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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 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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Inverse minimum spanning tree problem and reverse shortest-path problem with discrete values

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Progress in Natural Science:Materials International 2006年第6期16卷 649-655页

作者： LIU Longcheng and HE Yong (Department of Mathematics, zhejiang university, hangzhou 310027, china state key laboratory of cad & cg, zhejiang university, hangzhou 310027, china) Department of Mathematics Zhejiang University Hangzhou 310027 China state key laboratory of cad and cg Zhejiang University Hangzhou 310027 China

In this paper, we consider two network improvement problems with given discrete values: the inverse minimum spanning tree problem and the reverse shortest-path problem, where the decrements of the weight of the edges are given discrete values. First, for the three models of the inverse minimum spanning tree problem (the sum-type, the bottleneck-type and the constrained bottleneck-type), we present their respective strongly polynomial algorithms. Then, we show that the reverse shortest-path problem is strongly NP-complete.

关键词： minimum spanning tree shortest-path problem inverse problem reverse problem computational complexity.

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Multiple products of B-splines used in cad system

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Progress in Natural Science:Materials International 2006年第4期16卷 425-430页

作者： XU Huixia and WANG Guojin Institute of Images and Graphics, zhejiang university, hangzhou 310027, china state key laboratory of cad&cg, zhejiang university, hangzhou 310027, china Institute of Images and Graphics Zhejiang University Hangzhou 310027 China state key laboratory of cad and cg Zhejiang University Hangzhou 310027 China

The function upgrade of computer aided design (cad) system requested that the multiple product of B-spline functions should be represented as a linear combination of some suitable (usually higher-degree) B-splines. In this paper, we apply the theory of spline space and discrete B-splines to deduce the representation of the coefficients of all terms of the linear combination, which can be directly applied to software coding in system development.

关键词： computer aided design (cad) NURBS Marsden’s identity.

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Acquisition of time-varying 3D foot shapes from video

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Science china(Information Sciences) 2011年第11期54卷 2256-2268页

作者： GAO Fei,WANG Qing,GENG WeiDong & PAN YunHe state key lab of cad & cg,zhejiang university,hangzhou 310027,china state key lab of cad & cg Zhejiang University Hangzhou China

The 3D scanning of time-varying objects based on multi-view geometry has been a hot topic in computer vision in recent *** paper presents an active approach to acquiring 3D shapes of moving foot from multi-view video sequences based on the explicit marker points woven in *** reference 3D model of foot is firstly recovered from the starting frames in the multi-view video clips,and then the markers in each view are traced as a whole based on a continuous motion vector field built from the reference 3D *** missing vertices in the candidate 3D model caused by self-occlusion,non-uniform illumination and random noises are reliably estimated and reconstructed in 3D space by minimizing the changes of differential features in 3D geometry of the reference *** experimental results show that our method can robustly recover the 3D model of foot in complex background even if there is a relatively large movement between the adjacent frames,with an acceptable accuracy of the resulting 3D model.

关键词： time-varying shapes 3D foot modeling feature tracking multi-view geometry

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Electro-mechanical response of functionally graded beams with imperfectly integrated surface piezoelectric layers

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Science china(Physics,Mechanics & Astronomy) 2006年第5期49卷 513-525页

作者： YAN Wei1 & CHEN Weiqiu1,2 1. Department of Civil Engineering, zhejiang university, hangzhou 310027, china 2. state key lab of cad & cg, zhejiang university, hangzhou 310027, china Department of Civil Engineering Zhejiang University Hangzhou China state key lab of cad & cg Zhejiang University Hangzhou China

The time-dependent behavior of a simply-supported functionally graded beam bonded with piezoelectric sensors and actuators is studied using the state-space method. The creep behavior of bonding adhesives between piezoelectric layers and beam is characterized by a Kelvin-Voigt viscoelastic model, which is practical in a high temperature circumstance. Both the host elastic functionally graded beam and the piezoelectric layers are orthotropic and in a state of plane stress, with the former being inhomogeneous along the thickness direction. A laminate model is employed to approximate the host beam. Moreover, the coupling effect between the elastic deformation and electric field in piezoelectric layers is considered. Results indicate that the viscoelastic property of interfacial adhesives has a significant effect on the function of bonded actuators and sensors with time elapsing.

关键词： functionally graded beam piezoelectric layers Kelvin-Voigt model state-space method

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A new method for designing a developable surface utilizing the surface pencil through a given curve

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Progress in Natural Science:Materials International 2008年第1期18卷 105-110页

作者： Hongyan Zhao,Guojin Wang* Department of Mathematics and state key laboratory of cad&cg,zhejiang university,hangzhou 310027,china Department of Mathematics and state key laboratory of cad&cg Zhejiang University Hangzhou 310027 China

This paper proposes a new method for designing a developable surface by constructing a surface pencil passing through a given curve, which is quite in accord with the practice in industry design and *** utilizing the Frenet trihedron frame,we derive the necessary and suffcient conditions to construct a developable surface through a given *** the requirements in shoemak- ing and garment-manufacture industries,we also study the special case of specifying the given curve as a *** given geodesic can be classified into three types corresponding to each type of developable *** also present the polynomial representation of the developable *** algorithm is convenient and effcient for applications in engineering.

关键词： cad/CAM Developable surface Geodesic Frenet frame

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Joint segmentation and motion estimation of left ventricle with an anisotropic biomechanical model

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Progress in Natural Science:Materials International 2007年第2期17卷 226-229页

作者： ZHUANG Ling, LIU Huafeng, BAO Hujun ( state key laboratory of cad & cg, zhejiang university, hangzhou 310027, china state key laboratory of Modern Optical Instrumentation, zhejiang university, hangzhou 310058, china) state key laboratory of cad and cg Zhejiang University Hangzhou 310027 China state key laboratory of Modern Optical Instrumentation Zhejiang University Hangzhou 310058 China

Accurate estimation of shape and motion variability of the heart has important clinical implications for heart disease diagnosis. In this paper, we describe a framework which performs simultaneous segmentation and motion analysis of the left ventricle from 3D cardiac images. The left ventricle is formulated as an anisotropic linear elastic body represented by a set of tetrahedrons constructed from sampling nodes. The elastic body is evolved by both internal force and external force, and the external force imposed on each node is an integration of edginess measure, shape coherence measure, prior distributions of the myocardial tissues and temporal driven measure. The displacement field and the segmentation result are simultaneously solved at the equilibrium state between the internal energy and the external energy. The experiment with 3D canine MR images illustrated its abilities and benefits.

关键词： left ventricle motion simultaneous estimation deformable model image segmentation.

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Parameterization for fitting triangular mesh

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Progress in Natural Science:Materials International 2006年第11期16卷 1214-1221页

作者： LIN Hongwei**, WANG Guojin, LIU Ligang and BAO Hujun(state key laboratory of cad&cg, zhejiang university, hangzhou 310027, china) state key laboratory of cad and cg Zhejiang University Hangzhou 310027 China

In recent years, with the development of 3D data acquisition equipments, the study on reverse engineering has become more and more important. However, the existing methods for parameterization can hardly ensure that the parametric domain is rectangular, and the parametric curve grid is regular. In order to overcome these limitations, we present a novel method for parameterization of triangular meshes in this paper. The basic idea is twofold: first, because the isotherms in the steady temperature do not intersect with each other, and are distributed uniformly, no singularity (fold-over) exists in the parameterization; second, a 3D harmonic equation is solved by the finite element method to obtain the steady temperature field on a 2D triangular mesh surface with four boundaries. Therefore, our proposed method avoids the embarrassment that it is impossible to solve the 2D quasi-harmonic equation on the 2D triangular mesh without the parametric values at mesh vertices. Furthermore, the isotherms on the temperature field are taken as a set of iso-parametric curves on the triangular mesh surface. The other set of iso-parametric curves can be obtained by connecting the points with the same chord-length on the isotherms sequentially. The obtained parametric curve grid is regular, and distributed uniformly, and can map the triangular mesh surface to the unit square domain with boundaries of mesh surface to boundaries of parametric domain, which ensures that the triangular mesh surface or point cloud can be fitted with the NURBS surface.

关键词： parameterization regular parametric curve grid mesh fitting reverse engineering.

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Copy-and-paste operation of planar polygonal shapes

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Progress in Natural Science:Materials International 2007年第7期17卷 859-866页

作者： Yang Wenwu Feng Jieqing Huang Shengsheng Jin Xiaogang(state key laboratory of cad&cg,zhejiang university,hangzhou 310027,china) state key laboratory of cad and cg Zhejiang University Hangzhou 310027 China

A 2D polygonal shape copy-and-paste method is proposed which is based on a multiple planar shapes blending algorithm. First sub-shapes are specified and selected,which correspond to user-defined visual features on the input *** they are copied and pasted with contribution weights to generate new shapes via a modified intrinsic 2D shape blending *** can edit the generated shape intuitively and interactively by adjusting the contribution *** proposed method fills the gap in the object modeling method- ology based on the copy-and-paste *** the static 2D copy-and-paste operation,the proposed method can also be applied to 2D metamorphosis among multiple planar shapes.

关键词： copy-and-paste 2D shape blending metamorphosis

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RESEARCH OF MOVEMENT NAVIGATION BASED ON ASSEMBLY CONSTRAINT RECOGNITION

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Chinese Journal of Mechanical Engineering 2002年第1期15卷 6-10页

作者： Zhang Shuyou Gao Zhan Tan Jianrong Liu Zhenyu state key laboratory of cad&cg，zhejiang university，hangzhou 310027，china zhejiang university State Key Laboratory of CAD&CG Hangzhou 310027

The requirements and features of virtual assembly movement navigator areanalyzed to help operators flexibly manipulate virtual objects, precisely locate or assemble virtualparts in virtual environment. With the degree-of-freedom analysis, the assembly constrainthierarchical model is constructed and the system's constraints are built dynamically. Thus, allobjects in virtual environment can be located reasonally by the navigator. Moreover, the assemblyconstraint recognition in the process of assembly and movement correction is also discussed.

关键词： Virtual assembly Movement navigation Degree of freedom Assembly model Constraint recognition Movement correction

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