• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.8
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• pp.1377-1383
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• 2008

Parameterization of a 3D triangular mesh is a fundamental problem in various applications of geometric modeling and computer graphics. There are two major paradigms in mesh parameterization: energy functional minimization and the convex combination approach. In general, the convex combination approach is wifely used because of simple concept and one-to-one mapping. However, the approach has some problems such as high distortion near the boundary and time complexity. Moreover, the stability of the linear system may not be preserved according to the geometric information of the mesh. In this paper, we present an extension of the convex combination approach based on the mean value coordinates, which resolves the drawbacks of the convex combination approach. This may be a more practical solution because it is able to generate a stable linear system in a short time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.615-615
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• 1996

• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.196-220
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• 2021

This study formulates a new geometric parameterization scheme to effectively address numerical analysis subject to the variation of the fiber radius of a square unit cell. In particular, the proposed mesh-morphing approach may lead to a parameterized weak form whose bilinear and linear forms are affine in the geometric parameter of interest, i.e. the fiber radius. As a result, we may certify the reduced basis analysis of a square unit cell model for any parameters in a predetermined parameter domain with a rigorous a posteriori error bound. To demonstrate the utility of the proposed geometric parameterization, we consider a two-dimensional, steady-state heat conduction analysis dependent on two parameters: a fiber radius and a thermal conductivity. For rapid yet rigorous a posteriori error evaluation, we estimate a lower bound of a coercivity constant via the min-θ method as well as the successive constraint method. Compared to the corresponding finite element analysis, the constructed reduced basis analysis may yield nearly the same solution at a computational speed about 29 times faster on average. In conclusion, the proposed geometric parameterization scheme is conducive for accurate yet efficient reduced basis analysis.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.336-346
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• 2000

This paper presents a geometric method that can detect and compute all conic sections in the intersection of two tori. Conic sections contained in a torus must be circles. Thus, when two tori intersect in a conic section, the intersection curve must be a circle as well. Circles in a torus are classified into profile circles, cross-sectional circlet, and Yvone-Villarceau circles. Based on a geometric classification of these circles, we present a procedural method that can detect and construct all intersection circles between two tori. All computations can be carried out using simple geometric operations only: e.g., circle-circle intersections, circle-line intersections, vector additions, and inner products. Consequently, this simple structure makes our algorithm robust and efficient, which is an important advantage of our geometric approach over other conventional methods of surface intersection.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1129-1140
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• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.548-553
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• 2000

A new design of cylindrical capacitive sensor(CCS) for the displacement measurement of precision active magnetic bearing(AMB) spindle is presented in this paper. This research is motivated by the problem that existing 4-segment CCS is still sensitive to the $3^{rd}$ harmonic component of the geometric errors of a rotor. The procedure of designing new CCS starts from the modeling and error analysis of CCS. The angular size of CCS is set up as a design parameter, and new 8-segment CCS is introduced to possess an arbitrary angular size. The optimum geometry of CCS to minimize the effect of geometric errors is determined through minimum norm approach. Experimental results with test rotors have confirmed the improvement in geometric error suppression.

• Korean Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.293-303
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• 1998

The objective of this study is to develop a PC level freeform surface modeling system which explicitly represents information of part geometry. Surface modeler uses nonuniform rational B-spline (NURBS) function with nonuniform knot vector for the flexible modeling work. The results of this study are as follows. 1) By implementation surface modeler through applying representation scheme proposed to represent free-form surface explicity, the technical foundation to develop free-from surface modeling system using parametric method. 2) Besides the role to model geometric shape of a surface, geometric modeler is developed to model arbitrary geometric shape. By doing this, the availability of the modeling system is improved. Geometric modeler can be utilized application fields such as collision test of tool and fixture, and tool path generation for NC machine tool.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.462-465
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• 2000

It is important to compress three dimensional (3D) data efficiently, since 3D data are too large to store or transmit in general. In this paper, we propose a lossless compression algorithm of the 3D mesh connectivity, based on the vertex degree. Most techniques for the 3D mesh compression treat the connectivity and the geometric separately, but our approach attempts to exploit the geometric information for compressing the connectivity information. We use the geometric angle constraint of the vertex fanout pattern to predict the vertex degree, so the proposed algorithm yields higher compression efficiency than the conventional algorithms.

• International Journal of Highway Engineering
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• v.15 no.1
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• pp.143-154
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• 2013

PURPOSES: Design of approach roads of rest areas in highway has many drawbacks such as geometric design elements. There has been traffic accidents occured in these approach roads of rest areas. Thus, design criteria is required in order to protect accidents from being occurred. In case of Korea, geometric structure design criteria of entry facilities, such as toll-gate, interchange, junction etc was established. However there are no presence in a detailed standards for geometric structure of the rest area which affiliated road facilities. METHODS: In this study, analytic on accidents was carried out in regards to the entry of geometric structure of resting areas by utilizing a sight survey and an investigation research of traffic accidents. The survey was targeting 135 general service areas. Collisions with physical channelization and safety facilities occurred due to speeding, rapid entry, and etc at the entrance nose section. At the entrance connector roads, accidents caused by speeding, negligence, over-operation of handle of drivers were main reason of accidents. Discriminant analysis were conducted about geometric elements to distinguish influencing factors for traffic accidents. the lengths and access angles of the entrance connector roads were regarded as to have the high relation with traffic accidents. RESULTS: After classifying the design section of resting areas' entry as well as derive design elements on each section, a speed measurement by targeting entry of rest areas and car behavior surveys were performed, then each element's minimum standard was derived through the analyses. According to the speeds at the starting/end point of entrance connector road, the range of the junction setting angle of the entrance connector road is defined as $12^{\circ}{\sim}17^{\circ}$ and the connector length model was suggested. CONCLUSIONS: Suggest improvement plans for existing rest areas that can be applied realistically. This should be corresponded to the standards of entry and exit of developed rest areas.