Shape control of Bé;zier surfaces with iso-parametric monotone curvature constraints

Authors:
Yulin Wang;Shuchun Wang;Luzou Zhang;Bingyan Zhao
Affiliations:
Department of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, PR China and Department of Transport and Vehicle Engineering, Shandong University ...;Department of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, 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 and Department of MAE, University of California at Davis, CA
Venue:
Computer Aided Geometric Design
Year:
2003

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Abstract

This paper describes a sufficient condition of Monotone Iso-parametric Curvature Variation (MICV) for tensor product Bézier surfaces. The condition is a set of inequalities of the control points of the Bézier surface. Based on the MICV condition, a shape control method is presented to generate a MICV Bézier surface. The method is implemented as a nonlinearly constrained optimization problem subject to the MICV constrains. The optimal MICV surface is closest to the initial one in terms of the least square of the control points. Cases studies verify the effectiveness of the proposed method of shape control.