Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (1): 44-48.

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A Geometric Proof of the Convexity Preserving Property of NURBS Curves

  

  1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China)
  • Received:2003-11-27 Online:2006-03-30 Published:2023-12-19
  • About author:LIU Chao-yang(1964-),male,native of Xinye,Henan,a professor of Zhengzhou University, Ph.D.,engages in computer aided geometric design.
  • Supported by:
     Supported by the National Natural Science Found of China(10371113); Supported by the 2002 Henan Found of Younger Teacher;

Abstract: NURBS curves are convexity preserving, i.e. once the control polygon is convex, the associated NURBS curve will also be convex. In this paper this property is proved geometrically.

Key words:  , convexity preserving, knot-insertion, Bezier curve, NURBS curve

CLC Number: