Some Properties Of Uniform Hyperbolic Polynominal B-spline

Some base functions of polynomial B-spline are replaced by hyperbolic func-tions, which forms Uniform hyperbolic polynomial B-spline. It is the developmentof the B-spline. It has a wide range of application in designing curves and surfaces.This paper has researched the properties of it by comparing whit the properties ofBasic digital polynomial B-spline. List the same or similar properties of them. Andthis paper has get some new properties of Uniform hyperbolic polynomial B-spline.It has constructed a queue of nested closed subspaces by Uniform hyperbolic poly-nomial B-spline, and has researched the two-scale relations and the nature of basefunctions of it.Basic digital B-spline has been used to build wavelet bases. Spline waveletis very important in wavelet analysis. Multiresolution Analysis is the core con-cept of wavelet analysis. It is a general method to build wavelet bases by usingscale function to construct Multiresolution Analysis, and next to construct waveletbases. So , in the third part of this paper, I have discussed whether it was possibleto construct Multiresolution Analysis by Uniform hyperbolic polynomial B-spline.Unfortunately, because of the bases of Uniform hyperbolic polynomial B-spline arereplaced by hyperbolic functions, it doesn't meet the scalability condition. So, itcan't build Multiresolution Analysis. Anyway, I can't use Uniform hyperbolic poly-nomial B-spline to construct Multiresolution Analysis using the similar method ofBasic digital B-spline.