• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.713-718
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• 1994

Voronoi diagrams for closed shapes have many practical applications, ranging from numerical control machining to mesh generation. Shape offset based on Voronoi diagram avoids the topological problems encountered in traditional offsetting algorithms. In this paper, we propose a procedure for generating a Voronoi diagram and an exact offset for planar curve. A planer curve can be defined by free-form curve segements. The procedure consists of three steps : 1) segmentation by minimum curvature, 2) construction of Voronoi diagram, and 2) generation of the exact offset.

• 전기의세계
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• v.32 no.6
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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.

• Korean Journal of Computational Design and Engineering
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• v.14 no.5
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• pp.306-313
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• 2009

This paper presents the unique formation process of a volumetric space with the digital algorithm developed for Voronoi diagram in order to generate an effective parametric architectural form. By applying systematic parameters of architectural conditions within digital parametric tools, the interactions among sub-spaces developed by Voronoi diagram are enhanced by manipulating the spatial structures. In this paper, we discuss how the parametric distributing and zoning geometrical system can support designers in developing a free-formed space, and research on how this system creates a 3D volumetric space. With the in-depth research on the system and structure of Voronoi diagram, the approaches to the application of Voronoi diagram into architectural form generation are clarified to be an effective, creative and successful digital tool. The result of the application of the Voronoi diagram improves the design quality with systematic language in the sense that the sub-regions are created and controlled under the systematic and balanced hierarchy having dynamic relationships among each others with the restoration of the equilibrium of forces and tensions. This 3-dimensional Voronoi diagram provides another means for designers to solve architectural issues and to reinforce their design concepts.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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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.

• Korean Journal of Computational Design and Engineering
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• v.6 no.1
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• pp.31-39
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• 2001

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set. The circles are located in a Euclidean plane, the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work when the correct topology of the Voronoi diagram was given. Given three circle generators, the position of the Voronoi vertex is computed by treating the plane as a complex plane, the Z-plane, and transforming it into another complex plane, the W-plane, via the Mobius transformation. Then, the problem is formulated as a simple point location problem in regions defined by two lines and two circles in the W-plane. And the center of the inverse-transformed circle in Z-plane from the line in the W-plane becomes the position of the Voronoi vertex. After the correct topology is constructed with the geometry of the vertices, the equations of edge are computed in a rational quadratic Bezier curve farm.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.301-304
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• 2003

This raper propose a matching algorithm using voronoi diagram for rotation and translation invariant fingerprint identification. The proposed algorithm extracts geometrical structures that ate derived from voronoi diagram of a fingerprint image. Then distances and angles are extracted from the geometrical structure and saved indexing form for fingerprint matching. Experimental results show that the proposed algorithm invariant to fingerprint rotation and translation requirements and matching time.

• Journal of Korea Spatial Information System Society
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• v.11 no.1
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• pp.105-114
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• 2009

Recently, location-based services which provides k nearest POIs, e.g., gas stations, restaurants and banks, are essential such applications as telematics, ITS(Intelligent Transport Systems) and kiosk. For this, the Voronoi Diagram k-NN(Nearest Neighbor) search algorithm has been proposed. It retrieves k-NNs by using a file storing pre-computed network distances of POIs in Voronoi diagram. However, this algorithm causes the cost problem when expanding a Voronoi diagram. Therefore, in this paper, we propose an algorithm which generates a matrix of the shortest distance between border points of a Voronoi diagram. The shortest distance is measured each border point to all of the rest border points of a Voronoi Diagram. To retrieve desired k nearest POIs, we also propose a k-NN search algorithm using the matrix of the shortest distance. The proposed algorithms can m inim ize the cost of expanding the Voronoi diagram by accessing the pre-computed matrix of the shortest distances between border points. In addition, we show that the proposed algorithm has better performance in terms of retrieval time, compared with existing works.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.81-82
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• 2011

• ETRI Journal
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• v.10 no.3
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• pp.125-140
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• 1988

Computational geometry has wide applications in pattern recognition, image processing, VLSI design, and computer graphics. Voronoi diagrams in computational geometry possess many important properites which are related to other geometric structures of a set of point. In this pater the design of systolic algorithms for the static and the dynamic Voronoi diagrams is considered. The major motivation for developing the systolic architecture is for VLSI implementation. A new systematic transform technique for designing systolic arrays, in particular, for the problem in computational geometry has been proposed. Following this procedure, a type T systolic array architecture and associated systolic algorithms have been designed for constructing Voronoi diagrams. The functions of the cells in the array are also specified. The resulting systolic array achieves the maximal throughput with O(n) computational complexity.