• Journal of the Korea Computer Graphics Society
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• v.4 no.1
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• pp.11-19
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• 1998

Non-manifold topological operations such as Euler and Boolean operations provide a versatile environment for modeling domains. The implementation of these operations raises geometrical issues that need to be addressed to ensure the topological validity of the underlying model, and they uses the glue operation which provides a basic method to modify the topology of non-manifold models when vertices, edges and faces are contacting each other. Topological information such as adjacency relationships should be inferred when gluing non-manifold models. Two methods of reasoning can be employed to find the topological information : topological reasoning and geometrical reasoning. The topological method can infer the adjacency relationships by using stored topological information. On the other hand, the geometrical method can find topological ambiguities by considering the geometrical shape at the local area of gluing when the topological relations were not stored. This paper describes the geometrical reasoning method.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.237-248
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• 2023

The aim of this paper is to study the concept of s-topological d-algebras which is a d-algebra supplied with a certain type of topology that makes the binary operation defined on it d-topologically continuous. This concept is a generalization of the concept of topological d-algebra. We obtain several properties of s-topological d-algebras.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.291-296
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• 2011

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

• Journal of international Conference on Electrical Machines and Systems
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• v.1 no.3
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• pp.312-319
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• 2012

The operation principle of an axial flux-switching hybrid excitation synchronous machine (AFHESM) is analyzed and its topology structures are proposed in this paper. After some comprehensive analysis of the operation principle to axial flux electrical machine, flux-switching electrical machine and hybrid excitation electrical machine, the operation principle of AFHESM is given. Combined with some typical topological structures of hybrid excitation electrical machine, some possible topological structures are proposed and some comprehensive comparisons are carried out. The analysis results show that the stator-separated AFHESM has some advantages such as less AM turns, less impact on the demagnetization of PM, less magnetic flux-leakage and higher efficiency compared to other topologies.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.59-62
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• 2000

In this paper we introduce the notion of fuzzy ${\gamma}$-open sets by using an operation ${\gamma}$ on fuzzy topological space (X, $\tau$) and investigate the related fuzzy topological properties of the associated fuzzy topology $\tau$$\_$${\gamma}$/ and $\tau$. And ${\gamma}$-T$\_$i/(i=0,1,2) separation axioms are defined in fuzzy topological spaces and the validity of some results analogous to those in fuzzy T$\_$i/ spaces due to Ganguly and Saha [2] are examined.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.555-568
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• 2014

A set with an operation defined on a family of subsets is studied. The operation is used to generalize the topological space itself. The operation defines the operation-open subsets in the set. Relations are studied among two types of the interiors and the closures of subsets. Some properties of maximal operation-open sets are obtained. Semi-open sets and pre-open sets are defined in the sets with operations and some relations among them are proved.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.901-905
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• 2005

Monte Carlo localization is known to be one of the most reliable methods for pose estimation of a mobile robot. Much research has been done to improve performance of MCL so far. Although MCL is capable of estimating the robot pose even for a completely unknown initial pose in the known environment, it takes considerable time to give an initial estimate because the number of random samples is usually very large especially for a large-scale environment. For practical implementation of the MCL, therefore, a reduction in sample size is desirable. This paper presents a novel approach to reducing the number of samples used in the particle filter for efficient implementation of MCL. To this end, the topological information generated off- line using a thinning method, which is commonly used in image processing, is employed. The topological map is first created from the given grid map for the environment. The robot scans the local environment using a laser rangefinder and generates a local topological map. The robot then navigates only on this local topological edge, which is likely to be the same as the one obtained off- line from the given grid map. Random samples are drawn near the off-line topological edge instead of being taken with uniform distribution, since the robot traverses along the edge. In this way, the sample size required for MCL can be drastically reduced, thus leading to reduced initial operation time. Experimental results using the proposed method show that the number of samples can be reduced considerably, and the time required for robot pose estimation can also be substantially decreased.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.293-300
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• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• Korean Journal of Computational Design and Engineering
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• v.5 no.3
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• pp.242-254
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• 2000

This paper describes an efficient solid modeling method for thin-walled plastic or sheet metal parts, based on the non-manifold offsetting operations. Since the previous methods for modeling and converting a sheet into a solid have adopted the boundary representations for solid object as their topological framework, it is difficult to represent the exact adjacency relationship between topological entities of a sheet model and a mixture of wireframe and sheet models that can appear in the meantime of modeling procedure, and it is hard to implement topological operations for sheet modeling and transformation of a sheet into a solid. To solve these problems, we introduce a non-manifold B-rep and propose a sheet conversion method based on a non-manifold offset algorithm. Because the non-manifold offset aigorithm based on mathematical definitions results in an offset solid with tubular and spherical thickness-faces we modify it to generate the ruled or planar thickness-faces that are mostly shown in actual plastic or sheet metal parts. In addition, in order to accelerate the Boolean operations used the offset algorithm, we also develope an efficient face-face intersection algorithm using topological adjacency information.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10a
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• pp.166-168
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• 2001

3D GIS(Geographical Information System)은 2D GIS를 고도값을 고려한 3D 공간으로 확장한 GIS System이다. 3D GIS는 기존의 2D와는 다른 Data Format을 기반으로 훨씬 다양한 기능을 지원하는 Operation들을 제공한다. 본문에서는 각 노드들의 상관 관계를 묘사하는 데 장점을 가진 Topological Data Model에 대해 알아보고, 이 모델에서 지원이 가능한 여러 가지의 3D Operation들을 알아보고 도시내의 다양한 상황하에서 기능을 지원 할 수 있도록 한다.