Parametric Curve Rational Interpolation

In the numerical calculation,in a finite set of points,the function of the interpolation function is given,and the interpolation function is expressed in a simple formula.In this section,the complex interpolation function is approximated by a simple interpolation function.For example,some complex curves,surfaces,etc..We know that the curve and surface has the explicit,implicit and parametric said,but from the point of view of computer graphics and computational geometry,or the use of parameters to represent the better,because the method parameter representations of curves and surfaces,the shape from a specific coordinate dependence free,using mathematical methods,of free-form curves and surfaces to provide more accurate representation,so that you can be more easily with the aid of the computer can be realized.The interpolation form of rational interpolation is simple,and it has a good shape preserving and smooth,which is favorable to the local modification of interpolation.The rational interpolation function is more flexible and can reflect the properties of the rational interpolation function,such as the monotone,concave and convex.Due to the expression of recessive closed curve itself,the conventional polynomial interpolation is adopted or new rational spline interpolation of closed curve data points are not good description.This article from the policy of rational interpolation tonality,protect convexity,and so on direction to described the properties of the interpolation function.By introducing two parameters ?i and ?i,A using the representation of implicit function,respectively on x and y interpolation.On the premise of unchanged data,by the changes of parameters for the interactive modification.