Research On Splicing Technology Of Complex Surfaces

With the development of science and technology products to be higher,faster and stronger,the surface modeling of industrial products with complex and smooth surfaces has gradually become the research focus of the industry.They are widely used in transportation,aerospace and marine engineering,etc.In the process of the gradually development of the surface modeling technology,many complex surfaces are designed,which consists of multiple surfaces.Thus,in order to make the surfaces of these products form a complete surface in function and appearance.Many researchers proposed a new research direction,namely,surfaces splicing technology.In this thesis,we study the method of surfaces splicing based on the optimal adjustment of control points and weight factors,and based on the geometric partial differential equations.Then,an improved surfaces splicing method is proposed and the splicing experiment is performed.Specific research work and innovations of the paper are shown as follows:Firstly,we study the method of splicing directly between the two surfaces,according to the idea of adjusting the boundary control points and the corresponding weight factors.Specifically,we study the theory of NURBS surfaces splicing,the condition ofG~1 continuous splicing of NURBS surfaces and the relationship between the boundary control points and the corresponding weight factors.In specific cases,we can realize~1G continuous splicing between two surfaces by adjusting the boundary control points and the corresponding weight factors,and the average deviation value at the splice boundary is about 44.9%lower than that of theG~0 splicing.Secondly,we study a method of stitching with geometric essence according to the idea of constructing the transition surface between the surfaces to be spliced.We present a method for constructing transition surface,using the mixed finite element method based on the extended Loop’s subdivision scheme by introducing the fourth-order geometric partial differential equation.Concretely,we research the mixed variational form of the fourth-order geometric flow,the extended Loop’s subdivision method,the properties of the basis function in finite element space and the discretization of the fourth-order geometric partial differential equation.Then,the G~1 continuous stitching between the surfaces is achieved by the example of three pipe splicing.Lastly,an improved Bézier surfaces splicing method is established by combining with the above two methods.Moreover,the numerical experiments are implemented by using a kind of variable curvature car rearview mirror,and the effect of splicing is analyzed.Specifically,we study the basic principle of the improved splicing method,improve the expression of Bézier surfaces equation,and propose an fitting objective function in the least square sense.Our numerical results show that the improved method has the property ofG~2 continuous at the splice boundary,and the average deviation value at the splice boundary is about 51.2%lower than that of the traditional splicing,with good splicing effect.