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

10.1631/jzus.2006.AS0165


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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DOI - 10.1631/jzus.2006.AS0165


Abstract: 
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.

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Reference

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