Modeling energy-minimizing curves have many applications and are a basic problem of Geometric *** this paper,we propose the method for geometric design of energy-minimizing B′ezier ***,the necessary and sufficient co...
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Modeling energy-minimizing curves have many applications and are a basic problem of Geometric *** this paper,we propose the method for geometric design of energy-minimizing B′ezier ***,the necessary and sufficient condition on the control points for B′ezier curves to have minimal internal energy is *** 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 *** some control points,the other control points can be determined as the linear combination of the given control *** 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 *** also compare the proposed method with previous methods on efficiency and ***,several applications of the curve generation technique,such as curve interpolation with geometric constraints and modeling of circle-like curves are discussed.
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