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| New method for distinguishing planar rational cubic B-spline curve segments as monotone curvature variation |
| Xu Hui-Xia, Wang Guo-Jin |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China; State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China |
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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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Received: 06 September 2005
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