• Korean Journal of Computational Design and Engineering
• /
• v.6 no.1
• /
• pp.24-30
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.31-49
• /
• 2002

An R$^{n}$ -geometry (P$^{n}$ , L) is a generalization of the Euclidean geometry on R$^{n}$ (see Def. 1.1). We can consider some topologies (see Def. 2.2) on the line set L such that the join operation V : P$^{n}$ $\times$ P$^{n}$ \ $\Delta$ longrightarrow L is continuous. It is a notable fact that in the case n = 2 the introduced topologies on L are same and the join operation V : P$^2$ $\times$ P$^2$ \ $\Delta$ longrightarrow L is continuous and open [10, 11]. It is a fundamental topological property of plane geometry, but in the cases n $\geq$ 3, it is no longer true. There are counter examples [2]. Hence, it is a fundamental problem to find suitable topologies on the line set L in an R$^{n}$ -geometry (P$^{n}$ , L) such that these topologies are compatible with the incidence structure of (P$^{n}$ , L). Therefore, we need to study the topologies of the line set L in an R$^{n}$ -geometry (P$^{n}$ , L). In this paper, the relations of such topologies on the line set L are studied.

• Proceedings of the KSRS Conference
• /
• 2002.10a
• /
• pp.885-890
• /
• 2002

As Geographic Information Systems represents three-dimensional topological Information, the systems provide accurate and delicate services for user. In order to execute three-dimensional topological operations, a dimensional transformation and heterogeneous spatial models should be used. However, the existing systems that use the dimensional transformation and the heterogeneous models, are not only difficult to operate the spatial operators, but also happened to support non- interoperability. Therefore, in order to support the spatial operation as well as interoperability between dimensions, we propose three-dimensional spatial operators for the proposed models. We defined the three-dimensional spatial operators prior to designing the proposed model. We also implemented the operators of proposed model and evaluated the implemented model on the component environment. Finally, the proposed model is able to not only support interoperability among systems but also execute spatial queries efficiently on three-dimensional spatial objects.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.5 no.2
• /
• pp.20-28
• /
• 1996

Compound surface modeling is widely used for die cavities and punches. A compound surface is defined in 3-D space by specifying the topological relationship of several anlytic surface elements and a sculptured surface. A constructive solid gemonetry scheme is employed to model the analytic compound surface. the desired compound surface can be accomplished by specifying topological reationship in terms of boolean relations between pimitives and the sculptured surfaces. Additionally, a method is presented for checking and avoiding the tool interference occuued in machining the compound surface. Using this method. the interference of concave, convex, and side region can be checked easily and avoided rpapidly.

• Journal of the Korean Institute of Rural Architecture
• /
• v.13 no.2
• /
• pp.63-70
• /
• 2011

Despite the high historical and topological values, closed schools are rarely reutilized. The reason can be likely explained by integrity of the building structure and unawareness of the operation and maintenance for closed schools. The purpose of this study is finding a possibility of reusing closed schools by deploying SI (Skeleton and Infill) theory. SI theory is separating the "skeleton" like structure from "infill" such as interior furnishings to extend building life without complete demolishing of the building. It will allow satisfying various local community demands by alternating infill without demolishing of historical and topological value of the building. The experimental test was undertaken with closed school for this study. The local community's demands or opinions were reflected to develop a strategy for deploying infill system especially movable storage furniture to closed school. The study finds possibilities that SI theory can assist local community to 1) construct potential demand for utilizing closed school and 2) suggest strategy for operating and maintaining closed school.

• East Asian mathematical journal
• /
• v.22 no.2
• /
• pp.131-149
• /
• 2006

In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

• The Transactions of the Korean Institute of Electrical Engineers B
• /
• v.50 no.2
• /
• pp.79-85
• /
• 2001

In this paper, a novel Zero-Current-Transition (ZCT) technique, which provides Zero-Current-Switching (ZCS) turn-off of the main switch, the main diode and the auxiliary switch, is presented. The proposed auxiliary circuit consists of minimum elements only one auxiliary switch, resonant inductor and resonant capacitor. Also the reduced di/dt, which is obtained by resonant inductor, helps soft turn-on of the main switch. Besides, to eliminate the additional conduction loss and current stress on main switch, a topological variation was performed. The theoretical analysis and the operation principle of the new ZCT techniques are described in detail with a boost converter as an example. To verify the validity of the proposed ZCT techniques, the simulation and the experiment were performed under 1kW output power and 100kHz switching frequency.

• Kyungpook Mathematical Journal
• /
• v.61 no.1
• /
• pp.61-74
• /
• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Journal of the Korean association of regional geographers
• /
• v.6 no.3
• /
• pp.83-99
• /
• 2000

This paper purposes to provide a new perspective for better development of geography texts. For this purpose, we have applied spatial cognition development theory to children's drawings. We have suggested that children's spatial operation ability has three development stages according to their age: topological space, projective space, euclidean space. This study turns out that Piaget and Inhelder's spatial concept development theory is on the right track. However, we make clear that their division according to the age is not always accurate due to children's individual differences. These findings have educational implications as the following: First, it is dubious that most children can understand pictures, pictorial maps and illustrations in the third grader's textbook. Second, current textbooks require pictorial map understanding and drawing to third grade students and map drawing to fourth grade students. However, according to this study, the placement of these tasks are not fit for children's developmental stage because both tasks correspond to euclidean space operation. Therefore, we should remove them from the textbook for children at the age.

• Proceedings of the KSRS Conference
• /
• 2002.10a
• /
• pp.880-884
• /
• 2002

According to the development of computer technology, especially in 3D graphics and visualization, the interest for 3D GIS has been increasing. Several commercial GIS softwares are ready to provide 3D function in their traditional 2D GIS. However, most of these systems are focused on visualization of 3D objects and supports few analysis functions. Therefore in this paper, we design not only a spatial operation processor which can support spatial analysis functions as well as 3D visualization, but also implement a prototype to operate them. In order to support interoperability between the existing models, the proposed spatial operation processor supports the 3D spatial operations based on 3D geometry object model which is designed to extend 2D geometry model of OGIS consortium, and supports index based on R$^*$-Tree. The proposed spatial operation processor can be applied in 3D GIS to support 3D analysis functions.