Curvature monotony condition for rational quadratic b-spline curves

Authors:
Zhong Li;Lizhuang Ma;Dereck Meek;Wuzheng Tan;Zhihong Mao;Mingxi Zhao
Affiliations:
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;Department of Computer Science, University of Manitoba, Winnipeg, Canada;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
Venue:
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Year:
2006

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Abstract

The monotone curvature condition for rational quadratic B-spline curves is studied in this paper. At first, we present the necessary and sufficient conditions of monotone curvature for the uniform rational quadratic B-spline segment and we compare it to the curvature condition of rational quadratic Bezier curve. Then, we give the sufficient condition of monotone curvature for the nonuniform rational quadratic B-spline segment. At last, we obtain the condition of monotone curvature for general rational quadratic B-spline curves with any number of control points.