• Korean Journal of Mathematics
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• v.25 no.4
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• pp.555-561
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• 2017

We show that a closed curve invariant under inversions with respect to two intersecting circles intersecting at angle of an irrational multiple of $2{\pi}$ is a circle. This generalizes the well known fact that a closed curve symmetric about two lines intersecting at angle of an irrational multiple of $2{\pi}$ is a circle. We use the result to give a different proof of that a compact embedded cmc surface in ${\mathbb{R}}^3$ is a sphere. Finally we show that a closed embedded cmc surface which is invariant under the spherical reflections about two spheres, which intersect at an angle that is an irrational multiple of $2{\pi}$, is a sphere.

• International Journal of Contents
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• v.12 no.2
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• pp.42-48
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• 2016

We present efficient algorithms for computing centroid directions for each of the three types of monotonicity in a polyhedron: strong, weak, and directional monotonicity, which can be used for optimizing directions in many 3D manufacturing processes. Strongly- and directionally-monotone directions are the poles of great circles separating a set of spherical polygons on the unit sphere, the centroids of which are shown to be obtained by applying the previous result for determining the maximum intersection of the set of their dual spherical polygons. Especially in this paper, we focus on developing an efficient method for approximating the weakly-monotone centroid, which is the pole of one of the great circles intersecting a set of spherical polygons on the unit sphere. The original problem is approximately reduced into computing the intersection of great bands for avoiding complicated computational complexity of non-convex objects on the unit sphere, which can be realized with practical linear-time operations.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.2 s.140
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• pp.142-150
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• 2005

Recently, the gas transportation system for CNG(Compressed Natural Gas) has been developed and several innovative approaches are presented from the aspects of commercial demand. In this study, a new type of 20ft container shape CNG tank with two and four cylinder intersections by using the intersecting spheres has been proposed. And the structural analysis of CNG tank with Mildsteel, API High Tensile Steel, Al-alloy and FRP has been carried out to compare the different types of pressure vessels of materials used. The analysis result shows that the proposed intersectional cylindrical type of CNG tank can be applied to the gas transportation system. And further study on the commercial analysis and associated equipments should be carried out for the practical applications.

• Journal of the Korea Computer Graphics Society
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• v.6 no.1
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• pp.19-27
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• 2000

This paper proposes a non-self-intersecting multiresolution deformable model to extract and reconstruct three-dimensional boundaries of objects from volumetric data. Deformable models offer an attractive method for extracting and reconstructing the boundary surfaces. However, convensional deformable models have three limitations- sensitivity to model initialization, difficulties in dealing with severe object concavities, and model self-intersections. We address the initialization problem by multiresolution model representation, which progressively refines the deformable model based on multiresolution volumetric data in order to extract the boundaries of the objects in a coarse-to-fine fashion. The concavity problem is addressed by mesh size regularization, which matches its size to the unit voxel of the volumetric data. We solve the model self-intersection problem by including a non-self-intersecting force among the customary internal and external forces in the physics-based formulation. This paper presents results of applying our new deformable model to extracting a sphere surface with concavities from a computer-generated volume data and a brain cortical surface from a MR volume data.

• Journal of KIISE:Computer Systems and Theory
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• v.28 no.9
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• pp.479-490
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• 2001

In this paper, we consider the method of partitioning a sphere into faces with a set of spherical convex polygons $\Gamma$=$｛P_1...P_n｝$ for determining the maximum of minimum intersection. This problem is commonly related with five geometric problems that fin the densest hemisphere containing the maximum subset of $\Gamma$, a great circle separating $\Gamma$, a great circle bisecting $\Gamma$ and a great circle intersecting the minimum or maximum subset of $\Gamma$. In order to efficiently compute the minimum or maximum intersection of spherical polygons. we take the approach of edge-based partition, in which the ownerships of edges rather than faces are manipulated as the sphere is incrementally partitioned by each of the polygons. Finally, by gathering the unordered split edges with the maximum number of ownerships. we approximately obtain the centroids of the solution faces without constructing their boundaries. Our algorithm for finding the maximum intersection is analyzed to have an efficient time complexity O(nv) where n and v respectively, are the numbers of polygons and all vertices. Furthermore, it is practical from the view of implementation, since it computes numerical values. robustly and deals with all the degenerate cases, Using the similar approach, the boundary of a general intersection can be constructed in O(nv+LlogL) time, where : is the output-senstive number of solution edges.

• Journal of the Korea Computer Graphics Society
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• v.18 no.3
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• pp.1-7
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• 2012

In this paper, we propose a method to compute the interface between protein molecules. When a molecules is represented as a set of spheres with van der Waals radii, the distance from a spatial point p to the molecule corresponds to the distance from p to the closet sphere. The molecular interface is composed of equi-distant points from two molecules. Our algorithm decomposes the space into a set of voxels, and then constructs a voxel map by storing the information of spheres intersecting each voxel. By using the voxel map, we compute the distance between a point and the molecule. We also use GPU for the parallel processing, and efficiently approximate the interface of a pair of molecules.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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• pp.123-130
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• 2018

Triangulation is one of the fundamental problems in computational geometry and computer graphics community, and it has huge application areas such as 3D printing, computer-aided engineering, surface reconstruction, surface visualization, and so on. The Delaunay refinement algorithm is a well-known method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. In this paper, we propose a simple but efficient algorithm to triangulate Voronoi surfaces of Voronoi diagram of spheres in 3-dimensional Euclidean space. The proposed algorithm is based on the Ruppert's Delaunay refinement algorithm, and we modified the algorithm to be applied to the triangulation of Voronoi surfaces in two ways. First, a new method to deciding the location of a newly added vertex on the surface in 3-dimensional space is proposed. Second, a new efficient but effective way of estimating approximation error between Voronoi surface and triangulation. Because the proposed algorithm generates a triangular mesh for Voronoi surfaces with guaranteed quality, users can control the level of quality of the resulting triangulation that their application problems require. We have implemented and tested the proposed algorithm for random non-intersecting spheres, and the experimental result shows the proposed algorithm produces quality triangulations on Voronoi surfaces satisfying the quality criterion.

• Journal of the Korean association of regional geographers
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• v.7 no.1
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• pp.1-20
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• 2001

This study explored the changes of the patterns of land use and the social patterns of ownership of Kumnamno in Kwangju under the rule of Japanese colonialism by analyzing the townscape of Kumnamno in terms of the form and function of it. The research was done considering three periods: the year of 1912, 1930 and 1945. Kumnamno is the name of the street as well as the legal district name, and includes Kumnamno 1-ga, 2-ga, 3-ga, 4-ga and 5-ga. In the year 1912, Kumnamno was utilized as land, farmland and road. With the increase in population and the urbanization of the Kwangju area, it gradually began to be changed into land. By 1941, it was completely turned into land. Before and after the year 1910, the streets intersecting the Kumnamno area came into being as the roads of the Kwangju town, and were built with a lattice pattern. The road building of the Kumnamno began in accordance with the building of Kwangju station in 1922. The road building linking Kwangju Station to Chonnam Provincial Hall marked the first appearance of Kumnamno. The block from Ku-sung-no to Kumnamno 3-ga was built in 1925, the block from Kumnamno 3-ga to 2-ga in 1921, and Kumnamno 1-ga in 1930. It was not until the year 1933 that the construction of streets ranging from Ku-sung-no through Kumnamno 5-ga was finished. Examining the land ownership of the Kumnamno area in 1912, the Japanese possessed the land of Kumnamno 1-ga, 2-ga and 3-ga on the one hand and the Koreans possessed the land of 4-ga and 5-ga on the other hand. In 1930, the Japanese enlarged their sphere of influence and controlled the land located in all the areas of Kumnamno, and the Koreans reduced their ownership of Kumnamno 4-ga and 5-ga. There was a tendency for companies to occupy the land rapidly. In 1945, while the land owned by the Japanese decreased and the land owned by the Koreans did not change in quantity, the possessions of companies increased. To summarize, the Kumnamno area had some changes in the use of land during the above mentioned period. This was in part due to the construction of a street linking Kwangju Station to Chonnam Provincial Hall in order to strengthen the authority of the Japanese Government-General of Korea, as well as the expansion of the residential zone with the increase of the population of Kwangju.