• International Journal of CAD/CAM
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• 제5권1호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.842-847
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• 2005

Although there are many applications of Euclidean Voronoi diagram for spheres in a 3D space in various disciplines from sciences and engineering, it has not been studied as much as it deserves. In this paper, we present an edge-tracing algorithm to compute the Euclidean Voronoi diagram of 3-dimensional spheres in O(mn) in the worst-case, where m is the number of edges of Voronoi diagram and n is the number of spheres. After building blocks for the algorithm, we show an example of Voronoi diagram for atoms using actual protein data and discuss its applications for protein analysis.

• 한국산업경영시스템학회:학술대회논문집
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• 한국산업경영시스템학회 2002년도 춘계학술대회
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• pp.467-472
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• 2002

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.

• 한국CDE학회논문집
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• 제6권1호
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• pp.24-30
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• 2001

An efficient and robust algorithm to compute the exact Voronoi diagram of a circle set is presented. The circles are located in a two dimensional Euclidean space, 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. In particular, this paper discusses the topological aspect of the algorithm, and the following paper discusses the geometrical aspect. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation. Since the algorithm is based on the result of the point set Voronoi diagram and the flipping operation is the only topological operation, the algorithm is always as stable as the Voronoi diagram construction algorithm of a point set.

• 산업경영시스템학회지
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• 제42권3호
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• pp.52-60
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• 2019

This paper presents a numerically robust algorithm to construct a Voronoi diagram of circles in the plane. The circles are allowed to have intersections among them, but one circle cannot fully contain another circle. The Voronoi diagram is a tessellation of the plane into Voronoi regions of given circles. Each circle has its Voronoi region which is defined by a set of points in the plane closer to the circle than any other circles. The distance from a point p to a circle $c_i$ of center $p_i$ and radius $r_i$ is ${\parallel}p-p_i{\parallel}-r_i$, which is the closest Euclidean distance from p to the circle boundary. The proposed algorithm first constructs the point Voronoi diagram of centers of given circles, then it enlarges each point to the circle and expands its Voronoi region accordingly. This region-expansion process is done by local modifications and after completing this process for the whole circles the desired circle Voronoi diagram can be obtained. The proposed algorithm is numerically robust and we provide with a few examples to show its robustness. The algorithm runs in $O(n^2)$ time in the worst case and O(n) time on average where n is the number of the circles. The experiment shows that the region-expansion algorithm is robust and runs fast with strong linear time behavior.

• 한국통신학회논문지
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• 제29권12C호
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• pp.1686-1691
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• 2004

본 논문에서는 기존의 고속 유클리디언 거리 변환법을 개선한 새로운 계산 방법을 제안한다. 기존의 고속 유클리디언 거리 변환법이 가지고 있는 단점인 특징점의 수에 비례하여 계산량이 늘어나는 단점을 극복하기 위해서, 본 논문에서는 특징점들 중에서 비특징점과 4방향으로 연결되어 있는 특징점만을 이용하여 보로노이 다이어그램을 계산함으로써 유클리디언 거리 변화도(Euclidean distance map)의 계산 시간을 기존의 방법보다 평균 40%로 감소시켰다. 본 논문에서 제안한 방법의 효율성을 검증하기 위해서 크기의 바이너리 영상 16장에서 대해서 기존의 방법과 제안한 방법으로 똑같이 유클리디언 거리 변화도를 계산하여 계산 시간을 비교함으로써 그 효능을 입증하였다.

• International Journal of CAD/CAM
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• 제7권1호
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• pp.91-101
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• 2007

To understand the structure of molecules, various computational methodologies have been extensively investigated such as the Voronoi diagram of the centers of atoms in molecule and the power diagram for the weighted points where the weights are related to the radii of the atoms. For a more improved efficiency, constructs like an $\alpha$-shape or a weighted $\alpha$-shape have been developed and used frequently in a systematic analysis of the morphology of molecules. However, it has been recently shown that $\alpha$-shapes and weighted $\alpha$-shapes lack the fidelity to Euclidean distance for molecules with polysized spherical atoms. We present the theory as well as algorithms of $\beta$-shape and $\beta$-complex in $\mathbb{R}^3$ which reflects the size difference among atoms in their full Euclidean metric. We show that these new concepts are more natural for most applications and therefore will have a significant impact on applications based on particles, in particular in molecular biology. The theory will be equivalently useful for other application areas such as computer graphics, geometric modeling, chemistry, physics, and material science.

• 전기의세계
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• 제32권6호
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• pp.325-330
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• 1983

본 기술해설에서는 전산 기하학에서 다루는 많은 기본 문제들 중에서도 특히 평면상에 놓여있는 n개의 점들에 대한 여러문제, 예를 들면 Euclidean Minimum Spanning Tree을 구하는 문제, 점 사이의 거리가 가장 가까운 두점(two closest point pair)을 찾는 문제, Convex hull을 찾는 문제 등을 효율적으로 처리할 수 있는 Voronoi 도표 (Voronoi Diagram)라는 기본적인 structure에 대해 설명을 하고 이 Voronoi 도표가 위에서 언급한 문제를 해결하는데 이용됨을 살펴보고자 한다.

• 산업경영시스템학회지
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• 제35권4호
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• pp.235-243
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• 2012

The Voronoi diagram of spheres and power diagram have been known as powerful tools to analyze spatial characteristics of weighted points, and these structures have variety range of applications including molecular spatial structure analysis, location based optimization, architectural design, etc. Due to the fact that both diagrams are based on different distance metrics, one has better usability than another depending on application problems. In this paper, we compare these diagrams in various situations from the user's viewpoint, and show the Voronoi diagram of spheres is more effective in the problems based on the Euclidean distance metric such as nearest neighbor search, path bottleneck locating, and internal void finding.

• 대한전자공학회논문지TC
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• 제41권9호
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• pp.39-45
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• 2004

순차적인 관찰값을 바탕으로 하고 신호검출에 소요되는 시간이 고정된 신호검출기의 제작에 관한 방법을 제안하며 이는 하드웨어의 복잡도를 감소시키는 장점이 있다. 제안된 방법은 Voronoi 다이어그램과 Delaunay 분할을 사용한다. 제안된 신호검출기 제작은 또한 고정 지연 트리 검색 검출 (FDTS) 방법에 기반을 둔다. FDTS 는 효율적인 순차적 신호검출 알고리즘이며 심볼간 간섭이 존재하는 채널에서 결정 궤환 등화기법 (DFE)과 결합하여 최적화에 근접한 성능을 보인다. 이러한 접근방법에서는 Voronoi 다이어그램 혹은 등가적으로 Delaunay 분할에 포함된 정보를 활용하여 다차원 유클리드 공간에서의 상대적인 관찰값의 위치를 계산하며 이러한 방법이 효율적인 계산을 유도하는 신호검출기의 제작에 이용된다.