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Geometric construction of energy-minimizing Bézier curves

Science China(Information Sciences) 2011年第7期54卷 1395-1406页

作者： XU Gang 1,4,5,WANG GuoZhao 2 & CHEN WenYu 2,3 1 Institute of Graphics and Image,Hangzhou Dianzi University,Hangzhou 310018,China 2 Department of Mathematics,Zhejiang University,Hangzhou 310027,China 3 School of Computer Engineering,Nanyang Technological University,639798,Singapore 4 Galaad,INRIA Sophia-Antipolis,2004 Route des Lucioles,06902,France 5 State Key Lab of CAD & CG,Zhejiang University,Hangzhou 310027,China 1. Institute of Graphics and Image Hangzhou Dianzi University Hangzhou 310018 China4. Galaad INRIA Sophia-Antipolis 2004 Route des Lucioles 06902 Sophia Antipolis France5. State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China2. Department of Mathematics Zhejiang University Hangzhou 310027 China3. School of Computer Engineering Nanyang Technological University Singapore 639798 Singapore

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.

关键词： curve design minimal energy geometric construction interpolation with constraints circle-like curves

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