• Journal of Computational Design and Engineering
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• 제1권2호
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• pp.79-87
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• 2014

Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the two-dimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

• 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.

• 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.

• 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.

• Spatial Information Research
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• 제15권3호
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• pp.203-218
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• 2007

본 연구의 목적은 지리적 접근성이 떨어지는 행정 편의적 입지 및 관할 구역 설정 대신 과학적이고 합리적인 입지 및 관할 구역 설정의 준거를 마련하는 데 있다. 그리고 이 준거를 통해 시설물의 입지 연구를 위한 보다 실질적이고 합리적인 기본 공간단위를 제안하는 데 있다. 본 연구에서는 새로운 과학적, 합리적 기준으로 보로노이 다이어그램(Voronoi Diagram)의 기법을 이용하였다. 이 기법은, 새로운 관할구역을 제안할 수 있는 모델을 선정 구현하고, 모델의 현실성을 제고하기 위해 그 모델을 변형 응용하며, 변형 응용 방안 중 어떤 것이 가장 현실성과 적합성이 뛰어난지 상호 비교하여 평가한다. 이러한 절차를 통해 얻어진 결과는 관할 구역 설정의 객관화와 시설물 입지 연구를 위한 기본 공간 단위의 마련에 이용될 수 있다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권7호
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• pp.2345-2358
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• 2022

This paper presents a method to generate stained-glass animation from video inputs. The method initially segments an input video volume into several regions considered as fragments of glass by mean-shift segmentation. However, the segmentation predominantly results in over-segmentation, causing several tiny segments in a highly textured area. In practice, assembling significantly tiny or large glass fragments is avoided to ensure architectural stability in stained glass manufacturing. Therefore, we use low-frequency components in the segmentation to prevent over-segmentation and subdivide segmented regions that are oversized. The subdividing must be coherent between adjacent frames to prevent temporal artefacts, such as flickering and the shower door effect. To temporally subdivide regions coherently, we obtain a panoramic image from the segmented regions in input frames, subdivide it using a weighted Voronoi diagram, and thereafter project the subdivided regions onto the input frames. To render stained glass fragment for each coherent region, we determine the optimal match glass fragment for the region from a dataset consisting of real stained-glass fragment images and transfer its color and texture to the region. Finally, applying lead came at the boundary of the regions in each frame yields temporally coherent stained-glass animation.

• 대한지리학회지
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• 제46권3호
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• pp.366-381
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• 2011

일반적으로 이산적 입지 공간에서 경쟁적 입지 문제는 입지 후보지에 따라 수많은 조합의 경우가 발생하는 의사결정 문제이기 때문에, 수리적으로 계산하기가 쉽지 않다. 따라서 본 연구에서는 결정적 배분 형태를 가정한 이산적 입지 공간의 경쟁적 입지 문제를 보다 효율적으로 해결하기 위한 대안적 방법에 대해 논의한다. 제안된 방법론의 핵심은 입지 문제의 크기와 관련되는 잠재적 입지후보지의 개수를 기하학적 개념을 이용하여 줄이는 것이다. 사례 분석으로 경쟁이 가열화되고 있는 초고속 인터넷 시장을 대상으로 제안된 방법론을 적용하였는데 두 가지 다른 크기의 문제, 즉 연구 지역 전체에 대해 정의된 잠재적 입지 후보지와 GIS 기반의 기하학적 알고리즘에 의해 추출된 보다 적은 수의 잠재적 입지 후보지에 대해 계산 결과와 공간적 배열을 비교하였다. 사례 분석 결과, 두 문제 모두 고객 유치를 최대화시키는 동일한 최적 입지를 보여주는 한편, 적은 수의 잠재적 입지 후보지를 가진 경쟁적 입지 모델이 보다 효율적으로 해결될 수 있었다.