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김동욱,유광석,김덕수,Kokichi Sugihara 한국산업경영시스템학회 2003 한국산업경영시스템학회 학술대회 Vol.2003 No.추계
Presented in this paper is an algorithm to compute a Voronoi diagram of circles in a circle, where circles are located in a large circle. Given circles in a large circle, the region in the plane is divided into regions associated with the given circles. The proposed algorithm uses point Voronoi diagram, and then some topological remedies are applied so that we obtain proper initial topology including enclosing circle. From this initial topology, we can obtain the correct topology by a series of edge-flip operations. After getting the correct topology, the equations of edges are computed and represented in a rational quadratic B?zier curve form.
한 원에 포함된 원들의 보로노이 다이어그램을 계산하는 모서리 플립 알고리듬
김동욱,유광석,김덕수,Kokichi Sugihara 한국산업경영시스템학회 2003 한국산업경영시스템학회 학술대회 Vol.2003 No.추계
Presented in this paper is an algorithm to compute a Voronoi diagram of circles in a circle, where circles are located in a large circle. Given circles in a large circle, the region in the plane is divided into regions associated with the given circles. The proposed algorithm uses point Voronoi diagram, and then some topological remedies are applied so that we obtain proper initial topology including enclosing circle. From this initial topology, we can obtain the correct topology by a series of edge-flip operations. After getting the correct topology, the equations of edges are computed and represented in a rational quadratic Bézier curve form.
2차원 원들의 보로노이 다이어그램을 계산하기 위한 위상기반 알고리즘
이목원,차제현,송찬영,김재관,조영송,Kokichi Sugihara,김덕수 한국경영과학회 2014 한국경영과학회 학술대회논문집 Vol.2014 No.5
보로노이 다이어그램은 입자들의 공간특성을 추론하는데 유용하게 쓰인다. 특히, 2차원에서 원들의 보로노이 다이어그램은 그 자체로도 중요하지만 3차원에서 구들의 보로노이 다이어그램으로 확장시키는 것에도 중요한 의의를 가진다. 이 논문에서는 incremental한 방법으로 보로노이 다이어그램을 계산하는 위상기반의 알고리즘을 소개하고자 한다. 이 알고리즘은 강건하고 빠르게 2차원의 원에 대한 보로노이 다이어그램을 계산한다.
Unifying Method for Computing the Circumcircles of Three Circles
Kim, Deok-Soo,Kim, Dong-Uk,Sugihara, Kokichi Society for Computational Design and Engineering 2002 International Journal of CAD/CAM Vol.2 No.1
Given a set of three generator circles in a plane, we want to find a circumcircle of these generators. This problem is a part of well-known Apollonius' $10^{th}$ Problem and is frequently encountered in various geometric computations such as the Voronoi diagram for circles. It turns out that this seemingly trivial problem is not at all easy to solve in a general setting. In addition, there can be several degenerate configurations of the generators. For example, there may not exist any circumcircle, or there could be one or two circumcircle(s) depending on the generator configuration. Sometimes, a circumcircle itself may degenerate to a line. We show that the problem can be reduced to a point location problem among the regions bounded by two lines and two transformed circles via $M{\ddot{o}}bius$ transformations in a complex space. The presented algorithm is simple and the required computation is negligible. In addition, several degenerate cases are all incorporated into a unified framework.
2차원 원들의 보로노이 다이어그램을 계산하기 위한 위상기반 알고리즘
이목원,차제현,송찬영,김재관,조영송,Kokichi Sugihara,김덕수 대한산업공학회 2014 대한산업공학회 춘계학술대회논문집 Vol.2014 No.5
보로노이 다이어그램은 입자들의 공간특성을 추론하는데 유용하게 쓰인다. 특히, 2차원에서 원들의 보로노이 다이어그램은 그 자체로도 중요하지만 3차원에서 구들의 보로노이 다이어그램으로 확장시키는 것에도 중요한 의의를 가진다. 이 논문에서는 incremental한 방법으로 보로노이 다이어그램을 계산하는 위상기반의 알고리즘을 소개하고자 한다. 이 알고리즘은 강건하고 빠르게 2차원의 원에 대한 보로노이 다이어그램을 계산한다.
Algorithm for computing the circle set Voronoi diagram using edge-flip operations
Deok-Soo Kim,Donguk Kim,Kwangseok Yu,Junghun Lim,Dong-Soo Cho,Kokichi Sugihara 한국산업경영시스템학회 2002 한국산업경영시스템학회 학술대회 Vol.2002 No.추계
Presented in this paper is an algorithm to compute the Voronoi diagram of a circle set from the Voronoi diagram of a point set. The circles are located in Euclidean plane, the radii of the circles are non-negative and not necessarily equal, and the circles are allowed to intersect each other. The idea of the algorithm is to use the topology of the point set Voronoi diagram as a seed so that the correct topology of the circle set Voronoi diagram can be obtained through a number of edge flipping operations. Then, the geometries of the Voronoi edges of the circle set Voronoi diagram are computed. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation.