• Journal of the Korean Operations Research and Management Science Society
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• v.7 no.2
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• pp.41-48
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• 1982

This paper presents an efficient algorithm for finding a new facility(center) in the Euclidean plane in accordance with minimax criterion: that is, the facility is located to minimize the maximum weighted Euclidean distance. The method given in this paper involves computational geometry. Some possible extensions of this problem are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.741-755
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• 1998

We prove the asymptotic lens equivalence in manifolds without conjugate points. By using this property we show that under a metric condition of asymptotically Euclidean and the curvature condition decaying faster than quadratic, any surface $(R^2,g)$ without conjugate points is Euclidean.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.59-68
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• 2005

Euclidean Voronoi diagram of spheres in 3-dimensional space has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this, paper is the topological representation for Euclidean Voronoi diagram of spheres which is a typical non-manifold model. The proposed representation is a variation of radial edge data structure capable of dealing with the topological characteristics of Euclidean Voronoi diagram of spheres distinguished from those of a general non-manifold model and Euclidean Voronoi diagram of points. Various topological queries for the spatial reasoning on the representation are also presented as a sequence of adjacency relationships among topological entities. The time and storage complexities of the proposed representation are analyzed.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.319-326
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• 2003

In this paper, we obtain the optimal condition of the curvature bounds guaranteeing that Euclidean cones over Aleksandrov spaces of curvature bounded above preserve the curvature bounds, by considering the Euclidean cone CS$_{r}$ $^{n}$ over n-dimensional sphere S$_{r}$ $^{n}$ of radius r. More precisely, we show that for r<1, the Euclidean cone CS$_{r}$ $^{n}$ of S$_{r}$ $^{n}$ is a CBB(0) space, but not a CBA($textsc{k}$)-space for any real $textsc{k}$$\in$R.

• East Asian mathematical journal
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• v.31 no.4
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• pp.459-481
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• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.

• Journal of The Korean Society of Agricultural Engineers
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• v.57 no.4
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• pp.39-49
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• 2015

Since most medical facilities and medical personnel are concentrated in urban areas in South Korea, an imbalance of access to medical facilities causes a gap in medical resource availability between urban and rural areas. Accessibility to medical facilities is a means of assessment that evaluates a measure of inequality in utilization of medical resources. The evaluation of accessibility uses Euclidean distance, in general; however, this method has its limits in that Euclidean distance cannot reflect actual distance. This study aims to estimate real road distance from village halls to medical facilities in rural areas using Open Application Programming Interface (Open API) of an internet portal site. Using real road distance, we evaluated medical accessibility and compared it with Euclidean distance. The accessibility to primary medical institutions was valued relatively well, but secondary and tertiary medical institutions were vulnerable in Pyeonchang-gun. Comparing Euclidean distance with real road distance from village halls to medical facilities, real road distance appeared to be approximately 1.4 times that of Euclidean distance. This calculation is similar to the circuity factor of Gangwon-do in Korea that estimated to fix the limits of Euclidean distance and assumed real road distance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.12C
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• pp.1686-1691
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• 2004

In this paper, we present an improved method to calculate Euclidean distance transform based on Guan's method. Compared to the conventional method, Euclidean distance can be computed faster using Guan's method when the number of feature pixels is small; however, overall computational cost increases proportional to the number of feature pixels in an image. To overcome this problem, we divide feature pixels into two groups: boundary feature pixels (BFPs) and non-boundary feature pixels (NFPs). Here BFPs are defined as those in the 4-neighborhood of foreground pixels. Then, only BFPs are used to calculate the Voronoi diagram resulting in a Euclidean distance map. Experimental results indicate that the proposed method takes 40 Percent less computing time on average than Guan's method. To prove the performance of the proposed method, the computing time of Euclidean distance map by proposed method is compared with the computing time of Guan's method in 16 images that are binary and the size of 512${\times}$512.

• Bulletin of the Korean Mathematical Society
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• v.17 no.2
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• pp.123-132
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• 1981

• Journal of the Korean Society of Environmental Restoration Technology
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• v.24 no.6
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• pp.35-48
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• 2021

In Suwon, the overall hygiene of the city is threatened by the emergence of the rook(Corvus fugilegus) in the city. Rooks began to appear in November of 2016 and has continued to appear from November to March every year. In order to eradicate or to prepare an alternative habitat for rooks, this study aimed to identify the preferred habitat and specific environmental variables. Therefore, in this work, we aim to understand the predicted distribution of rooks in Suwon City with citizen science and through MaxENT, the most widely utilized habitat modeling using citizen science to analyze the preferred habitat of harmful tides appearing in urban areas. In this study, seven environmental variables were chosen: biotope group complex, building floor, vegetation, euclidean distance from farmland, euclidean distance from streetlamp, and euclidean distance from pole and DEM. Among the estimated models, after the time period of sunrise (08:00~18:00) the contribution percentage were as following: euclidean distance from arable land(39.2%), DEM(25.5%), euclidean distance from streetlamp(22.3%), euclidean distance from pole(7.1%), biotope group complex(4.9%), building floor(1%), vegetation(0%). In the time period after sunset(18:00~08:00) the contribution percentage were as following: biotope group complex(437.4%), euclidean distance from pole(26.8%), DEM(13.4%), euclidean distance from streetlamp(11.8%), euclidean distance from farmland(7.9%), building floor(1.4%), vegetation(1.3%).

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1467-1474
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• 2014

In this paper, we consider the two computer intensive methods for extended Euclidean algdrithm. Two methods we propose are C-programming based approach and Microsoft excel based method, respectively. Thses methods are applied to the derivation of greatest commnon devisor, multiplicative inverse for modular operation and the solution of diophantine equation. Concrete investigation for extended Euclidean algorithm with the computer intensive process is given. For the application of extended Euclidean algorithm, we consider the RSA encrytion method which is still popular recently.