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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

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

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.

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&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.

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&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

Controllable highly regular triangulation

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Science china(Information Sciences) 2011年第6期54卷 1172-1183页

作者： HUANG Jin, ZHANG MuYang, PEI WenJie, HUA Wei & BAO HuJun cad&cg state key lab of zhejiang university, hangzhou 310058, china cad&cg state key lab of zhejiang university

This paper presents a novel algorithm for generating a highly regular triangle mesh under various user requirements. Three scalar fields are first computed on the input mesh. Then, the intersections of their isocontours with one another are used to construct the highly regular mesh result. The proposed algorithm uses the N-symmetry direction field to guide the edge orientation. Size control is achieved by using a density function on the surface. All user requirements are incorporated into an energy optimization framework of the scalar fields, and then the isocontours of the generated scalar fields are used to construct a high quality result that satisfies all requirements. The experimental results show that the proposed method can successfully handle various user requirements and complex shapes.

关键词： surface remeshing triangulation semi-regular mesh highly regular mesh N-symmetry direction field

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

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

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.

RESEARCH ON THE CONSTRAINT MAPPING FROM FUNCTION TO ASSEMBLY

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Chinese Journal of Mechanical Engineering 2003年第3期16卷 305-308页

作者： Tan JianrongJi YangjianLiu ZhenyuChen HongliangYue Xiaolistate key laboratory of cad&cg,zhejiang university,hangzhou 310027, china zhejiang university State Key Laboratory of CAD&CG Hangzhou 310027

Assembly sketch is not only the visualization of abstract function, but alsothe template of detail design. Two kinds of information are needed to create assembly sketch:structure and assembly constraint. Most researches are aimed at bow to obtain Structures fromfunction, but the problem of how to obtain assembly constraint from function is ignored. Followingthe definition of assembly unit and the classification of function, a hierarchical mapping methodfrom function to assembly constraint is put forward, and the mapping method includes two steps. Thefirst step is the mapping from function to assembly semantics which is assembly expression andaccordant with engineer's design habit. The second one is the mapping from assembly semantics tobasic assembly constraints that are convenient for computer to handle. The mapping method is appliedto DDMS (design, drafting and management system) successfully.

关键词： Constraint mapping Assembly constraint Assembly design Function design

RESEARCH OF GUIDANCE TECHNOLOGY FOR ASSEMBLY MODELING IN VIRTUAL ENVIRONMENT

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Chinese Journal of Mechanical Engineering 2001年第2期14卷 139-143,150页

作者： Zhang Shuyou Liu Zhenyu Tan Jianrong state key laboratory of cad&cg,zhejiang university 浙江大学计算机辅助设计与图形学国家重点实验室浙江

Technology of movement and knowledge guidance in virtual assembly is presented The designer can move the mechanical part precisely under the movement guidance The movement guidance is implemented based on constraint recognition and assembly degree of freedom analysis A multi hierarchy knowledge base is built to represent the assembly knowledge and information The virtual assembly system judges the requirement of the designer based on the context of design task and searches for the useful knowledge and information, which can be provided to the designer in a natural way

关键词： Virtual assembly Virtual reality Movement guidance Knowledge guidance