بررسی توابع بی-اسپلاینها

Abstract

    One of the most important works in the field of computational mathematics has always been of interest and plays a fundamental role in solving mathematical problems numerically is spline functions. specially B-spline functions with distinct advantages. The purpose of this study is to investigate B-spline functions and introduce numerical B-splines by Taylor coefficient theorem. In the argument of numerical analysis, which is one of the fields of mathematics,  B-spline functions (basic spline) is the function that has the least support in terms of an assumed degree, smoothness, and region elevation, contain points that are equidistant. Numerical B-splines play an important and active role in approximation theory.  By using numerical B-splines of 1,2and 3 degrees we can obtain the case of Taylor's coefficients.  B-spline functions are a form of CD-spline functions, that is, all the characteristics of B-spline functions are also present in CD-spline functions as well. One of the applications of B-spline functions is in drawing curves that are composed of parts of polynomial curves. This type of curve is called B-spline curve. Any spline function of a given degree can be written in terms of a linear combination of b-splines of the same degree.  B-spline functions can be used for curve fitting and numerical derivation of laboratory data.  B-spline functions are important because they form the space of splines. In computer-aided design and computer graphics, spline functions are constructed as linear combinations of B-splines with a set of control points.