Coons surface are analyzed and studied,and the corresponding complementary methods of Coons surface with given boundary,Coons surface with given boundary and cross-border tangent vector,Coons surface with given boundary and cross-border tangent vector and cross-border guide vector are established respectively.In order to simplify the expression of surface,the corner information and mixing function are used to define the boundary surface and cross-border tangent vector,and the patching method based on bicubic Coons surface is studied.(3)The basic principle and modeling method of Coons surface are studied and developed.On the basis of interpolating four boundary curves,the constraint conditions of interpolating internal crosshairs are added.The mixed function is deduced again,and the Coons surface representation method in different cases is established.On this basis,the complementary methods of Coons surface with given boundary,Coons surface with given boundary and cross-border tangent vector,Coons surface with given boundary and cross-border tangent vector and cross-border guide vector are established respectively.At the same time,in order to simplify the expression of the surface,the corner information and mixing function are used to define the boundary surface and cross-border tangent vector,and the patching method of bicubic Coons surface based on interpolation crosshair is studied.