One Order Trigonometric B-spline Curves

Trigonometric spline function is an important approximation function in the theory and study field of function approximation,and it has been proved to be very effective in the design and generation of curves or surfaces.It can describe free curves and surfaces simply and ideally.As trigonometric B-spline with simple construction,stable calculation,it is widely applied.In fact, the generated curves often need to change shape to adjust different requirements.The construction and properties of one order trigonometric B-spline basic function is presented in this paper. We focus on curve shape changes through control point changes and the control point changes are fulfilled by transforming matrix with shape parameters.Major conducted works as follows:Firstly,the paper explains the theory of trigonometric B-spline curve shape adjustment and its method.Secondly,the paper gives out the construction of one order trigonometric B-spline basic func-tions.The properties of the basic functions and the case of multiple knots of the basic functions are discussed.This kind basic functions can be used to construct one order trigonometric B-spline curves.Furthermore,this paper constructs one order trigonometric B-spline curves with all edge tangent to a given control polygon and one order trigonometric B-spline interpolation curves.Finally,by the method of control points transformation,a kind of spline curve with shape parameters is presented.More specifically,the paper gives out the construction of one order trigonometric B-spline curves with shape parameters by the method of control points transformation and curve shape change caused by shape parameter adjustment.In the method,one order trigonometric B-spline hasn’t been changed during the process of adjusting the position and quantity of control points.So we just need to discuss that how the value of parameter changes the shape of one order trigono-metric B-spline curves.In addition,based on the facts that one order trigonometric B-spline curves have outstanding locality characteristics and mainly depend on control points and basic func-tions, we focus on the extent which parameter changes the local shape of curves.Also we can adjust the shape of curves by the method.