Smoothing And Interpolation Of Discrete Data

The results of theoretical and applied research of CAGD is getting richer be-cause of the development of computer technology.The surface modeling method is a main research in CAGD.Interpolation is a representation of curve and surface based on discrete data.While subdivision is a representation of discrete curve and surface based on refinement meshes,and is in line with the idea of in-terpolation.Any number of discrete data can be meshed into continuous triangle meshes.Therefore,this paper introduces two methods based on the triangular mesh,one of which is the progressive interpolation method based on Loop sub-division,and the other is the-triangular-mesh subdivision interpolation spline surface design method.The Loop subdivision surface based progressive interpolation is an extension of the progressive interpolation technique for B-splines.The idea is to iteratively calculate the vertices of the given mesh M,eventually generate a new control mesh M,whose subdivision surface is interpolating mesh M.In this paper,we have proved the convergence of this method for closed and open meshes.This method is both global and local,and can calculate meshes with any number of vertices and topologies.Subdivision surface is the spline surface which has the one-order,and the surface is just continuous.Using spline to construct interpolated function can generate continuous and smooth interpolation surface with any order.Increasing the order of the spline function can increase the smooth order of the correspond-ing surface.A unique value of subdivision surface is the characteristics of surface generation without parametric process.Therefore,the Loop subdivision method can be used to generate the support set of the spline surface,avoiding the difficul-ty of solving a large number of linear equations during the parameterized process.Combining the subdivision method with the spline method can generate a high-order smooth subdivision spline interpolation surface.For the construction of spline functions,this paper proposes to select the nodes in the meshes firstly,and then generate the corresponding spline function.It simplifies the difficulty of se-lecting basis functions in the construction of traditional method.