• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.253-260
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• 2003

In computer-aided geometric modeling(CAGD), subdivision surfaces are frequently employed to construct free-form surfaces. In the present study, Loop scheme and Catmull-Clark scheme are applied to generate smooth surfaces. To be consistent with the limit points of target surface, the initial sampling points are properly rearranged. The pointwise errors of curvature and position in the sequence of subdivision process are evaluated in both Loop scheme & Catmull-Clark subdivision scheme. In partcural, a general subdivision method in order to generate considering extraordinary points are implemented free from surface with arbitrary sampling point information.

• Korean Journal of Geomatics
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• v.5 no.1
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• pp.35-42
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• 2005

Precise geometric registration is required in multi-source data fusion process to obtain synergistic results successfully. However, most of the previous studies focus on the assumption of perfect registration or registration in a limited local area with intuitively derived simple geometric model. In this study, therefore, we developed a robust method for geometric registration based on a systematic model that is derived from the geometry associated with the data acquisition processes. The key concept of the proposed approach is to utilize smooth planar patches extracted from LIDAR data as control surfaces to adjust exterior orientation parameters of the aerial images. Registration of the simulated LIDAR data and aerial images was performed. The experimental results show that the RMS value of the geometric discrepancies between two data sets is decreased to less than ${\pm}0.30\;m$ after applying suggested registration method.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.3_4
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• pp.239-246
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• 2004

Image snapping for an image moves the cursor location to nearby features in the image, such as edges. In this paper, we propose geometric snapping for 3D triangular meshes, which is extended from image snapping. Similar to image snapping, geometric snapping also moves the cursor location naturally to a location which represents main geometric features in the 3D triangular meshes. Movement of cursor is based on the approximate curvatures which appear geometric features on the 3D triangular meshes. The proposed geometric snapping can be applied to extract main geometric features on 3D triangular meshes. Moreover, it can be applied to extract the geometric features of a tooth which are necessary for generating the occlusal surfaces in dental prostheses.

• Journal of the Korea Computer Graphics Society
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• v.2 no.1
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• pp.31-38
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• 1996

Many efforts for finding smooth curves and surfaces satisfying given constraints have been made, and interpolation and approximation theories with the help of computers have played an important role in this endeavour. Most research in curve and surface modeling has been largely dominated by the theory of parametric representations. While they have been successfully used in representing physical objects, parametric surfaces are confronted with some problems when objects are represented and manipulated in geometric modeling systems. In recent year, increasing attention has been paid to implicit algebraic surfaces since they are often more effective than parametric surfaces are. In this paper, we summarize the geometric properties and computational processes of objects represented using implicit algebraic functions and explain of the implementation of design tools which can design curves and surfaces of revolution. These surfaces of revolution are played an importance role in effective areas such as CAD and CAM.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.301-308
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• 2005

In this study, we implement a framework that directly links a general tensor-based shell finite element to NURBS geometric modeling. Generally, in CAD system the surfaces are represented by B-splines or non-uniform rational B-spline(NURBS) blending functions and control points. Here, NURBS blending functions are composed by two parameters defined in local region. A general tensor-based shell element also has a two-parameter representation in the surfaces, and all the computations of geometric quantities can be performed in local surface patch. Naturally, B-spline surface or NURBS function could be directly linked to the shell analysis routine. In our study, we use NLib(NURBS libraray) to generate NURBS for shell finite analysis. The NURBS can be easily generated by interpolating or approximating given set of data points through NLib.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.794-801
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• 2006

The linkage framework of geometric modeling and analysis based on the NURBS technology is developed in this study. The NURBS surfaces are generated by interpolating the given set of data points or by extracting the necessary information to construct the NURBS surface from the IGES format file which is generated by the commercial CAD systems in the present study. Numerical examples shows the rate of displacement convergence according to the paramterization methods of the NURBS surface. NURBS can generate quadric surfaces in an exact manner. It is the one of the advantages of the NURBS. A trimmed NURBS surface that is often encountered in the modeling process of the CAD systems is also presented in the present study. The performance of the developed geometrically exact shell element integrated with the exact geometric representations by the NURBS equation is compared to those of the previous reported FE shell elements in the selected benchmark problems.

• Journal of Computational Design and Engineering
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• v.2 no.3
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• pp.129-136
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• 2015

This paper proposes a novel method for shape design of a Bezier surface with given boundary curves. The surface is defined as the minimizer of an extended membrane functional or an extended thin plate functional under the guidance of a specified normal field together with an initial prescribed surface. For given boundary curves and the guiding normal field, the free coefficients of a Bezier surface are obtained by solving a linear system. Unlike previous PDE based surface modeling techniques which construct surfaces just from boundaries, our proposed method can be used to generate smooth and fair surfaces that even follow a specified normal field. Several interesting examples are given to demonstrate the applications of the proposed method in geometric modeling.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.11-20
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• 2009

The conventional methods of boundary-conformed 2D surfaces generation usually yield some problems. This paper deals with two boundary-conformed 2D surface generation methods, one conventional approach, the linear Coons method, and a new method, boundary-conformed interpolation. In this new method, unidirectional 2D surface has been generated using some of the geometric properties of the given boundary curves. A method of simultaneous displacement of the interpolated curves from the opposite boundaries has been adopted. The geometric properties considered for displacements include weighted combination of angle bisector and linear displacement vectors at all the data-points of the two opposite generating curves. The algorithm has one adjustable parameter that controls the characteristics of transformation of one set of curves from its parents. This unidirectional process has been extended to bi-directional parameterization by superimposing two sets of unidirectional curves generated from both boundary pairs. Case studies show that this algorithm gives reasonably smooth transformation of the boundaries. This algorithm is more robust than the linear Coons method and capable of resolving the 2D boundary-conformed parameterization problems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.505-511
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• 2002

In the present study, we visualize the linkage framework between geometric modeling and shell finite element based on B-spline representation. For the development of a consistent shell element, geometrically exact shell elements based on general curvilinear coordinates is provided. The NUBS(Non Uniform B-Spline) is used to generate the general free form shell surfaces. Employment of NUBS makes shell finite element handle the arbitrary geometry of the smooth shell surfaces. The proposed shell finite element .model linked with NUBS surface representation provides efficiency for the integrated design and analysis of shell surface structures. The linkage framework can potentially provide efficient integrated approach to the shape topological design optimizations for shell structures.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.593-611
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• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.