Designing fair curves using monotone curvature pieces

Authors:
Yulin Wang;Bingyang Zhao;Luzou Zhang;Jiachuan Xu;Kanchang Wang;Shuchun Wang
Affiliations:
Department of Transport and Vehicle Engineering, Shandong University of Technology, 255012, Zibo, PR China and Department of Mechanical Engineering and Automation, Beijing University of Aeronautic ...;Department of Transport and Vehicle Engineering, Shandong University of Technology, 255012, Zibo, PR China and Department of MAE, University of California, Davis, CA;Department of Transport and Vehicle Engineering, Shandong University of Technology, 255012, Zibo, PR China;Department of Transport and Vehicle Engineering, Shandong University of Technology, 255012, Zibo, PR China;Department of Transport and Vehicle Engineering, Shandong University of Technology, 255012, Zibo, PR China;Department of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, PR China
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

Sufficient Monotone Curvature Variation (MCV) conditions for planar Bézier and B-spline curves are described in this paper. Based on the MCV conditions which are presented, a shape control method for Bézier and B-spline curves is proposed. This method is described as finding a solution of an optimization problem subject to the MCV constraints. Since the shape control method for curves retains the desirable MCV pieces and eliminates all unwanted curvature waves, designers could easily modify curves to meet their design intentions. Practical curve examples for automobile body design verify the proposed method and demonstrate its applicable potentials.