• Journal of Computational Design and Engineering
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• v.1 no.2
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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).

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.133-141
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• 1991

The empirical method is used to integration adjustment for the coordinates revision of a national control point but the existing values are not to be changed or changed with small variation by suitable datum selection (for example, fixed points). This paper treats the modified weighted station parameter adjustment by quasi-observations, and the method used only variance elements of existing coordinates which is substituted for all covariance elements. The movement detection of unstable points and the junction adjustment of new networks are successfully executed by the method, in integration of new secondary networks to old-secondary-triangulation points which are in the absence of the original observations in Korea. The investigation results reveal that the accuracy of old-secondary-triangulation points is ${\pm}16^{{\prime}{\prime}}$(${\pm}0.08m$), which results from the densification of test network and the analyses of old survey specifications. and is ${\pm}2.3^{{\prime}{\prime}}$ in fixing of old-secondary-triangulation points.

• Wind and Structures
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• v.16 no.6
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• pp.617-627
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• 2013

In wind load calculations based on pressure measurements, the concept of 'tributary area' is usually used. The literature has less guidance for a systematic computational methodology for calculating tributary areas, in general, and for scattered pressure taps, in particular. To the best of the author's knowledge, there is no generic mathematical equation that helps calculate the tributary areas for irregular pressure taps. Traditionally, the drawing of tributary boundaries for scattered and intensively distributed taps may not be feasible (a time and resource consuming task). To alleviate this problem, this paper presents a proposed numerical approach for tributary area calculations on rectangular surfaces. The approach makes use of the available coordinates of the pressure taps and the dimensions of the surface. The proposed technique is illustrated by two application examples: first, quasi-regularly distributed pressure taps, and second, taps that have scattered distribution on a rectangular surface. The accuracy and the efficacy of the approach are assessed, and a comparison with a traditional method is presented.

• International Journal of CAD/CAM
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• v.7 no.1
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.3
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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.

• Journal of Korean Public Health Nursing
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• v.17 no.1
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• pp.132-143
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• 2003

The purpose of this study was to verify the effects of psychodrama group counselling, and to determine its applicability as a nursing intervention for the promotion of mental health of clients in their developmental stages. Methodological triangulation was used for research design. For quantitative study, quasi experimental study design with nonequivalent control group was used to test the effects of psychodrama group counselling. For each experimental and control group convenient samples of 15 nursing students were selected, and observed from May to Nov. 2000. For experimental group, the treatment was given for 2 hours each week, totaling 20 hours. The questionnaire consisted of 24 items of physical symptoms from CMI. 40 items of Spielberger Anxiety Scale, and 21 items of Beck Depression Scale. Reflective journal was written by the experimental group. The data were analyzed using chi-square and Mann-Whitney U test. For the qualitative study, the contents of the reflective journal were analyzed into categories and classifications. The results of the study were as follows; 1. There was a significant difference on physical health status between the experimental and the control group 2. There was a significant difference between two groups on the mean scores of mental health before and after psychodrama group counselling. 3. The qualitative analysis of reflective journal resulted in 4 categories and 13 classifications, which was reflected by the experience of the psychodrama group counselling. The four categories were self introspection, psychological support, improvement of interpersonal relationship and self development. The thirteen classifications are self-discovery, discovering others, emotional catharsis, positive thinking, formation of consensus, comforting, being free, being comfortable, understanding, maturing personal relationship, acquiring self-confidence, new challenges, and planning for the future. Based on the study findings, the psychodrama group counselling had promoted not only physical but also mental health of nursing students. The characteristics identified by the study suggested the applicability of psychodrama group counselling as an effective measure of nursing intervention for clients.