Research On Surface Modeling Method Based On Diagonal Curve In CAD

Curve and surface modeling design in CAD is a very important research content,and it is widely used in industrial design,fashion design,aerospace and other fields.Bdzier curve modeling problems based on known endpoints,and modeling problems of Bezier surface based on the knowvn boundary control points are very hot research topics.The diagonal curve of the tensor product surface is an important measure to measure the surface characteristics and has a great influence on the geometry of the surface.There is a certain constraint relationship between the control points of the diagonal curve and the control points of the surface.At present,there is little work published on the Bezier surface modeling problem associated with the diagonal curve.In view of this situation,this paper studies the surface modeling methods based on the diagonal curve,which mainly include1.In this paper,a method to construct a Bezier surface with the minimal diagonal energy for the given boundary control points is proposed.Based on the theory of extremely minimal energy curves and surfaces,according to the linear relationship between the control points of the surface diagonal and the control points of the surface,taking the sum of the energy of the two diagonal curves on the surface as the objective function,taking the unknown internal control points as the argument,by satisfying the gradient of the objective function to zero,the necessary and sufficient conditions for the internal control points of Bezier surface with the minimal diagonal energy to be satisfied are proposed.In this paper,the stretch energy and bending energy of the diagonal curve are mainly considered.In the actual research,the Bezier surface cannot be uniquely determined only by the necessary and sufficient conditions derived,so combining the Lagrangian multiplier method and the minimal internal energy of the surface,the general framework of constructing Bezier surface with minimal diagonal energy is proposed.The effectiveness of the proposed method is verified by designing corresponding modeling examples and comparing them with the general Bezier surfaces which have minimal internal energy.2.Based on the actual need to construct a surface through the diagonal curve of the Bezier surface,this paper presents a method for constructing Bezier surfaces from given diagonal curves and boundary curves.Firstly,according to the relationship between the diagonal curve and the boundary curve,the geometric information of them input by the user is corrected;Then,using the Lagrangian multiplier method,the internal energy function of the surface is taken as the objective function,and the linear relationship between the diagonal curve and the surface control points is used as the constraint condition to obtain the internal control points to be determined and construct the surface.The resulting surface not only interpolates the modified diagonal and boundary curves,but also has minimal internal energy to meet the relevant requirements of surface modeling.