参数G_2连续保凸插值的充分条件

Sufficient condition of convexity-preserving interpolation with parameter G_2-continuity

对给定数据点进行曲线、曲面的保形插值,是几何外形设计的一个重点和难点问题,保单调和保凸插值则是保形插值的两个基本问题.本文讨论了Bezier参数曲线G2连续保凸插值的曲率方程求解问题,给出了确定参数曲线控制顶点曲率方程存在惟一上界解的充分条件和几何证明.这种保凸插值曲线的形状可通过曲率因子调整.

In geometric shape design, shape-preserving interpolating of curve and surface by given data is an important and difficult subject, and both monotonicity-preserving and convexity-preserving interpolation are two basic problems, In this paper, we discuss solution of curvature equation of convexity preserving interpolation with parameter Bezier curves G^2-continuity, and a suflicient condition and geometric proof are given that in curvature equation of controlling vertex exists a unique upper bound solution. Shape of convexity-preserving interpolation curves can be modified by using curvature values.