• Honam Mathematical Journal
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• v.39 no.4
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• pp.515-525
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• 2017

In this paper, we study planar normal section curves. We have interpreted curvatures of normal section curves. On the other hand we have investigated sufficient and necessary conditions for a normal section curve to be biharmonic.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.127-134
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• 1998

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.482-486
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• 2009

Scale-invariant feature is an effective method for retrieving and classifying images. In this study, we analyze a scale-invariant planar curve features for developing 2D shapes. Scale-space filtering is used to determine contour structures on different scales. However, it is difficult to track significant points on different scales. In mathematics, curvature is considered to be fundamental feature of a planar curve. However, the curvature of a digitized planar curve depends on a scale. Therefore, automatic scale detection for curvature analysis is required for practical use. We propose a technique for achieving automatic scale detection based on difference of curvature. Once the curvature values are normalized with regard to the scale, we can calculate difference in the curvature values for different scales. Further, an appropriate scale and its position are detected simultaneously, thereby avoiding tracking problem. Appropriate scales and their positions can be detected with high accuracy. An advantage of the proposed method is that the detected significant points do not need to be located in the same contour. The validity of the proposed method is confirmed by experimental results.

• Korean Journal of Computational Design and Engineering
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• v.15 no.2
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• pp.115-123
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• 2010

We present an efficient algorithm for computing the Hausdorff distance between two planar curves. The algorithm is based on an efficient trimming technique that eliminates the curve domains that make no contribution to the final Hausdorff distance. The input curves are first approximated with biarcs within a given error bound in a pre-processing step. Using the biarc approximation, the distance map of an input curve is then approximated and stored into the graphics hardware depth-buffer by rendering the distance maps (represented as circular cones) of the biarcs. We repeat the same procedure for the other input curve. By sampling points on each input curve and reading the distance from the other curve (stored in the hardware depth-buffer), we can easily estimate a lower bound of the Hausdorff distance. Based on the lower bound, the algorithm eliminates redundant curve segments where the exact Hausdorff distance can never be obtained. Finally, we employ a multivariate equation solver to compute the Hausdorff distance efficiently using the remaining curve segments only.

• International Journal of Ocean System Engineering
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• v.2 no.2
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• pp.63-70
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• 2012

This paper presents a new curvature based kinematic displacement theory and a numerical method to calculate the planar displacement of structures from a geometrical viewpoint. The theory provides an opportunity to satisfy the kinematic equilibrium of a planar structure using a progressive numerical approach, in which the cross sections are assumed to remain plane, and the deflection curve was evaluated geometrically using the curvature values despite being solved using differential equations. The deflection curve is parameterized with the arc-length, and was taken as an assembly of the chains of circular arcs. Fast and accurate solutions of most complex deflections can be obtained with few inputs.

• Journal of the Korean Mathematical Society
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• v.14 no.2
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• pp.153-158
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• 1978

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1617-1622
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• 1991

Plane sweep is a general method in computational geometry. There are many efficient theoretical algorithms designed using plane sweep technique. However, their practical implementations are still suffering from the topological inconsistencies resulting from the numerical errors in geometric computations with finite-precision arithmetic. In this paper, we suggest new implementation techniques for the plane sweep algorithms to resolve the topological inconsistencies and construct the planar object boundaries from given input curve segments.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.130-145
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• 2023

In this paper, we define some integral curves connected with a framed curve in Euclidean 3-space. These curves include framed generalized principal-direction curve, framed generalized binormal-direction curve, framed principal-donor curve and framed Darboux-direction curve. We obtain some relations between the framed curvatures of new defined framed curves and framed curvatures of given framed curve. By using the obtained relationships we give some characterizations for such curves. We also give methods for constructing framed helix and framed slant helix from planar curves.

• Korean Journal of Computational Design and Engineering
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• v.4 no.4
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• pp.312-317
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• 1999

An inflection point on a curve is a point where the curvature vanishes. An inflection point is useful for various geometric operations such as the approximation of curves and intersection points between curves or curve approximations. An inflection point on planar Bezier curves can be easily detected using a hodograph and a derivative of hodograph, since the closed from of hodograph is known. In the case of rational Bezier curves, for the detection of inflection point, it is needed to use the first and the second derivatives have higher degree and are more complex than those of non-rational Bezier curvet. This paper presents three methods to detect inflection points of rational Bezier curves. Since the algorithms avoid explicit derivations of the first and the second derivatives of rational Bezier curve to generate polynomial of relatively lower degree, they turn out to be rather efficient. Presented also in this paper is the theoretical analysis of the performances of the algorithms as well as the experimental result.

• Journal of the Korean Electrochemical Society
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• v.7 no.2
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• pp.69-79
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• 2004

To correctly simulate performance characteristics of fuel cells with a modeling method, various physical and chemical phenomena must be considered in fuel cells. In this study, performance characteristics of planar solid oxide fuel cells were simulated by a commercial CFD code, CFD-ACE+. Through simultaneous considerations for mass transfer, heat transfer and charge movement according to electrochemical reactions in the 3-dimensional planar SOFC unit stack, we could successfully predict performance characteristics of solid oxide fuel cells under operation for structural and progress variables. In other words, we solved mass fraction distribution of reactants and products for diffusion and movement, and investigated qualitative and quantitative analysis for performance characteristics in the SOFC unit stack through internal temperature distribution and polarization curve for electrical characteristics. Through this study, we could effectively predict performance characteristics with variables in the unit stack of planar SOFCs and present systematic approach for SOFCs under operation by computer simulation.