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应用数学学报  1990, Vol. 13 Issue (1): 56-63    DOI:
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四阶n次B样条曲线的单调逼近性及奇拐点分析
叶正麟
西北大学
MONOTONE APPROXIMATION AND ANALYSIS OF INFLEXION AND SINGULAR POINTS OF 4-n B-SPLINE CURVES
Ye Zheng-lin
Northwest University
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摘要 通常的B样条曲线,Bézier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{V3(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.
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叶正麟
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Abstract: A class of B-spline curves with an additional parameter n is suggested which converges monotonously to its control polygon to the sense that the sequence of their convex hulls {V3(n)} is monotonic decreasing and approaches the control polygon as n tends to infinity.The distribution of inflexion and singular points of the planar curves is analysised by using the visual geometric methods different from those in [1-6],avoiding the difficulty in analysis roots of algebraic equations.Some simple and pratical methods of producing the curve that has no singular points or has only one indispensable inflexion are given.
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收稿日期: 1987-06-15;
引用本文:   
叶正麟. 四阶n次B样条曲线的单调逼近性及奇拐点分析[J]. 应用数学学报, 1990, 13(1): 56-63.
Ye Zheng-lin. MONOTONE APPROXIMATION AND ANALYSIS OF INFLEXION AND SINGULAR POINTS OF 4-n B-SPLINE CURVES[J]. Acta Mathematicae Applicatae Sinica, 1990, 13(1): 56-63.
 
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