• 한국산업경영시스템학회:학술대회논문집
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• 한국산업경영시스템학회 2002년도 춘계학술대회
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• pp.461-466
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• 2002

In many applications of computer aided geometric design and computer graphics, B-spline is one of the most popular representation for curves and surfaces, and the evaluation of B-spline curves and surfaces is the most frequently used operation. For the evaluation and others, the power form representation of the curves and surfaces is preferred because it is possible to speed-up the operation using Horner's rule. In this paper, we present a new algorithm for the above-mentioned conversion focusing on a dynamic case. Experiment shows that the proposed algorithm significantly outperforms the conventional approach when one or more control points of a B-spline curve and surface are dynamically moving.

• 한국정밀공학회지
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• 제20권5호
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• pp.47-56
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• 2003

Geometric cutting-simulation and verification play an important role in detecting NC machining errors in mold & die manufacturing and thereby reducing correcting time & cost on the shop floor. Current researches in the area may be categorized into view-based, solid-based, and discrete vector-based methods mainly depending on workpiece models. Each methodology has its own strengths and weaknesses in terms of computing speed, representation accuracy, and its ability of numerical inspection. The paper proposes a hybrid modeling scheme for workpiece representation with z-map model and discrete vector model, which performs 3-axis and 5-axis cutting-simulation via tool swept surface construction by connecting a sequence of silhouette curves.

• Journal of information and communication convergence engineering
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• 제9권2호
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• pp.207-211
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• 2011

This paper presents a method for facial feature representation and recognition from the Covariance Matrices of the Gabor-filtered images. Gabor filters are a very powerful tool for processing images that respond to different local orientations and wave numbers around points of interest, especially on the local features on the face. This is a very unique attribute needed to extract special features around the facial components like eyebrows, eyes, mouth and nose. The Covariance matrices computed on Gabor filtered faces are adopted as the feature representation for face recognition. Geodesic distance measure is used as a matching measure and is preferred for its global consistency over other methods. Geodesic measure takes into consideration the position of the data points in addition to the geometric structure of given face images. The proposed method is invariant and robust under rotation, pose, or boundary distortion. Tests run on random images and also on publicly available JAFFE and FRAV3D face recognition databases provide impressively high percentage of recognition.

• Journal of Mechanical Science and Technology
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• 제19권2호
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• pp.558-566
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• 2005

We propose a feature-based multi-resolution representation of B-rep solid models using history-based Boolean operations based on the merge-and-select algorithm. Because union and subtraction are commutative in the history-based Boolean operations, the integrity of the models at various levels of detail (LOD) is guaranteed for the reordered features regardless of whether the features are subtractive or additive. The multi-resolution solid representation proposed in this paper includes a non-manifold topological merged-set model of all feature primitives as well as a feature-modeling tree reordered consistently with a given LOD criterion. As a result, a B-rep solid model for a given LOD can be provided quickly, because the boundary of the model is evaluated without any geometric calculation and extracted from the merged set by selecting the entities contributing to the LOD model shape.

• 한국수학사학회지
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• 제27권5호
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• pp.329-345
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• 2014

CAGD(Computer Aided Geometric Design) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their efficient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical quantities of importance such as curvatures, intersection curves between two surfaces and offset surfaces. The $B\acute{e}zier$ curves, B-spline, rational $B\acute{e}zier$ curves and NURBS(Non-Uniform Rational B-Spline) are basically and widely used in CAGD. The definitions and properties of these curves are presented in this paper. And a brief history of study on the bound for derivative of rational curves in CAGD is also presented.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.552-552
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• 2000

In recent years, a number of successful nesting approaches have been developed by using the various heuristic algorithms, and due to their application potential several commercial CAD/CAM packages include a nesting module for solving the layout problem. Since a large portion of the complexity of the part nesting problem results from the overlapping computation, the geometric representation is one of the most important factors to reduce the complexity of the problem. The proposed part representation method can easily handle parts and raw materials with widely varying geometrical shape by using the redesigning modules. This considerably reduces the amount of processed data and consequently the run time of the computer. The aim of this research is to develop parametric macro for two-dimensional cutting stock on the Auto-CAD system. Therefore, this research can be called "pre-nesting"

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.193-200
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• 2001

In this study, the methodology to develop a data model for steel box girder bridge based on STEP part 104 is presented. The concept of STEP and the schema of part 104 are briefly reviewed, and then the procedure of data model standardization is described. A new data model for steel box girder bridge is developed by incorporating with not only the geometric and topological representation schema of the part 42 but also the representation structure information of the part 43 and the detailed finite element analysis information of the part 104. The prototype of integrated finite element analysis(FEA) system by interfacing STEP physical file is also presented. The applicability of developed data model for FEA is verified by preprocessor system of FEA.

• 한국CDE학회논문집
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• 제10권5호
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• pp.314-327
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• 2005

This paper describes the volumetric data modeling and analysis methods that employ volumetric NURBS or VNURBS that represents heterogeneous objects or fields in multidimensional space. For volumetric data modeling, we formulate the construction algorithms involving the scattered data approximation and the curvilinear grid data interpolation. And then the computational algorithms are presented for the geometric and mathematical analysis of the volume data set with the VNURBS model. Finally, we apply the modeling and analysis methods to various field applications including grid generation, flow visualization, implicit surface modeling, and image morphing. Those application examples verify the usefulness and extensibility of our VNUBRS representation in the context of volume modeling and analysis.

• 한국CDE학회논문집
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• 제7권2호
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• pp.121-130
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• 2002

The concept of Level Of Detail (LOD) was introduced and has been used to enhance display performance and to carry out certain engineering analysis effectively. We would like to use an adequate complexity level for each geometric model depending on specific engineering needs and purposes. Solid modeling systems are widely used in industry, and are applied to advanced applications such as virtual assembly. In addition, as the demand to share these engineering tasks through networks is emerging, the problem of building a solid model of an appropriate resolution to a given application becomes a matter of great necessity. However, current researches are mostly focused on triangular mesh models and various operators to reduce the number of triangles. So we are working on the multi-resolution of the solid model itself, rather than that of the triangular mesh model. In this paper, we propose multi-resolution representation of B-rep model by reordering and converting design features into an enclosing volume and subtractive features.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.883-896
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• 2022

A hereditary base-b representation, used in the celebrated Goodstein's theorem, can easily be converted into a labeled rooted tree. In this way it is possible to give a more elementary geometric proof of the aforementioned theorem and to establish a more general version, geometrically proved. This view is very useful for better understanding the underlying logical problems and the need to use transfinite induction in the proof. Similar problems will then be considered, such as the so-called "hydra game".