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Modeling energy-minimizing curves have many applications and are a basic problem of Geometric Modeling.In this paper,we propose the method for geometric design of energy-minimizing B′ezier curves.Firstly,the necessary and sufficient condition on the control points for B′ezier curves to have minimal internal energy is derived.Based on this condition,we propose the geometric constructions of three kinds of B′ezier curves with minimal internal energy including stretch energy,strain energy and jerk energy.Given some control points,the other control points can be determined as the linear combination of the given control points.We compare the three kinds of energy-minimizing B′ezier curves via curvature combs and curvature plots,and present the collinear properties of quartic energy-minimizing B′ezier curves.We also compare the proposed method with previous methods on efficiency and accuracy.Finally,several applications of the curve generation technique,such as curve interpolation with geometric constraints and modeling of circle-like curves are discussed.
Modeling energy-minimizing curves have many applications and are a basic problem of Geometric Modeling. In this paper, we propose the method for geometric design of energy-minimizing B’ezier curves. Firstly, the necessary and sufficient conditions on the control points for B ’Ezier curves to have minimal internal energy is derived.Based on this condition, we propose the geometric constructions of three kinds of B’ezier curves with minimal internal energy including stretch energy, strain energy and jerk energy. Gain some control points, the other control points can be determined as the linear combination of the given control points. We compare the three kinds of energy-minimizing B’ezier curves via curvature combs and curvature plots, and present the collinear properties of quartic energy-minimizing B’ezier curves. We also compare the proposed method with previous methods on efficiency and accuracy. Finally, several applications of the curve generation technique, such as curve interpolation with geometric constraints and modeling of circle-like curves are discussed.