• Korean Journal of Optics and Photonics
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• v.5 no.1
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• pp.25-30
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• 1994

We derive a set of formuale which show one-to-one correspondence between the the unitary Jones matrices of transparent anisotropic media and the rotational transformations on the Poincare sphere. By using the formuale one can determine the vectorial representation of the rotational transformation on the Poincare sphere which specifies the direction of the axis and the angle of the rotation in terms of the three parameters specific to the corresponding unitary Jones matrix, and conversely the the three parameters of the uniatry Jones matrix in terms of the vectorial representation of the corresponding rotational transformation on the Poincare sphere. To understand the polarization transmission characteristics of an optical system consisting of transparent linear anisotropic media, start with the Jones calculus to get the unitary Jones matrix for the whole system and then convert it to a rotational transformation on the Poincare sphere, from which we can intuitively understand the effect of the optical system on the polarization state of the light passing through the system.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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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.

• Journal of the Korea Furniture Society
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• v.27 no.1
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• pp.1-7
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• 2016

De Stijl in order to began in the Netherlands in 1917 is an art movement that becomes the theoretical background of modernism design was the foundation geometric abstraction. Steel design for that they offered a new paradigm at that time art, in various fields such as industrial design is still applied, especially works of De Stijl in the design area of urniture it became the beginning of the modern furniture. The starting point of this study is to analyze the two-dimensional representation characteristics to understand the background of the formation with the basic concepts of De Stijl. Therefore the generation of the surface to be displayed in the work of De Stijl and to analyze the divided element, and not if learn their expression characteristics. Also the line and the plane of the two-dimensional modeling properties of De Stijl, after described colors, and studied the characteristics of De Stjil writers for typical analyzes the moldability shown in their work, which based on, we try to present a new representation technique.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.769-774
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• 2006

In this paper, we discuss the problem of non-mutual detectability using the invariant zero. We propose a representation method for excess spaces by linear equation based on the Rosenbrock system matrix. As an alternative to the system enlargement method proposed by White[1], we propose an appropriate form of an enlarged system to make a set of faults mutually detectable by assigning sufficient geometric multiplicity of invariant zeros. We show the equivalence between the two methods and a necessary condition for the system enlargement in terms of the geometric and algebraic multiplicities of invariant zeros.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.301-308
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• 2005

In this study, we implement a framework that directly links a general tensor-based shell finite element to NURBS geometric modeling. Generally, in CAD system the surfaces are represented by B-splines or non-uniform rational B-spline(NURBS) blending functions and control points. Here, NURBS blending functions are composed by two parameters defined in local region. A general tensor-based shell element also has a two-parameter representation in the surfaces, and all the computations of geometric quantities can be performed in local surface patch. Naturally, B-spline surface or NURBS function could be directly linked to the shell analysis routine. In our study, we use NLib(NURBS libraray) to generate NURBS for shell finite analysis. The NURBS can be easily generated by interpolating or approximating given set of data points through NLib.

• Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.370-384
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• 2016

Computer-aided materials design requires new modeling approaches to characterize and represent fine-grained geometric structures and material compositions at multiple scales. Recently, a dual-Rep approach was developed to model materials microstructures based on a new basis function, called surfacelet. As a combination of implicit surface and wavelets, surfacelets can efficiently identify and represent planar, cylindrical, and ellipsoidal geometries in material microstructures and describe the distribution of compositions and properties. In this paper, these primitive surfacelets are extended and composite surfacelets are proposed to model more complex geometries. Composite surfacelets are constructed by Boolean operations on the primitives. The surfacelet transform is applied to match geometric features in three-dimensional images. The composition of the material near the identified features can then be modeled. A cubic surfacelet and a v-joint surfacelet are developed to demonstrate the reverse engineering process of retrieving material compositions from material images.

• School Mathematics
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• v.4 no.3
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• pp.347-360
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• 2002

This study analyzed the mathematical and didactical contexts of the Euclid's proof about Pythagorean theorem and compared with the teaching methods about Pythagorean theorem in school mathematics. Euclid's proof about Pythagorean theorem which does not use the algebraic methods provide students with the spatial intuition and the geometric thinking in school mathematics. Furthermore, it relates to various mathematical concepts including the cosine rule, the rotation, and the transfor-mation which preserve the area, and so forth. Visual demonstrations can help students analyze and explain mathematical relationship. Compared with Euclid's proof, Algebraic proof about Pythagorean theorem is very simple and it supplies the typical example which can give the relationship between algebraic and geometric representation. However since it does not include various spatial contexts, it forbid many students to understand Pythagorean theorem intuitively. Since both approaches have positive and negative aspects, reciprocal complementary role is required in pedagogical aspects.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.113-120
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• 1998

Calculation of intersection points by two curves is fundamental to computer aided geometric design. Bezier clipping is one of the well-known curve intersection algorithms. However, this algorithm is only applicable to Bezier curve representation. Therefore, the NURBS curves that can represent free from curves and conics must be decomposed into constituent Bezier curves to find the intersections using Bezier clipping. And the respective pairs of decomposed Bezier curves are considered to find the intersection points so that the computational overhead increases very sharply. In this study, extended Bezier clipping which uses the linear precision of B-spline curve and Grevill's abscissa can find the intersection points of two NURBS curves without initial decomposition. Especially the extended algorithm is more efficient than Bezier clipping when the number of intersection points is small and the curves are composed of many Bezier curve segments.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.311-311
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• 2000

We propose a DP-based formulation for matching line patterns by defining a robust and stable geometric representation that is based on the conceptual organizations. Usually, the endpoint proximity and collinearity of image lines, as two main conceptual organization groups, are useful cues to match the model shape in the scene. As the endpoint proximity, we detect junctions from image lines. We then search for junction groups by using geometric constraint between the junctions. A junction chain similar to the model chain is searched in the scene, based on a local comparison. A Dynamic Programming-based search algorithm reduces the time complexity for the search of the model chain in the scene. Our system can find a reasonable matching, although there exist severely distorted objects in the scene. We demonstrate the feasibility of the DP-based matching method using both synthetic and real images.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.406-412
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• 1996

Optimal trajectory for a robot manipulator minimizing actuator torques or energy consumption in a fixed traveling time is obtained in the presence of obstacles. All joint displacements are represented in finite terms of Fourier cosine series and the coefficients of the series are obtained optimally by nonlinear programming. Thus, the geometric path need not be prespecified and the full dynamic model is employed. To avoid the obstacles, the concept of penalty area is newly introduced and this penalty area is included in the performance index with an appropriate weighting coefficient. This optimal trajectory will be useful as a geometric path in the minimum-time trajectory planning problem.