Optimization Design Of Surface Through Geodesic Network

In this paper,the optimization designing of polynomial Bézier surface and quasi-Coons interpolation surface through the geodesic network is studied.In the surface design through the geodesic network around a point,according to the three kinds of constraints(binormal constraint,geodesic crossing constraint and vertex enclosure constraint)that the curve network becomes geodesic network on a general surface,In this paper,the optimized designing method of constructing the geodesic network on the surface by step is given.firstly,the control points of the interpolating surface are determined in two steps: the first step is to determine the control points of the common boundary and the adjacent common boundary of the surface by the geodesic interpolation condition,In the second step,the other control points of the surface are obtained from the minimization of the surface spline energy functional.At the same time,the quasi-Coons optimization design method of the interpolating surface is also given,and the surfaces constructed by the two methods are compared.The experimental results show the effectiveness of the two methods.In the surface design of geodesic network passing through any topological structure,the minimum degree requirements of Bézier curve network satisfying the existence constraints of interpolating surface are analyzed,This paper analyzes the constraints of the existence conditions of interpolating surface on the control points of the quintic Bézier curve network.On this basis,the optimal design and combination of Bézier surface with degree(7,7)interpolating the curve networks is the geodesic network on the surface,and the points of the interpolating surface can be determined by subregional computing.At the same time,the construction method of the quasiCoons interpolating surface of the geodesic network is also given,The constructed surface is also degree(7,7).Finally,an example is given.In this paper,two methods of surface construction through geodesic network are proposed: one is based on the step-by-step strategy,the other is based on the quasi-Coons method.The stepby-step strategy makes the control points of the surface can be calculated in subreginal linear way,which accords with the local quality of geodesic network.At the same time,combined with the optimization method,the surface has the optimal property,It has good physical properties,easy shape control and easy interactive operation.The quasi-Coons interpolation surface construction method is simple,intuitive and easy to understand.However,the surface shape is completely determined by geodesic interpolation conditions,and the generated surface shape is difficult to control,The use of optimization method makes up the inherent defect of this method to some extent.