• 한국CDE학회논문집
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• 제11권2호
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• pp.97-106
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• 2006

Voronoi diagrams have been known for numerous important applications in science and engineering including CAD/CAM. Especially, the Voronoi diagram for 3D spheres has been known as very useful tool to analyze spatial structural properties of molecules or materials modeled by a set of spherical atoms. In this paper, we present two algorithms, the edge-tracing algorithm and the region-expansion algorithm, for constructing the Voronoi diagram of 3D spheres and applications to protein structure analysis. The basic scheme of the edge-tracing algorithm is to follow Voronoi edges until the construction is completed in O(mn) time in the worst-case, where m and n are the numbers of edges and spheres, respectively. On the other hand, the region-expansion algorithm constructs the desired Voronoi diagram by expanding Voronoi regions for one sphere after another via a series of topology operations, starting from the ordinary Voronoi diagram for the centers of spheres. It turns out that the region-expansion algorithm also has the worst-case time complexity of O(mn). The Voronoi diagram for 3D spheres can play key roles in various analyses of protein structures such as the pocket recognition, molecular surface construction, and protein-protein interaction interface construction.

• 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.

• 한국통신학회논문지
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• 제38A권3호
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• pp.224-239
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• 2013

임펄스 잡음에 강인한 2차 회전변환 기법을 적용한 QPSK 시스템에서 최대우도 복호기의 비트오율 성능을 정확하게 분석하였다. 이 분석 방법은 보로노이 셀에서 2차원 가우시안 Q-함수의 리만 적분을 응용한 것이다. 일반적인 2차 회전변환 기법에 대하여 보로노이 셀의 다양한 특징을 기하학적 방법으로 분석하여 정리하였다. 이러한 분석 결과를 이용하여 비트오율을 최소화하는 회전변환 파라미터를 도출하였으며, 기존의 근사적인 성능 해석 방법과의 차이도 고찰하였다.

• Spatial Information Research
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• 제10권3호
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• pp.439-453
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• 2002

수자원분야에서 DEM을 활용한 연구들이 활발히 진행되고 있으며, 특히 지형 및 수문분석의 기초가 되는 유역과 하천 추출은 GIS 분석에서 일반화되어 있다. 그러나 경사가 완만한 지형에서는 가늘고 긴 슬리버 폴리곤 형태의 유역이나 직선형태의 하천이 추출되므로, 활용측면에서 비 효율적이다 본 연구에서는 완경사지역에서 발생하는 비정상적인 유역과 하천을 효과적으로 추출하기 위해, 하천을 중심으로 완충구간을 설정한 후 점진적인 표고변화를 적용하였다. 특히 점진적인 표고변화를 부여하기 위해 보로노이 다이어그램(Voronoi Diagram)을 활용한 등거리 할당모형을 적용하였다. 또한 추출한 하천인식 DEM과 원시 DEM을 이용하여 유역 및 하천을 추출한 후, 완경사 지역에서의 유역 및 하천의 형태를 상호 비교함으로서 본 연구의 효용성을 평가하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2005년도 창립60주년 기념 추계 학술대회
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• pp.11.2-11.2
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• 2005

• 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.

• 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.

• 한국정밀공학회지
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• 제29권7호
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• pp.785-792
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• 2012

Foam structure is usually hard to model due to the complexity of the geometry of cells. So, many simplified models to represent complicated foam structures have been proposed, but most of them are not actually describe the random feature of the cell structure well. So, in this study, two dimensional isotropic and anisotropic closed cell structures of the foam were modeled using the concept of Voronoi cells. The elasto-plastic deformation behavior under compressive loads was investigated by finitie element analysis, and the results were compared with ideal honeycomb structure. In addition, the effect of anisotropy of Voronoi cell structures of the foam on Young's modulus and yield stress under compressive loads was studied.

• 한국CDE학회논문집
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• 제15권1호
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• pp.33-42
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• 2010

In this study, new medial surface calculation methods using Voronoi diagrams are investigated for the point samples extracted on closed surface models. The medial surface is defined by the closure of all points having more than one closest point on the shape boundary. It is a one of essential geometric information in 3D and can be used in many areas such as 3D shape analysis, dimension reduction, freeform shape deformation, image processing, computer vision, FEM analysis, etc. In industrial parts, the idealized solid parts and shell shapes including sharp edges and vertices are frequently used. Other medial surface extraction methods using Voronoi diagram have inherent separation and branch problems, so that they are not appropriate to the sharp edged objects and have difficulties to be applied to industrial parts. In addition, the branched surfaces on sharp edges in shell shapes should be eliminated to obtain representative medial shapes. In order to avoid separation and branch problems, the new approach by analyzing the shapes and specially sampling on surfaces has been developed.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.822-827
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• 2003

Topological maps have drawn more attention recently because they are compact, provide natural interfaces, and are applicable to path planning easily. To build a topological map incrementally, Voronoi diagram was used by many researchers. The Voronoi diagram, however, has difficulty in applying to arbitrarily shaped objects and needs long computation time. In this paper, we present a new method for global topological map from the local topological maps incrementally. The local topological maps are created through a thinning algorithm from a local grid map, which is built based on the sensor information at the current robot position. A thinning method requires simpler computation than the Voronoi diagram. Localization based on the topological map is usually difficult, but additional nodes created by the thinning method can improve localization performance. A series of experiments have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can create satisfactory topological maps.