The Two Order Trigonometric Spline Function With The Shape Parameter

Spline function is an effective approximation tool in functional approximation.Espe-cially,the trigonometric spline function is constructed by continuous piecewise trigonometric function.This function has all the advantages of the algebraic splines and good periodic-ity.It is convenient to solving the derivative and intergral.The trigonometric spline function is widely used in the design of curves and surfaces.The quadratic trigonometric polynomial curves with the shape parameter are discussed in this paper.This paper contains three parts:Firstly,the quadratic piecewise trigonometric polynomial curve with a shape parameter is discussed.Based on the idea of adjusting the control points.By using two-order trigono-metric Bezier polynomial basis functions,the piecewise trigonometric polynomial curves are constructed.The significance of the parameter of curve is the convex combination of control points.Furthermore,the general parameter setting method is given.And geometric contin-uous conditions of the parameters for the adjacent trigonometric polynomial curves are given.Secondly,using the two order trigonometric Bezier polynomial basis,two-order trigono-metric B-spline basis functions are constructed.And their properties are discussed.The two-order trigonometric B spline function and curve are constructed by the spline basis.It is continuous piecewise quadratic polynomial function.Otherwise,nine different types of curves can be obtained by changing the range of the shapes in the two-order trigonometric B spline curve.Finally,the geometric continuous conditions of the trigonometric B spline curves are discussed.