Interpolation Curves with Generalized Convexity-Preserving

In order to find a simple and effective convex curve interpolation, this paper proposes a method of using piecewise Bezier curve to construct a smooth interpolation curve. For a given set of point sequence, according to the direction of the polyline produced by the data points, we determine the vector of the curve at the every interpolating point. And then by using the concept of generalized convexity point sequence, we obtain the control points of the piecewise Bezier curves of degree three between every two points in view of the design algorithm. This four points determine a Bezier curves of degree three. Thus, we construct the piecewise smooth Bezier curves which pass through the data points. The middle two control points of each piece curve are determined by four adjacent points. The present method is available for an arbitrary set of point sequence, and enjoys the following advantages： Convexity-preserving; Local shape adjustable; Do not need to solve a system of equations; Simple algorithm and less computation. In the end, it shows that the method is very efficient through some examples.