• Honam Mathematical Journal
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• v.28 no.1
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• pp.83-111
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• 2006

After introducing Tropical Algebraic Varieties, we give a polyhedral description of tropical hypersurfaces. Using TOPCOM and GAP, we show that there exist 59 types of two dimensional tropical quadric surfaces. We also show a criterion for a quadric hypersurface to be non-degenerate in terms of a tropical rank.

• Journal of computational fluids engineering
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• v.19 no.1
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• pp.1-6
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• 2014

Since experiments on the actual operational status are said to be very impractical because of their economic and repeatability problems, it is difficult to understand the thermal profiles of aerospace or military equipments. Thus, the CFD codes with considering the radiation heat transfer are used to compensate the defect. In case, analyzing the radiation exchanges between the object surfaces are very important. Because the temperature and the IR signal distributions of the object surface are significantly affected by the radiative heat transfer. To achieve accurate thermal radiation exchange between surfaces, it is important to calculate the radiation view factor precisely. Finer subdivision of meshes can be used to increase the accuracy of radiation view factor, but if the mesh is subdivided infinitely, the time required for calculation increases significantly and thus decreasing the efficiency. If the subdivision is not sufficient, assurance of accuracy is not guaranteed. In this paper, optimal mesh subdivision method using the solid angle has been successfully tested and found to be useful in increasing the efficiency of calculating the shape factors.

• Korean Journal of Computational Design and Engineering
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• v.4 no.3
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• pp.269-283
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• 1999

Surface/surface intersection is a common and important problem in geometric modeling and CAD/CAM. Several methods have been used to approach this problem. All possible intersection curves can be obtained by using the subdivision algorithm, while it requires a great deal of memory and is somewhat inefficient. The tracing algorithm is much faster than the subdivision algorithm, and can find points on the intersection curve sequentially. But, the tracing algorithm has some problems in the intersection curves on surface boundaries. In this paper, an Improved tracing algorithm that includes some ideas such as a new trace-terminating condition for the intersection curves on surface boundaries, detecting closed intersections and extension for composite surfaces is suggested. This algorithm consists of three step: generating state points for curve tracing, tracing intersection curves and sorting pieces of the intersection curves. The results of this algorithm and comparisons to the 'DESIGNBASE' and 'ACIS' system are presented.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.151-160
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• 2004

In the present study, Loop scheme is 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 the Loop subdivision scheme. A first-order shear deformable Loop subdivision triangular element which can handle transverse shear deformation of moderately thick shell are developed. The developed element is more general than the previous one based on classical shell theory, since the new one includes the effect of transverse shear deformation and has standard six degrees of freedom per node. The quartic box spline function is used as interpolation basis function. Numerical examples for the benchmark static shell problems are analyzed to assess the performance of the developed subdivision shell element and locking trouble.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1084-1089
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• 1992

Process planning is a key feature that an intelligent CAD/CAM system should possess. In this paper, we address the problem of determinig process configuration to manufacture the free surfaces. For analyzing the surface, the method of surface subdivision is used. The developed algorithm evaluates the processability of the given surface by applying the three/four/five-axes procedures sequentially. To illustrate and test the developed algorithm, numerical simulations are presented.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.121-126
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• 1998

It is one of important issues to find intersection curve? in representation of complex surfaces on a computer. Three typical methods, i.e. the tracing method, the subdivision method, and hybrid method, are often applied to find intersection curves between sculptured surfaces. In this paper two topics are dealt with for efficiency and robustness of the hybrid method. One tropic is about how to determine step sizes variably during tracing, the ethel is about how to find tangential points between surfaces. Tracing by variable step size finds intersections rapidly and requires less memory size. Some illustrations show tangential points between surfaces.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.551-556
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• 2009

3-D CAD (Computer Aided Design) system is an indispensable tool for manufacturing. A lot of engineers have studied for the methods to generate a curved surface on an N-sided shape, which is the basic technology of 3-D CAD systems. This surface generation, however, has three problems on the case of long and narrow shapes: the resultant surface is distorted, the surface is not continuous to adjacent surfaces, or additional user inputs are required to generate the surface. Conventional methods have not yet solved these problems at the same time. In this paper, we propose the method to generate internal curves that divide a long and narrow shape into regular N-sided sections so as to divide the shape into an N-sided section and four-sided ones. Our method controls the shape of internal curves by dividing an N-sided long and narrow shape into an N-sided section and four-sided ones, and solves distortion of the generated curved surface. In addition, each of the generated sections is interpolated with G1-continuous surfaces. This process does not require any user's further input. Therefore, the three problems mentioned above will be solved at the same time.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.116-127
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• 2014

This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.17 no.4
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• pp.39-46
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• 2018

Two surfaces that have relative motion show different characteristics according to surface roughness or surface patterns in all lubrication areas. For two rough surfaces with mixed lubrication, this paper proposes a new approach that includes the contact characteristics of the surfaces and a probabilistic method for a numerical analysis of lubrication. As the contact area of the two surfaces changes according to the loading conditions, asperity contact is very important. An average flow model developed by Patir-Cheng is central to the study of lubrication for rough surfaces. This average flow model also refers to a multi-asperity contact model for deriving a modified Reynolds equation and calculating the lubricant characteristics of a bearing surface with random roughness during fluid flow. Based on the average flow model, this paper carried out a numerical analysis of lubrication using a contact model by considering a load change made by the actual contact of asperities between two surfaces. Lubrication properties show different characteristics according to the surface patterns. This study modeled various geometric surface patterns and calculated the characteristics of lubrication.

• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.144-154
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• 2000

We propose an algorithm for obtaining a triangular approximation of a trimmed NLRBS surface. Triangular approximation is used in the pre-processing step of many applications such as RP(Rapid Prototyping), NC(Numerical Control) and FEA(Finite Element Analysis), etc. The algorithm minimizes the number of triangular elements within tolerance and generates a valid triangular mesh for STL file and NC tool path generation. In the algorithm, a subdivision method is used. Since a patch is a basic element of triangular mesh creation, boundary curves of a patch are divided into line segments and the division of curves is applied for the interior of the surface. That is, boundary curves are subdivided into line segments and two end points of each line segment are propagated to the interior of the surface. For the case of a trimmed surface, triangulation is carried out using a model space information. The algorithm is superior because the number of elements can be controlled as the curvature of the surface varies and it generates the triangular mesh in a trimmed region efficiently. To verify the efficiency, the algorithm was implemented and tested for several 3D objects bounded by NURBS surfaces.