• Journal of Computational Design and Engineering
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• v.3 no.1
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• pp.14-23
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• 2016

The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.12
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• pp.6986-6992
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• 2014

The generalized Voronoi graph (GVG) is a topological map of a constrained environment. This is defined in terms of workspace distance measurements using only sensor-provided information, with a robot having a maximum distance from obstacles, and is the optimum for exploration and obstacle avoidance. This is the safest path for the robot, and is very significant when studying the GVG edges of highly articulated robots. In previous work, the point-GVG edge and Rod-GVG were built with point robot and rod robot using sensor-based control. An attempt was made to use a higher degree of freedom robot to build GVG edges. This paper presents GVG-based a new local roadmap for the two-link robot in the constrained two-dimensional environment. This new local roadmap is called the two-identical-link generalized Voronoi graph (L2-GVG). This is used to explore an unknown planar workspace and build a local roadmap in an unknown configuration space $R^2{\times}T^2$ for a planar two-identical-link robot. The two-identical-link GVG also can be constructed using only sensor-provided information. These results show the more complex properties of two-link-GVG, which are very different from point-GVG and rod-GVG. Furthermore, this approach draws on the experience of other highly articulated robots.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.2
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• pp.141-147
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• 2009

We introduce a noble method to find a variation of the optimal path problem. The problem is to find the optimal decomposition of an original planar region such that the number of paths in the region is minimized. The paths are required to uniformly cover each subregion and the directions of the paths in each sub-region are required to be either entirely vertical or entirely horizontal. We show how we can transform the path problem into a graph s-t cut problem. We solve the transformed s-t cut problem using the Ford-Fulkerson method and show its performance. The approach can be used in zig-zag milling and layerd manufacturing.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.6
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• pp.90-101
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• 1996

Determination of assembly sequence of components is a key issue in assembly operation. Although a number of articles dealing with assembly sequence determination have appeared, an efficient and general methodology for complex products has yet to appear. The objective of this paper is to present the problems and models used to generate assembly sequence from design data. An essential idea of this research is to acquire a finite number of voxels from any complex geometric entity, such as 3D planar polygons, hollow spheres, cylinders. cones, tori, etc. In order to find a feasible assembly sequence, the following four steps are needed: (1) The components composing of an assembly product are identified and then the geometric entities of each component are extracted. (2) The geometric entities extracted in the first step are translated into a number of voxels. (3) All the mating or coupling relations between components are found by considering relations between voxels. (4) The components to be disassembled are determined using CCGs (Component Coupling Graph).

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.1
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• pp.107-116
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• 1999

대칭성(symmetry)은 그래프의 구조와 특성을 시각적으로 표현할 때 중요한 미적 기준 중의 하나이다. 또한 대칭성을 보여주는 드로잉은 전체 그래프가 크기가 작은 부그래트들로부터 반복적으로 구성됨을 보여줌으로써 전체 그래프에 대한 이해를 쉽게 푸는 해주는 장점이 있다. 하지만 일반적인 그래프에서 기하하적 대칭성(geometric symmetry)을 탐지하는 문제는 이미 NP-complete 임이 증명되었으므로 이에 대한 연구는 평면 그래프(planar graph)의 극히 제한적인 부분집합인 트리, 외부 평면 그래프, 임베딩된 (embedded) 평면 그래프 등에 초점이 맞추어져 왔다. 본 논문에서는 평면 그래프에서의 기하학적 대칭성 문제를 연구하였다. 평면 그래프를 이중 연결 성분들로 분할한 다음 이를 각각 다시 삼중 연결 성분들로 분할하여 트리를 구성하고 축소(reduction)개념을 도입함으로써 기하학적 대칭성을 탐지하는 O(n2)시간 알고리즘을 제시하였다. 여기서 n은 그래프의 정점의 개수이다. 이 알고리즘은 평면 그래프를 최대한 대칭적으로 드로잉하는 알고리즘 개발에 이용될 수 있다.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.1-12
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• 2020

A pathos block line cut-vertex graph of a tree T, written P BL_c(T), is a graph whose vertices are the blocks, cut-vertices, and paths of a pathos of T, with two vertices of P BL_c(T) adjacent whenever the corresponding blocks of T have a vertex in common or the edge lies on the corresponding path of the pathos or one corresponds to a block B_i of T and the other corresponds to a cut-vertex c_j of T such that c_j is in B_i; two distinct pathos vertices P_m and P_n of P BL_c(T) are adjacent whenever the corresponding paths of the pathos P_m(v_i, v_j) and P_n(v_k, v_l) have a common vertex. We study the properties of P BL_c(T) and present the characterization of graphs whose P BL_c(T) are planar; outerplanar; maximal outerplanar; minimally nonouterplanar; eulerian; and hamiltonian. We further show that for any tree T, the crossing number of P BL_c(T) can never be one.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04a
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• pp.685-687
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• 2002

RNA pseudoknot은 RNA 삼차 구조를 형성하는 중요한 구조요소일 뿐만 아니라, RNA 분자에서 중요한 역할을 한다. 지금까지 RNA pseudoknot 구조를 시각화하는 도구는 개발되어 있지 않기 때문에 대부분의 pseudoknot 구조의 시각화 작업은 수작업으로 이루어지고 있다. 본 논문은 RNA pseudoknot을 시각화를 위한 새로운 pseudoknot 표현 기법과 시각화 알고리즘에 대해서 소개한다. 새로운 표현기법은 모든 H-type pseudoknot을 uniform planar graph로 나타내고 RNA sequence의 진행방향을 따라가기가 쉽게 되어있다. 알고리즘을 이용하여 PseudoViewer라는 프로그램을 개발하였으며 PseudoViewer는 어떠한 시스템에서도 작동할 수 있는 Java로 구현되었다. 그 결과는 pseudoknot을 명확히 구분되고 보기 쉽도록 시각화됨을 보여준다.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.213-218
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• 2014

J. Malkevitch defined the coded path in r-valent polytopal graphs of uniform face structure and showed many interesting properties of the coded paths. In this paper, we study the simplicity of coded paths in an m-valent planar multigraph which is not a polytopal graph.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.123-126
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• 2005

This paper is a sequel to our earlier research on biplanar drawings [4] and biplanar crossing numbers [3]. The biplanar crossing number $cr_2$(G) of a graph G is $min\{cr(G_1+cr(G_2)\}$, where $cr$ is the planar crossing number and $G =G_1{\cup}G_2$. In this paper we show that $cr_2(G){\leq}{\frac{3}{8}}cr(G)$.

• Journal of the Korea Society of Computer and Information
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• v.18 no.11
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• pp.159-165
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• 2013

This paper proposes a O(E) polynomial-time algorithm that has been devised to simultaneously solve edge-coloring problem and graph classification problem both of which remain NP-complete. The proposed algorithm selects an edge connecting maximum and minimum degree vertices so as to determine the number of edge coloring ${\chi}^{\prime}(G)$. Determined ${\chi}^{\prime}(G)$ is in turn either ${\Delta}(G)$ or ${\Delta}(G)+1$. Eventually, the result could be classified as class 1 if ${\chi}^{\prime}(G)={\Delta}(G)$ and as category 2 if ${\chi}^{\prime}(G)={\Delta}(G)+1$. This paper also proves Vizing's planar graph conjecture, which states that 'all simple, planar graphs with maximum degree six or seven are of class one, closing the remaining possible case', which has known to be NP-complete.