G~2 Continuous Preserving Genera-Lized Convex Curve Interpolation Based On Bézier Curve

Curve interpolation has a long history.There are various interpolation methods,from traditional polynomial interpolation to the commonly used spline interpolation,and the recent basic function interpolation methods,which have a wide range of practical applications or theoretical significance.The curve interpolation studied in this paper is mainly to construct a smooth curve through the point column which are ordered.In general,the higher the number of interpolation curves,the more complex the shape of the curve and the more difficult it is to control.This paper mainly studies the construction of segmented low-order Bézier curves,which are combined into a smooth interpolation curve through all given points by ordered stitching.The curve meets the required G1 or G2 continuous conditions at any interpolation point which is the joint,and the shape of the curve can be adjusted locally.In this paper,using the concept of generalized bumps and according to the intrinsic properties of the polylines connected by ordered points,three new control points are inserted between each adjacent two points based on G1 continuous conditions,and the segment curve is constructed with the five adjacent control points that constitute the four-time Bézier curve.The whole curve is guaranteed to be generalized convex continuous.We also introduces the new construction of a generalized convex G1 continuous curve with the three-time Bézier curve.The methods are simple in algorithm,have a unified calculation format,and are convenient to calculate.Finally,an example is given to illustrate the effectiveness of the method.