The Study Of Quartic B-spline Function With The Parameters And Its Application

In the field of the approximation of function,studies of spline function occupy an extremely important position.We can use the spline function to solve the design problem of the curve/surface in the process of research and production.We know each segment of spline function is a polynomial.In that way,the polynomial function has the advantage of simple,feasible and continuous.It is differentiable and integrable everywhere.What is more important is its low frequency,and small amount of calculation.Therefore,the spline function not only keeps its advantages but also overcomes the shortcomings such as its too volatile and not smooth.Additionally it possesses locally adjustable in paragraphs and able to maintain a continuous good properties.Especially the B-spline function,because it has the characteristics of simple structure,convenient for calculation,flexible to use and the natural smooth connection.Therefore,as the base function of spline function,B-spline function has been widely used in many fields such as geometry modeling.In the production and application,people often need to change the shape of the curve/surface the construction from a spline function,which refers to the problems of the shape of the curve/surface adjustment.This paper analyses and discusses quartic B-spline curve shape adjustment problems.The main work is as follows:Firstly,the paper summarizes the spline function and spline curve research status at home and abroad,the theory and method and the development course of parameter spline curve and then expounds the general research situation of spline curve with shape parameter and the structure of quartic B-spline curve with adjustment parameter is given.Secondly,the paper analyses the curve which is designed above and discusses the local shape adjustment of the curve.This paper mainly uses the method of transformation matrix to generate the required quartic B-spline curve and determines the geometric meaning of the parameter.This paper also discusses the continuity of the curve and achieves a certain continuity conditions.Thirdly,the paper discusses the method to adjust general B-spline curve.The paper analyzes the construction of B-spline curve and use the method of adjacenting two control points to create new points of control adjust the shape of the curve,.Then the paper discusses the problem of continuous parametric curves.Finally,the paper shows some examples of adjusting quartic B-spline curve shape graphics.The method of the paper mainly from the angle of the control points to make the curve deformation,to make it with a certain parameters,then change the parameters value.But its basic functions do not change,so we can directly use some good properties of the basic functions and do not need to discuss.When the basic function is too much,we can easily use this method to generate of the curves of different shapes.