论参数曲线曲面的几何不变性

ON GEOMETRIC INVARIABILITY OF PARAMETRIC CURVES AND SURFACES

本文在揭示一般参数曲线、曲面总可以采用完全或部分规范基函数表示的基础上,给出了几何不变性定理:空间参数曲线、平面参数曲线、参数曲面经过与坐标系的相对运动后,形状保持不变,且其完全或部分规范基函数表示不变。并介绍了几何不变性在计算机辅助几何设计(CAGD)与计算机绘图中的应用及一些实例。

The conclusion on geometric invariability of parametric curves and surfaces given by differential geometry is that the shapes of parametric curves and surfaces are independent to co-ordi-nate system taken.This paper reveals that parametric curves and surfaces can usually take a kindof representation with full or patial normalized basic fuctions.Based on the representation,the pa-per gives geometric invariability theorem;the shapes of spaeial parametric curves(7),plane para-metric curves(13),parametric surfaces(14)and their representations with full or patial norma-lized basic functions keeping invariable after a relative motion between them and co-ordinate sys-tem taken.Finally,some of applications of geometric invariablity in Computer-Aided GeometricDesign(CAGD)and Computer Graphics and examples are given.