Study On The Method Of Smooth And Convexity-Preserving Interpolation

In Computer-Aided Geometry Design and related fields,the convexity-preserving interpolation is a very basic and important research subject. There are a lot of good convexity-preserving interpolation method,which can be divided into continuous function and discrete subdivision method.Function based method is used to solve a series of continuity and convexity conditions, and the Bezier spline curves, riangular Bezier spline and so on. The method of subdivision such as Dyn’s four points method,the parameters are introduced to achieve the curve convexity at each subdivision. In order to overcome the drawbacks of the existing methods, a convexity-preserving interpolation method based on the intrinsic properties of a set of convex data points is proposed.The method introduces the concept of the generalized convexity of data points. For a set of generalized convex data points, directly insert the control points of Bezier segment into every two data points according to the direction of the polyline produced by the data points; The control points are obtained by the condition of its convexity being the same as that of the data points, and by assuming the smooth connecting between two adjacent Bezier segments; The control points of every Bezier segment are only determined by 4 adjacent data points, thus the curve is local shape adjustable.For a given plane, the general points are listed, and the method is similar to the convex point, but the need for a more detailed classification is discussed. The resulting curve has following advantages:1,ensure smooth; 2, curve shape locally adjustable; 3, without solving system of equations; 4, the algorithm is simple, easy popularization, etc..