Journal of Zhejiang University-SCIENCE A

, Volume 7, Supplement 2, pp 165–173 | Cite as

New method for distinguishing planar rational cubic B-spline curve segments as monotone curvature variation

  • Xu Hui-xia 
  • Wang Guo-jin 


In order to fair and optimize rational cubic B-spline curves used frequently in engineering, and to improve design system function, some formulae on the degree and the knot vector, of the product of three B-spline functions, are presented; then Marsden’s identity is generalized, and by using discrete B-sline theory, the product of three B-spline functions is converted into a linear combination of B-splines. Consequently, a monotone curvature variation (MCV) discriminant for uniform planar rational cubic B-spline curves can be converted into a higher degree B-spline function. Applying the property of positive unit resolution of B-spline, an MCV sufficient condition for the curve segments is obtained. Theoretical reasoning and instance operation showed that the result is simple and applicable in curve design, especially in curve fair processing.

Key words

Discrete B-spline The product of B-spline functions Rational B-spline curve Monotone curvature variation 

CLC number



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Copyright information

© Zhejiang University 2006

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.State Key Laboratory. of CAD&CGZhejiang UniversityHangzhouChina

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