• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.343-350
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• 2005

In this paper we prove two results about tilings of orthogonal polygons. (1) P be an orthogonal polygon with rational vertex coordinates and let R(u) be a rectangle with side lengths u and 1. An orthogonal polygon P can be tiled with similar copies of R(u) if and only if u i algebraic and the real part of each of its conjugates is positive; (2) Laczkovich proved that if a triangle $\Delta$ tiles a rectangle then either $\Delta$ is a right triangle or the angles of $\Delta$ are rational multiples of $\pi$. We generalize the result of Laczkovich to orthogonal polygons.

• Journal of the Korea Society of Computer and Information
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• v.16 no.6
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• pp.179-186
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• 2011

This paper suggests the minimum number of vertex guards algorithm. Given n rooms, the exact number of minimum vertex guards is proposed. However, only approximation algorithms are presented about the maximum number of vertex guards for polygon and orthogonal polygon without or with holes. Fisk suggests the maximum number of vertex guards for polygon with n vertices as follows. Firstly, you can triangulate with n-2 triangles. Secondly, 3-chromatic vertex coloring of every triangulation of a polygon. Thirdly, place guards at the vertices which have the minority color. This paper presents the minimum number of vertex guards using dominating set. Firstly, you can obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, you can obtain dominating set from visibility graph or visibility matrix. This algorithm applies various art galley problems. As a results, the proposed algorithm is simple and can be obtain the minimum number of vertex guards.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.3
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• pp.63-69
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• 2012

Given art gallery P with n vertices, the maximum (sufficient) number of mobile guards is${\lfloor}n/4{\rfloor}$ for simple polygon and${\lfloor}(3n+4)/16{\rfloor}$ for simple orthogonal polygon. However, there is no polynomial time algorithm for minimum number of mobile guards. This paper suggests polynomial time algorithm for the minimum number of mobile guards. Firstly, we obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, we select vertex u with ${\Delta}(G)$ and v with ${\Delta}(G)$ in $N_G(u)$ and delete visible edges from u,v and incident edges. Thirdly, we select $w_i$ in partial graphs and select edges that is the position of mobile guards. This algorithm applies various art galley problems with simple polygons and orthogonal polygons art gallery. As a results, the running time of proposed algorithm is linear time complexity and can be obtain the minimum number of mobile guards.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1022-1027
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• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered metal bearing and flexible structures by using the finite element method and the mode superposition method considering the asymmetry of the gyroscopic effect and sintered metal bearing. The eigenvalues and eigenvectors are calculated by solving the eigenvalue problem and the adjoint eigenvalue problem by using the restarted Arnoldi iteration method. The decoupled equations of motion can be obtained from global finite element motion equations by using the orthogonal relation between the right eigenvectors and left eigenvectors. The decoupled equations of motion are used to analyze the unbalance response of a high speed polygon mirror scanner motor. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.9
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• pp.1146-1151
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• 2019

Histogram H is an x-monotone rectilinear polygon with a horizontal edge, called by a base, connecting the leftmost vertical edge and the rightmost vertical edge. Here the rectilinear polygon is a polygon with only horizontal and vertical edges and the x- monotone polygon P is a polygon in which every line orthogonal to the x-axis intersects P at most twice. Walking counterclockwise on the boundary of a histogram H yields a sequence of left turns and right turns at its vertices. Conversely, a given sequence of the turns at the vertices can be realized by a histogram. In this paper, we consider the problem of finding a histogram to realize a given turn sequence. Particularly, we will find the histograms to minimize its area and its bounding box. It will be shown that both of the problems can be solved by linear time algorithms.

• Steel and Composite Structures
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• v.23 no.1
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• pp.31-40
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• 2017

This article aims at presenting multi objective optimization of parameters that affect crashworthiness characteristics of bi-tubular structures using Taguchi method with grey relational analysis. To design the experiments, the $L_9$ orthogonal array has been used and based on that, the inner tubes have been fabricated by varying the three influence factors such as reference diameter, length difference and numbers of sides of the polygon with three levels, but all the outer cylinders have the same diameter and length 90 mm and 135 mm respectively. Then, the tailor made bi-tubular steel structures were subjected into quasi static axial compression. From the test results it is found that the crushing behaviors of bi-tubular structures with different combinations were fairly significant. The important responses (crashworthiness indicators) specific energy absorption and crush force efficiency have been evaluated from load - displacement curve. Finally optimal levels of parameters were identified using grey relational analysis, and significance of parameters was determined by analysis of variance. The optimum crashworthiness parameters are reference diameter 80 mm, length difference 0 mm and number of sides of polygon is 3, i.e., triangle within the selected nine bi-tube combinations.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.83-86
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• 2005

This paper presents a method for point-based 3D building reconstruction using LiDAR data and digital map. The proposed method consists of three processes: extraction of building roof points, identification of roof types, and 3D building reconstruction. After extracting points inside the polygon of building, the ground surface, wall and tree points among the extracted points are removed through the filtering process. The filtered points are then fitted into the flat plane using ODR(Orthogonal Distance Regression). If the fitting error is within the predefined threshold, the surface is classified as a flat roof. Otherwise, the surface is fitted and classified into a gable or arch roof through RMSE analysis. Based on the roof types identified in automated fashion, the 3D building reconstruction is performed. Experimental results showed that the proposed method classified successfully three different types of roof and that the fusion of LiDAR data and digital map could be a feasible method of modelling 3D building reconstruction.

• Journal of information and communication convergence engineering
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• v.9 no.1
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• pp.105-109
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• 2011

In this paper, we study the dominating-free sest which is defined as follows: k points called servers and n points called clients in the plane are given. For a point p in the plane is said to be dominated by a client c if for every server s, the distance between s and p is greater than the distance between s and c. The dominating-free set is the set of points in the plane which aren't dominated by any client. We present an O(nklogk+$n^2k$) time algorithm for computing the dominating-free set under the $L_1$-metric. Specially, we present an O(nlogn) time algorithm for the problem when k=2. The algorithm uses some variables and 1-dimensional arrays as its principle data structures, so it is easy to implement and runs fast.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.117-121
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• 2005

In this work, we first present our study on the decoding schemes for space-time block code as well as our comments on their complexity. Then, we propose a new modified complex sphere decoding scheme, which has lower computational load than that of conventional complex sphere decoders. In the proposed scheme, the boundary for searching is defined by the intersection of an approximate polygon of searching circle and disk of lattice constellation. Therefore, the proposed scheme can reduce the searching boundary and it can avoid missing searching points as well. The performance of the proposed scheme, which is verified by computer simulations, consolidates our scheme.

• Journal of information and communication convergence engineering
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• v.3 no.2
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• pp.72-75
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• 2005

In this work, we first present our study on the decoding schemes for space-time block code as well as our comments on their complexity. Then, we propose a new modified complex sphere decoding scheme, which has lower computational load than that of conventional complex sphere decoders. In the proposed scheme, the boundary for searching is aided with the intersection of approximate polygon of searching circle and disk of constellation. Therefore, the proposed scheme can reduce the searching boundary while can avoid missing searching points. The performance of the proposed scheme is verified by computer simulation that consolidates our scheme.