三次B啨zier曲线间的几何延拓算法

Geometric Extension of Nonadjacent Cubic Bézier Curves

在保持几何连续及光顺的条件下,将一条已知的三次B啨zier曲线延拓到另一条与其不相邻接的三次B啨zier曲线,其中间媒介同样是三次B啨zier曲线,可以是一条,也可以是2条,而且其形状可以由用户加以调整·同时利用几何拼接的条件构造出形状可调的延拓曲线,进而对近似于曲线弧长、曲线能量、曲率变化率的几类目标函数分别极小化,以生成各种光顺的曲线·

This paper extends a given cubic Bézier curve to another nonadjacent one using one or two cubic Bézier curves to connect them with some geometric continuous conditions. The extension curves are constructed by the geometric continuous conditions by minimizing some fairing functions based on the shortest arc-length, minimum energy and minimum curvature variation of the curves respectively. Shape parameters are introduced in the process of optimization and can be adjusted by the user to control the shape of the extension curves.