• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• KIPS Transactions on Software and Data Engineering
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• v.4 no.10
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• pp.465-472
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• 2015

We propose a novel plane detection in disparity space and evaluate its performance. Our method simplifies and makes scenes in disparity space easily dealt with by approximating various surfaces as planes. Moreover, the approximated planes can be represented in the same size as in the real world, and can be employed for obstacle detection and camera pose estimation. Using a stereo matching technique, our method first creates a disparity image which consists of binocular disparity values at xy-coordinates in the image. Slants of disparity values are estimated by exploiting a line simplification algorithm which allows our method to reflect global changes against x or y axis. According to pairs of x and y slants, we label the disparity image. 4-connected disparities with the same label are grouped, on which least squared model estimates plane parameters. N plane models with the largest group of disparity values which satisfy their plane parameters are chosen. We quantitatively and qualitatively evaluate our plane detection. The result shows 97.9%와 86.6% of quality in our experiment respectively on cones and cylinders. Proposed method excellently extracts planes from Middlebury and KITTI dataset which are typically used for evaluation of stereo matching algorithms.

• Journal of the Korea Computer Graphics Society
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• v.6 no.1
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• pp.37-50
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• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.

• The Bulletin of The Korean Astronomical Society
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• v.32 no.1
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• pp.103.1-103.1
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• 2007

• The Bulletin of The Korean Astronomical Society
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• v.32 no.1
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• pp.101.1-101.1
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• 2007

• Korean Institute of Interior Design Journal
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• no.40
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• pp.68-75
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• 2003

The purpose of this study is to find out the expression style of space in Rietveld's early works in comparison with Mondrian's paintings. Through investigating the development of their works and analyzing the composition and disposition type of elements such as point, line, plane, color in the selected works, we can draw the following conclusions. .First, Rietveld pursues the dissolution of traditional volume and the de-composition of elements as Mondrian does. Second, the painterly property of plane is emphasized by the projection of separately floating elements on the picture plane. Third, the separating the layer of lines from the layer of planes and the re-combination of these two layers present the superimpositional image of three-dimensional objects. This leads into new conception of architectural space and develops the transparency and the extension of plan in modem architecture.

• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.262-269
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• 2003

An approach to compute characteristic curves such as section curves, reflection characteristic lines, and asymptotic curves on a surface is introduced. Each problem is formulated as a surface-plane inter-section problem. A single-valued function that represents the characteristics of a problem constructs a property surface on parametric space. Using a contouring algorithm, the property surface is intersected with a horizontal plane. The solution of the intersection yields a series of points which are mapped into object space to become characteristic curves. The approach proposed in this paper eliminates the use of traditional searching methods or non-linear differential equation solvers. Since the contouring algorithm has been known to be very robust and rapid, most of the problems are solved efficiently in realtime for the purpose of visualization. This approach can be extended to any geometric problem, if used with an appropriate formulation.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.3
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• pp.1-6
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• 1990

When TE waves incident to the infinite conductor grating plane, current distributions on the strip is found by the spectral domain analysis and the moment method. Current distributions on the strip as the parameter of incident angle of waves are calculated for the grating plane of which strip space is $0.05{\lambda}{\sim}5{\lambda}$, and of which the ration of strip width to its space is 0.4 - 0.8 . In order to varify the validity of the present method, the numerical results are compared with other method.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.145-169
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• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.

• Journal of Astronomy and Space Sciences
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• v.3 no.2
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• pp.81-92
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• 1986

The z-coordinate distribution of cepheids was studied and the finding of Fernie(1968) that the cepheid layer is inclined to ward a formal Galactic plane and the Sun is located above the cepheid plane was confirmed. It was found that the z-distribution fits better to the parabolic form than a barometric form and a scale height of 54 pc was found. The well known phenomenon that the periods of classical cepheids decrease away from the Galactic center was crudely interpreted as due to an age gradient rater than an abundance gradient under the assumption that relations between the period and galactocentric distance, and between the abundance and period are linear.