• Honam Mathematical Journal
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• v.40 no.4
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• pp.701-718
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• 2018

In this paper, we will study the constant mean curvature (CMC) surfaces foliated by ellipses in three dimensional Euclidean space $E^3$. We prove that: (1): Surfaces foliated by ellipses are CMC surfaces if and only if it is a part of generalized cylinder. (2): All surfaces foliated by ellipses are not minimal surfaces. (3): CMC surfaces foliated by ellipses are developable surfaces. (4): CMC surfaces foliated by ellipses are translation surfaces generated by a straight line and plane curve.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.801-815
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• 2021

Ellipses have a lot of interesting geometric properties. It is quite natural to ask whether such properties of ellipses and some related ones characterize ellipses. In this paper, we study some chord properties and area properties of ellipses. As a result, using the curvature and the support function of a strictly convex curve, we establish four characterization theorems of ellipses and hyperbolas centered at the origin.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.559-567
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• 2006

We are interested in the distance problem between two objects in three dimensional Euclidean space. There are many distance problems for various types of objects including line segments, boxes, polygons, circles, disks, etc. In this paper we present an iterative algorithm for finding the distance between two given ellipses. Numerical examples are given.

• Journal of the Korean Society for Precision Engineering
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• v.33 no.3
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• pp.207-216
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• 2016

A gerotor is suitable for miniature manufacturing because it has high discharge per 1 cycle and a simple structure, while also being widely used for lubrication oil of engines and as a hydraulic source of automatic transmission. In the automobile industry, improvements in fuel efficiency and noise reduction have recently come to the fore. It has also been necessary to continuously improve the flow rate and noise of internal gear pumps for better fuel efficiency through optimal gerotor and port shape design. In this study, to develop an optimal gerotor with a new lobe shape, 2-ellipses-combined, the equation of the lobe shape was derived, and CFD analysis results were compared for 2-ellipses with those of the previous gerotors (3-ellipses and ellipse1-involuteellipse2). A performance test for the oil pump with the optimal rotor (2-ellipses) was carried out and showed good agreement with the results obtained from CFD analysis.

• The Journal of the Korea Contents Association
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• v.10 no.4
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• pp.186-197
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• 2010

The things that you cannot miss when reading Chekhov's plays are "pauses" and ellipses lining up in the middle of the lines. I think what meaning to amplify and how to express a great number of "pauses" and ellipses when one directs Chekhov's works may be a crucial element that makes his works more Chekhov-like. First, proper uses of "pauses" and ellipses may be helpful for determining the characteristics of the characters. So silence in Chekhov drama allows his plays considered relatively lacking actions to become totally different drama texts with musical dynamics, that is, functions as directive or acting material to be treated delicately.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.6
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• pp.11-20
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• 2007

This paper proposes a new efficient method to detect ellipses using a segment merging based Randomized Hough Transform. The key idea of the proposed method is to separate single line segments from an edge image, to estimate ellipses from any pair of the single line segments using Randomized Hough Transform (RHT), and to merge the ellipses. This algorithm is able to accuracy estimate the number of ellipses and largely improves the computational time by reducing iterations.

• Journal of Korea Water Resources Association
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• v.44 no.4
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• pp.327-338
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• 2011

This study examined the quantification problem of a storm shape using the concept of equivalent ellipses. The equivalent ellipses of a storm event were estimated at every time step with respect to the several thresholds of rainfall intensity, which was also examined in terms of their size and number. In addition, the average equivalent ellipse was decided, and the confidence intervals of major axis, minor axis, and rotational angle were calculated to evaluate if the average equivalent ellipse could be the representative one. As results, the following results could be derived. First of all, the number of equivalent ellipses and the size of equivalent ellipses increase as the threshold increase. Secondly, the appropriate ratio of major and minor axises of equivalent ellipse is 2 : 1. Finally, the average rotational angle estimated with respect to several threshold rainfall intensities were all found not to be statistically different from that of all representative rotational angles.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.10
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• pp.1508-1515
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• 2003

In this study, the image processing program for deducing parameters of the elliptic shape of the partially overlapped liquid droplets was developed using the randomized Hough transform and the parameter decomposition. The procedure for the shape detection consists of three steps. For the first step, the candidate centers of ellipses are determined by the geometric property of the ellipse. Next, the rest parameters are estimated by the randomized Hough transform. In the final step for the post-processing, optimally approximated parameters of ellipses are determined. The developed program was applied to the simulated overlapped ellipses, real overlapped droplets, and real spray droplets. The shape detection was very excellent unless there existed inherent problems in original images. Moreover, this method can be used as an effective separating method for the overlapped small particles.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.121-142
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• 2002

We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In [1] the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm if mainly based on the steepest descent procedure with the view of ensuring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1783-1788
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• 2003

In this study, the image processing program for deducing parameters of the elliptic shape of the partially overlapped liquid droplets was developed using the randomized Hough transform and the parameter decomposition. The procedure for the shape detection consists of three steps. For the first step, the candidate centers of ellipses are determined by the geometric property of the ellipse. Next, the rest parameters are estimated by the randomized Hough transform. In the final step for the post-processing, optimally approximated parameters of ellipses are determined. The developed program was applied to the simulated overlapped ellipses, real overlapped droplets, and real spray droplets. The shape detection was very excellent unless there existed inherent problems in original images. Moreover, this method can be used as an effective separating method for the overlapped small particles.