Research On Boolean Aperation Of Cellular Adaptive Subdivision Surface

Surface Boolean operation is one of the most basic but complex problems in CAD /CAM system.It is widely used in 3D printing,NC machining tool path planning,3D surface modeling and solid modeling.In the current CAD / CAM system,complex surface models are more and more widely used,and the intersection in surface Boolean operation is more and more complex,which requires higher and higher computational performance of surface Boolean operation.Compared with NURBS method and polygon mesh method,subdivision surface modeling method has attracted extensive attention in the field of complex surface design and manufacturing.At present,many scholars have studied the Boolean operation of subdivision surface,but the research on the Boolean operation of cellular adaptive subdivision surface has not been reported in the literature.Therefore,the research of this subject is not only conducive to solve the problem of data redundancy of subdivision surface,but also conducive to the construction of Boolean operation method of high-performance subdivision surface.The research results are conducive to the application of subdivision surface in a wider range of industrial fields.The main research contents of this paper can be divided into the following four aspects:(1)The construction method of Catmull Clark subdivision surface model is studied.The geometric subdivision rules and topological subdivision rules of Catmull Clark subdivision surface are studied and analyzed.On this basis,the topological structure characteristics of subdivision surface patches are studied,and a method of representing Catmull Clark subdivision surface by cellular data structure patches is created,which provides a basis for subsequent cellular adaptive subdivision and surface Boolean operation;The properties of limit mesh and control mesh of Catmull Clark subdivision surface are analyzed,the method of constructing subdivision surface model based on limit surface is proposed,and the calculation method of limit vertex position and normal direction of Catmull Clark subdivision surface are studied,which provides a basis for the realization of subdivision surface model.(2)The cellular adaptive subdivision method based on Gaussian curvature metric is studied.A cellular adaptive subdivision algorithm based on Gaussian curvature is proposed.Firstly,the cellular adaptive subdivision criterion is described,and the Gaussian curvature value of the internal regular vertex is calculated.Then,the topological characteristics of adaptive subdivision cell structure are analyzed,and the crack elimination strategy is studied.Finally,the effectiveness of the algorithm is verified by a model example.(3)The intersection algorithm of Boolean operation model of cellular adaptive subdivision surface is studied.Based on the piecewise representation of subdivision surface,combined with the divide and conquer strategy,the intersection calculation between subdivision surface models is transformed into the intersection calculation of subdivision surface patches.The calculation method of intersection line between patches of subdivision surface is studied,which is divided into three parts: Calculation of the first intersection point,search of subsequent intersection point and judgment of termination intersection.The effectiveness of the intersection algorithm between cellular adaptive subdivision surfaces is verified by a model example.(4)The Boolean operation method of cellular adaptive subdivision surface is studied.Based on the intersection of cellular adaptive subdivision surface,the clipping of Boolean operation model of cellular adaptive subdivision surface is studied,and the clipping operation efficiency is improved by simplifying the intersection line.The position relationship of two complex cellular adaptive subdivision surfaces is determined by projecting them in the X,y and Z axes.According to the position judgment results,a specific cellular adaptive subdivision surface is selected to obtain the Boolean operation results.Finally,the feasibility and effectiveness of the algorithm are proved by an example of Boolean operation of cellular adaptive subdivision surface.The algorithm test results show that the method can correctly calculate the Boolean operation results of cellular adaptive subdivision surface.