An Investigation On A Kind Of The Interpolating Basis Similar To Subdivision Basis

In Computer-Aided Geometry Design and related fields,the interpolation is a very basic and important research subject.Interpolation method is based on a set of ordered data points,Using the data points to structural curve or surface.There are a lot of good interpolation method,But they have some limitations.For example,some classical polynomial interpolation method,need to solve a series of equations to obtain interpolation curve or surface,need large amount of calculation and the method is not stabilization.Change the data points will lead to the change of the whole interpolation curve or surface.We need to solve complex high order equation achieve in the continuity of higher-order curve surface.Subdivision curves can not use mathematical expressions to express,Useing clear mathematical function simulation basis function to construct the curve segment surface was proposed recently,attention and praise from the interna-tional scholars.The main purpose of this work is to develop a kind of interpolating basis functions with good properties for constructing interpolatory curves and surfaces.We first introduce classical segmentation method,by computer graphical repre-sentation of the basis function,and summarized the required structure interpolation segment the property of the basis functions.Then introduce a new class of function-s with local support.Combined with the Sine function with parameter optimization,we obtain a new kind of interpolating basis functions with similar properties to that of interpolatory subdivision basis functions.We call it is proposed to segment the interpo-lation function.Compared with other similar basis functions in the literature,the new basis functions possess exact local support property.Choose different parameter val-ue interpolation basis function,can adjust the scope of local supporting.The resulting curve has following advantages:1,ensure smooth;2,curve shape locally adjustable;3,without solving system of equations;4,By changing the interpolation points,can easily change the shape interpolation curved surface;5,the algorithm is simple,easy popular-ization,etc.The curve example constructed using the new basis shows better visual ef-fect compared with the well-known Akima' s method,while other examples constructed by using the new basis exhibit similar visual effect compared with other similar basis functions in the literature.And can realize the surface smooth stitching,have very strong practicability.