四阶n次B样条曲线的单调逼近性及奇拐点分析

MONOTONE APPROXIMATION AND ANALYSIS OF INFLEXION AND SINGULAR POINTS OF 4-n B-SPLINE CURVES

通常的B样条曲线,Bezier曲线,还是有理参数曲线都不收敛于它们的控制多边形.本文给出的一类四阶n次B样条曲线(当n=3时即为三次B样条曲线),在其凸包族{V_3(n)}单调嵌套且收敛于曲线的控制多边形的意义下,单调地逼近于此控制多边形.在平面曲线情形,本文利用不同于[1—6]中的方法,避开分析代数方程的根的困难,

A class of B-spline curves with an additional parameter n is suggested which conver-ges monotonously to its control polygon in the sense that the sequence of their convex hulls{V_3(n)} is monotonic decreasing and approaches the control polygon as n tends to infi-nity. The distribution of inflexion and singular points of the planar curves is analysisedby using the visual geometric methods different from those in [1-6], avoiding the diffi-culty in analysis roots of algebraic equations. Some simple and pratical methods of producingthe curve that has no singular points or has only one indispensable inflexion are given.