有理B-样条曲线的离散构造与保型性问题

ON THE DISCRETE CONSTRUCTIONS AND SHAPE-PRESERVING PROPERTY OF RATIONAL B-SPLINE CURVES

在各种计算机辅助外型设计与制造中,曲线、曲面等几何造型是一个基本问题.这是因为现实客观世界中存在着许多不能用直线、平面和二次曲线(面)等简单几何模型所表示的几何实体,如汽车、船舶、飞机外型和地质、物理。

In this paper, the discrete constructions and the algorithms are studied for rational B-splinecurves. From the point of view of geometry, we introduce the rational discrete B-spline curvesby which the convexity theorem and the V-D property are simply proved.