• Journal of KIISE:Computer Systems and Theory
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• v.27 no.4
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• pp.416-419
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• 2000

Let G be an n-vertex convex polygon whose vertices are in general position. We consider an illumination problem of locating two floodlights on the boundary of G, which illuminates G and whose larger angle is as small as possible. We present an O($n^2$) time algorithm under the extended real-RAM model.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.43 no.2 s.308
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• pp.81-92
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• 2006

This paper proposes a robustness watermarking for 3D mesh model based on projection onto convex sets (POCS). After designing the convex sets for robustness and invisibility among some requirements for watermarking system, a 3D-mesh model is projected alternatively onto two constraints convex sets until the convergence condition is satisfied. The robustness convex set are designed for embedding the watermark into the distance distribution of the vertices to robust against the attacks, such as mesh simplification, cropping, rotation, translation, scaling, and vertex randomization. The invisibility convex set are designed for the embedded watermark to be invisible. The decision values and index that the watermark was embedded with are used to extract the watermark without the original model. Experimental results verify that the watermarked mesh model has invisibility and robustness against the attacks, such as translation, scaling, mesh simplification, cropping, and vertex randomization.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.5
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• pp.848-860
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• 1994

Generally, to get the minimum distance between two arbitrary shapes that are composed of circular arcs and lines, we must calculate distances for all the possible pairs of the components from two given shapes. In this paper, we propose an efficient method for the minimum distance problem between two shapes by using their structural features after extracting the reduced component lists which are essential to calculate the minimum distance considering the relationship of shape location. Even though the reduced component lists may contain all the components of the shapes in the worst case, in the average we can reduce the required computation much by using the reduced component lists. This method may be efectively applied to calculating the minimum distance between two shapes which are generated by the CAD tool, like in the nesting system.

• Journal of Korea Multimedia Society
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• v.6 no.7
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• pp.1302-1311
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• 2003

This paper presents a more stable method of multiresolution editing for a triangular mesh. The basic idea of our paper is to embed an editing area of a mesh onto a 2D region and to produce 3D surfaces which interpolate the editing-information. In this paper, we adopt the extended convex combination approach based on the shape-preserving parameterization for the embedding, which guarantees no self-intersection on the 2D embedded mesh. That is, the result of the embedding is stable. Moreover, we adopt the multi-level B-spline approach to generate the surface containing all of 3D editing-information, which can make us control the editing area in several levels. Hence, this method supports interactive editing and thus can produce intuitive editing results.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.393-396
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• 2000

본 연구에서는 필렛엔드밀을 이용하여 복합곡면을 가공하기 위한 새로운 접근방법을 제안한다. 이 방법은 "곡선기반 접근방법"으로 기존의 "점기반 접근방법"에 비하여 몇 가지 특징들을 가지고 있다. 본 연구에서는 다면체로 표현된 곡면을 대상으로 하고 있는데, 볼록한 모서리와 꼭지점에서는 정확히 옵셋시키고 오목한 부위에서는 옵셋 곡면이 겹치는 것을 허용한다. 옵셋된 곡면을 절단 평면으로 자르고, 같은 평면상에 있는 교선 중에서 겹치는 부분의 윗 부분을 택하면 공구 간섭이 제거된 공구 경로를 얻게된다. 즉 계산이 복잡한 오목지역에서의 옵셋 시 발생되는 간섭을 2차원 평면상에서 제거함으로써 계산 과정을 단순화시키고 안정적으로 만든다. 본 연구에서 제안한 방법은 PC에서 VC++로 구현되었으며 몇 가지 적용 예를 보여 주고 있다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.11A
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• pp.870-881
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• 2009

The rapid development of healthcare information management for 3D medical digital library, 3D PACS and 3D medical diagnosis has addressed security issues with medical IT technology. This paper presents multiple 3D medical image data for protection, authentication, indexing and diagnosis information hiding applied to healthcare information management. The proposed scheme based on POCS watermarking embeds the robust watermark for doctor's digital signature and information retrieval indexing key to the distribution of vertex curvedness and embeds the fragile watermark for diagnosis information and authentication reference message to the distance difference of vertex. The multiple embedding process designs three convex sets for robustness, fragileness and invisibility and projects 3D medical image data onto three convex sets alternatively and iteratively. Experimental results confirmed that the proposed scheme has the robustness and fragileness to various 3D geometric and mesh modifiers at once.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.495-506
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• 2003

In this study, 1 investigated some properties on the special hyper-dimensional figures made by the principle of the performance of equivalent forms representation. I supposed 2 definitions on the making n-dimensional figure : a cone type(hypercube) and a pillar type(simplex). We can explain that there exists only 6 4-dimensional regular polytopes as there exists only 5 regular polygons. And there are many hyper-dimensional figures, they all have sufficient condition to show the general Euler' Characteristics. And especially, we could certificate that the simplest cone type and pillar types are fitted to Pascal's Triangle and Hasse's Diagram, each other.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.212-215
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• 2008

In this paper, we develop the optimal path planning algorithm using the improved Dijkstra algorithm and the particle swarm optimization. To get the optimal path, at first we construct the MAKLINK on the world environment and then make a graph associated with the MAKLINK. The MAKLINK is a set of edges which consist of the convex set. Some of the edges come from the edges of the obstacles. From the graph, we obtain the Dijkstra path between the starting point and the destination point. From the optimal path, we search the improved Dijkstra path using the graph. Finally, applying the particle swarm optimization to the improved Dijkstra path, we obtain the optimal path for the mobile robot. It turns out that the proposed method has better performance than the result in [1] through the experiment.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.53-56
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• 2000

The problem ( Ρ ) of optimizing a linear function d$\^$T/x over the set of efficient set for a multiple objective linear program ( Μ ) is difficult because the efficient set is nonconvex. There some interesting properties between the objective linear vector ｄ and the matrix of multiple objectives C and those properties lead us to establish criteria to solve ( Ρ ) with a linear program. In this paper we investigate a system of the linear equations C$\^$T/${\alpha}$=d and construct two linearly independent positive vectors ${\mu}$, ν such that ${\alpha}$=${\mu}$-ν. From those vectors ${\mu}$, ν, solving an weighted sum linear program for finding an efficient extreme point for the ( Μ ) is a way to get an optimal solution ( Ρ ). Therefore our theory gives an easy way of solving nonconvex program ( Ρ ) with a weighted sum linear program.