• 전자공학회논문지S
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• 제34S권2호
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• pp.63-70
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• 1997

This paper proposes a new algorithm for recognizing polyhedral objects using a single 2-D image. It is base don a new representation scheme having two level hierarchey. In the lower level, geometrical features of each primitive surface are represented using their signatures and the variation of signature due to rotation is represented suing the rotation map. In the higher level, topological features are represented in the inter-surface description table(SDT). Based on the proposed representaton scheme, loer level database searched to find a matching primitive surface. The srotation map determines the degree of rotation as well as the matchness. If all surfaces in a test object find their matching primitive surfaces, its structural information is compared with the SDTs of object models. If primitive surfaces of a test object equal to tha tof certain model and satisfy inter-surfaces relationship in SDT, a test object is recognized as the model.

• 대한조선학회지
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• 제22권3호
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• pp.19-26
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• 1985

This paper deals with the representation and fairing of ship hull using a B-spline surface which is known as a 3-D model in computer aided free-form design. The first part of this paper is devoted to the fundamental concepts of B-spline theory and its geometrical characteristics. In its second part are described the facillities for efficient application, fast rendering of B-spline surface, and intersection of B-spline surfaces. The examples are presented with actual application to a real ship in the last part. And also a new concept of evaluating the surface fairness by the Gaussian curvature isolines is briefly discussed and its examples are presented.

• 대한전자공학회논문지
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• 제27권6호
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• pp.851-860
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• 1990

This paper presents a recognition method which interprets 3-D object in terms of several silhouettes of quadtree and octree. Object representation used in object matching should be invariant with respect to locatin and orientation of the object. Generalized octree is projected on to image plane along the principal axes. Regular octree is made from orthogonal directions, but generalized octree is independent to viewing directions. Recognition process is achieved in two-stage matching. The quadtrees and octrees of unknown object with minimum dissimilarities are matched with the quadtrees and octrees of the models. So as to verify efficiency of 3-D object representation and accuracy of object recognition, experiments are performed for 14 different type of geometrical models and its results have been shown.

• 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"

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제22권3호
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• pp.337-347
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• 2008

도형으로서의 직선을 좌표평면에서 대수적으로 표현하는 과정에서 곧음이라는 직선의 고유한 성질은 삼각형의 닮음에 의해 x값의 변화량에 대한 y값의 변화량의 비가 일정하다는 성질로 구체화되고, 이로부터 기울기의 개념이 자연스럽게 등장한다. 이때 기울기는 좌표평면에서 직선의 직선다움 즉, 직선성(直線性)을 나타내주는 수학적 개념으로 서로 평행인 직선을 구분하지 않을 때 한 직선의 불변량이라 할 수 있고, 직선의 방정식은 일정한 비로서의 기울기가 지닌 성질을 대수적으로 표현한 것이라 할 수 있다. 본 논문에서는 좌표평면에서의 직선 및 직선성(直線性)으로서의 기울기 개념이 학교수학에서 어떻게 다루어지고 있는지 분석하고, 개선 방안에 대하여 논의한다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권5호
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• pp.2607-2627
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• 2017

Nonnegative matrix factorization (NMF) has received considerable attention due to its effectiveness of reducing high dimensional data and importance of producing a parts-based image representation. Most of existing NMF variants attempt to address the assertion that the observed data distribute on a nonlinear low-dimensional manifold. However, recent research results showed that not only the observed data but also the features lie on the low-dimensional manifolds. In addition, a few hard priori label information is available and thus helps to uncover the intrinsic geometrical and discriminative structures of the data space. Motivated by the two aspects above mentioned, we propose a novel algorithm to enhance the effectiveness of image representation, called Dual graph-regularized Constrained Nonnegative Matrix Factorization (DCNMF). The underlying philosophy of the proposed method is that it not only considers the geometric structures of the data manifold and the feature manifold simultaneously, but also mines valuable information from a few known labeled examples. These schemes will improve the performance of image representation and thus enhance the effectiveness of image classification. Extensive experiments on common benchmarks demonstrated that DCNMF has its superiority in image classification compared with state-of-the-art methods.

• 호남수학학술지
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• 제28권3호
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• pp.317-326
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• 2006

Based on the geometrical representation of a generalized intuitionistic fuzzy set, we take into account all three parameters describing generalized intuitionistic fuzzy set and propose new methods to calculate the correlation coefficient for generalized intuitionistic fuzzy sets by means of mathematical statistics.

• 대한자기공명의과학회:학술대회논문집
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• 대한자기공명의과학회 2002년도 제7차 학술대회 초록집
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• pp.109-109
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• 2002

Purpose： The aim of the study is to see the representation patterns of human visual cortex by perceiving some geometrical shapes. Method： 3 humans as subjects for the fMRI experiment. A classical block or box car design was used as experimental paradigm. 3 different types of fan shapes and concentric circles were presented.

• 대한수학교육학회지:학교수학
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• 제9권4호
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• pp.487-506
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• 2007

본 연구는 14명의 중학교 2학년 수학영재들이 아르키메데스 다면체를 소재로 한 공간기하과제를 해결하면서 보여주는 정당화 유형과 수학적 표현에 대한 연구이다. 문헌 연구를 통해 정당화 유형과 수학적 표현 분석을 위한 분석틀을 마련하고 이들의 다양한 반응들을 분석하였다. 정당화 유형에서는 부분적인 분석을 통해 형식화를 추구하는 학생과 비형식적이며 경험적인 정당화이지만 모든 구성요소를 고려하여 전체적 정당화를 시도하는 두 반응간의 비교를 통해 비형식적 정당화의 유용성에 분명한 주의를 기울일 필요가 있었다. 수학적 표현에서 시각적 표현은 문제해결을 위한 아이디어를 찾고, 구조를 파악하는데 유용한 역할을 하고 있었으며, 기호적 표현을 점진적으로 발전시키는 과정에서 수학적 개념을 표현 속에 함축시키고 정제시켜 정교한 기호(Harel & Paput. 1994)를 창출하려는 욕구를 발견할 수 있었다.