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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.101 P.165~173


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

Author(s):  Xu Hui-Xia, Wang Guo-Jin

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   gjwang@hzcnc.com

Key Words:  Discrete B-spline, The product of B-spline functions, Rational B-spline curve, Monotone curvature variation

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Xu Hui-Xia, Wang Guo-Jin. New method for distinguishing planar rational cubic B-spline curve segments as monotone curvature variation[J]. Journal of Zhejiang University Science A, 2006, 7(101): 165~173.

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T1 - New method for distinguishing planar rational cubic B-spline curve segments as monotone curvature variation
A1 - Xu Hui-Xia
A1 - Wang Guo-Jin
J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.AS0165

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-spline 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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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