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Efficient Construction of B-Spline Curves with minimal Internal energy

Computers, Materials & Continua 2019年第3期58卷 879-892页

作者： Gang Xu Yufan Zhu Lishan Deng Guozhao Wang Bojian Li Kin-chuen Hui School of Computer Science and Technology Hangzhou Dianzi UniversityHangzhouZhejiang310018China Department of Mathematics Zhejiang UniversityHangzhouZhejiang310018China Department of Mechanical and Automation Engineering Chinese University of Hong KongHong Kong999077China.

In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask *** linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear *** existence and uniqueness of the solution for the linear system are also *** results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.

关键词： minimal energy B-spline curves geometric construction discrete mask method sparse linear system.

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Geometric construction of energy-minimizing Bézier curves

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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 Institute of Graphics and Image Hangzhou Dianzi University Hangzhou China Galaad INRIA Sophia-Antipolis Sophia Antipolis France State Key Lab of CAD & CG Zhejiang University Hangzhou China Department of Mathematics Zhejiang University Hangzhou China School of Computer Engineering Nanyang Technological University Singapore 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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Results on energies for trees with a given diameter having perfect matching

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Journal of Shanghai University(English Edition) 2011年第6期15卷 493-500页

作者：王文环康丽英 Department of Mathematics College of SciencesShanghai University

Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of *** a tree T in Γd2n,let Pd＋1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd＋*** can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] ＋ 1 q2d 33 1.

关键词： tree perfect matching diameter minimal energy

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energy Optimization of Deployable Tensegrity Structure

Energy Optimization of Deployable Tensegrity Structure

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第三十届中国控制会议

作者： SKELTON Robert E. University of California San Diego 92093 USA

＜正＞This paper presents a numerical method to design a tensegrity structure which can deploy itself to a desired shape and cost the minimal *** from the dynamic model in matrix the static model in vector form which is easy to solve the force density is *** self-deploy control problem is described as a math model by using this new vector model and the condition whether there exists a solution is given *** algorithm is adopted to get the optimal *** optimization method investigated is applied to two examples and simulation results demonstrate that the theory works well.

关键词： minimal energy Tensegrity Deployable Control Constrained Optimization

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