Journal of Zhejiang University SCIENCE A
(Monthly)

2006   Vol. 7   Suppl. II   p. 165-173

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

Xu Hui-Xia^1,2, Wang Guo-Jin^†‡1,2

(¹Department of Mathematics, Zhejiang University, Hangzhou 310027, China)
(²State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China)
^‡ Corresponding Author
^†E-mail: gjwang@hzcnc.com
Received Sept. 6, 2005 revision accepted Mar. 3, 2006

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.

Key words: Discrete B-spline, The product of B-spline functions, Rational B-spline curve, Monotone curvature variation
doi:10.1631/jzus.2006.AS0165             CLC number: TP391

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