保形几何Hermite插值

The Shape Preserving Geometric Hermite Interpolation

本文将保形概念引入到几何:Hermite插值,利用三次Bezier曲线段构造了一条GC2连续的保形参数三次几何:Hermite插值曲线,曲线在相邻两个型值点之间,由两段三次:Bezier曲线组成。该曲线的所有Bezier点由型值点及相应的曲率信息直接计算产生,无需求解矢量方程组,因此该曲线计算简单,局部修改方便。

This paper introduces the concept of shape-preserving into Geometrical Hermite Interpo-lation(GHI). Based on the cubic Bezier curve segment, an algorithm for constructing GC2-continuos shape preserving parametric cubic GHI curve is presented, between two adjacent data points, the curve is composed of two cubic Bezier segments. All Bezier points of the curve can be computed directly by using data points and curvatures, there is no need to solve the vector system of equations, the calculation is thus simple and the local modification is convenient.