• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.349-356
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• 1998

We give the new formulas counting the total number of all lines planes and tetrahedrons in the n-dimensional Boolean space.

• 한국CDE학회논문집
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• 제4권1호
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• pp.43-51
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• 1999

Producing the relevant information (features) from the CAD models of CAM, called feature recognition or extraction, is the essential stage for the integration of CAD and CAM. Most feature recognition methods, however, have problems in the recognition of intersecting features because they do not handle the intersection geometry properly. In this paper, we propose a machining feature recognition algorithm, which has a solid model consisting of orthogonal primitives as input. The algorithm calculates candidate features and constitutes the Intersection Geometry Matrix which is necessary to represent the spatial relation of candidate features. Finally, it recognizes machining features from the proposed candidate features dividing and growing systems using half space and Boolean operation. The algorithm has the following characteristics: Though the geometry of part is complex due to the intersections of design primitives, it can recognize the necessary machining features. In addition, it creates the Maximal Feature Volumes independent of the machining sequences at the feature recognition stage so that it can easily accommodate the change of decision criteria of machining orders.

• 한국CDE학회논문집
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• 제1권1호
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• pp.20-32
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• 1996

The boundary evaluation technique for Boolean operation on non-manifold models which is regarded as the most popular and powerful method to create and modify 3-D CAD models has been developed. This technique adopted the concept of Merge and Selection in which the CSG tree for Boolean operation can be edited quickly and easily. In this method, the merged set which contains complete information about primitive models involved is created by merging primitives one by one, then the alive entities are selected following the given CSG tree. This technique can support the hybrid representation of B-rep(Boundary Representation) and CSG(Constructive Solid Geometry) tree in a unified non-manifold model data structure, and expected to be used as a basic method for many modeling problems such as data representation of form features, and the interference between them, and data representation of conceptual models in design process, etc.

• 한국CDE학회논문집
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• 제5권4호
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• pp.301-311
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• 2000

For effective part modifications which is necessary in the design process frequently, variational geometric modeling with constraint management being used in a wide. Most variational geometric modeling methods, however, manage just the constraints about sketch elements used for generation of primitives. Thus, not only constraint propagation but also re-build of various modeling operations stored in the modeling history is necessary iota part geometry modifications. Especially, re-build of high-cost Boolean operations is apt to deteriorate overall modeling efficiency abruptly. Therefore, in this paper we proposed an algorithm that can handle all geometric entities of the part directly. For this purpose, we introduced eight type geometric constraints to the various geometric calculations about all geometric entities in sweepings and Boolean operations as well as the existing constraints of the sketch elements. The algorithm has a merit of rapid part geometric modifications through only constraint propagation without rebuild of modeling operations which are necessary in the existing variational geometric modeling method.

• 한국CDE학회논문집
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• 제5권4호
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• pp.312-318
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• 2000

In this study, an exclusive CAD/CAM system is developed for enhancing the effectiveness and productivity of CNC universal cylindrical grinding machines on which the external/facing/internal grinding cycles and the wheel dressing cycles are integratively carried out. The CAD/CAM system can manage the various processes such as geometry design, NC code generation, NC code verification, DNC operation, and so on. Especially, the feature-based modeling concept is introduced to improve the geometry design efficiency. And the NC code verification is realized by virtual manufacturing technique based on the real-time analysis of NC codes and the boolean operation between workpiece and wheel.

• 한국CDE학회논문집
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• 제11권4호
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• pp.235-245
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• 2006

This paper proposes a CSG-based representation scheme for heterogeneous objects including multi-material objects and Functionally Graded Materials (FGMs). In particular, this scheme focuses on the construction of complicated heterogeneous objects guaranteeing desired material continuities at all the interfaces. In order to create various types of heterogeneous primitives, we first describe methods for specifying material composition functions such as geometry-independent, geometry-dependent functions. Constructive Material Composition (CMC) and corresponding heterogeneous Boolean Operators (e.g. material union, difference, intersection. and partition) are then proposed to illustrate how material continuities are dealt with. Finally, we describe the model hierarchy and data structure for computer representation. Even though the proposed scheme alone is sufficient for modeling all sorts of heterogeneous objects, the proposed scheme adopts a hybrid representation between CSG and decomposition. That is because hybrid representation can avoid the unnecessary growth of binary trees.

• 한국실내디자인학회논문집
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• 제23권4호
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• pp.129-139
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• 2014

The objective of this research is to suggest new geometric possibilities in digital architecture by investigating the characteristics of hybridization in digital geometry. The research begins with theoretical background research such as defining hybridization, investigating hybrid thinking, and studying the theory of digital geometry, along with the four conceptual characteristics of hybridization that could be drawn, such as temporality, liquidity, complexity, and connectivity. Based on these characteristics, the generative method of hybrid digital geometric languages such as Blob, Particle, Morph, Loft, and Boolean was analyzed with case research in contemporary digital architecture. As a result, diverse hybrid geometric keywords were extracted; these keywords suggest potential meanings of hybridization such as accidentality, mobility, diversity, and identity. Different elements represent the "mobility" in time by the force and wave, and they are "accidentally" combined in gradual change. The united species in "diverse" characters are seamlessly connected and emerge as a new "identity." The research maximizes the generative possibilities in digital geometry and provides a theoretical basis to apply the digital hybrid methods to architectural design by suggesting the potential meanings and possibilities in hybridization.

• 한국컴퓨터그래픽스학회논문지
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• 제3권2호
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• pp.77-84
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• 1997

3차원 물체를 표현하는 솔리드 모델링 기법으로 Constructive Solid Geometry(CSG)와 경계표현 (Boundary Representation: BRep)이 널리 쓰이고 있다. 현대의 솔리드 모델링 시스템들은 대개 이 두 기법을 모두 지원하고 있으며, CSG와 BRep간 상호 변환은 매우 중요한 문제이다. 하지만, BRep에서 CSG로의 변환은 아직 완전히 해결되지 않은 과제이다. 이 논문은 BRep을 CSG의 특수한 형태인 Destructive Solid Geometry(DSG)로 변환하는 3차원 기하 추론 알고리즘을 소개한다. BRep에서 DSG를 만들어내는 알고리즘은 CAD와 CAM을 통합시키는 특정 형상 인식 분야에 직접 응용될 수 있다.

• 대한수학회보
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• 제31권2호
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.869-872
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• 2003

This paper presents a geometric machining simulation algorithm to enhance the reliability and user-friendliness of a comprehensive computer aided process planning (CAPP) system by verifying generated NC data. In order to represent the complex machining geometry with high accuracy, the proposed algorithm is developed based on a boundary representative (B-rep) solid modelling kernel. Solid models are used to represent the part geometry. tool swept volume and material removal volume by Boolean unite and subtract operations. By integrating a machining simulation procedure into the CAPP system, the systematic analysis of the tool path can be implemented synthetically. To demonstrate and check the validity of suggested system, a simple example of simulation is represented and the result is discussed.