• Journal of the Korean Statistical Society
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• v.16 no.1
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• pp.45-51
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• 1987

The condition that two hyper-ellipsoids have no points in common is derived using the simultaneous diagonalization of the two hyper-ellipsoids. It is observed that the simultaneous diagonalization is composed of rotation and extension followed by another rotation. An approximation to this condition in terms of the generalized distance is discussed.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.285-295
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• 2000

It is well-known that there is no analogue to the Riemann mapping theorem in the higher dimensional case. Therefore, it would be an interesting question to find sufficient conditionsl for domains to be biholomorphically equivalent to the unit bal. In this paper, we investigate this questionin the case where the given domains are generalized complex ellipsoids with spherical boundary points.

• Journal of Korea Game Society
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• v.19 no.6
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• pp.99-106
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• 2019

This paper addresses a method to compute the closest approach distance between two ellipsoids in their inter-center direction. This is the key technique for collision detection and response between ellipsoids. We formulate a set of conditions with the inter-center distance, the contact point and the contact normal vector of the two externally-contacting ellipsoids. The equations are solved robustly and efficiently using a hybrid of Newton's method and the bisection method with root bracketing. We demonstrate the robustness and efficiency of the proposed method in various experiments.

• Journal of Korea Game Society
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• v.19 no.1
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• pp.5-14
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• 2019

This paper presents a practical method to compute the closest approach distance of two ellipsoids in their inter-center direction. This is the key technique for collision handling in the dynamic simulation of rigid and deformable bodies approximated with ellipsoids. We formulate a set of equations with the inter-center distance and the contact point and normal for the two ellipsoids contacting each other externally. The equations are solved using fixed-point iteration and Aitken's delta-squared process. In addition, we introduce a novel stopping criterion expressed in terms of the error in distance. We demonstrate the efficiency and practicality of our method in various experiments.

• ETRI Journal
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• v.36 no.3
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• pp.333-342
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• 2014

Most hyper-ellipsoidal clustering (HEC) approaches use the Mahalanobis distance as a distance metric. It has been proven that HEC, under this condition, cannot be realized since the cost function of partitional clustering is a constant. We demonstrate that HEC with a modified Gaussian kernel metric can be interpreted as a problem of finding condensed ellipsoidal clusters (with respect to the volumes and densities of the clusters) and propose a practical HEC algorithm that is able to efficiently handle clusters that are ellipsoidal in shape and that are of different size and density. We then try to refine the HEC algorithm by utilizing ellipsoids defined on the kernel feature space to deal with more complex-shaped clusters. The proposed methods lead to a significant improvement in the clustering results over K-means algorithm, fuzzy C-means algorithm, GMM-EM algorithm, and HEC algorithm based on minimum-volume ellipsoids using Mahalanobis distance.

• Journal of the Optical Society of Korea
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• v.20 no.2
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• pp.234-238
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• 2016

A new method to design a low distortion, even relative illumination, optical see-through head-mounted display (HMD) with a freeform reflective mirror (FFRM) based on the two similar ellipsoids structure is proposed. The HMD we have realized has a simple structure which consists of two similar ellipsoid surfaces, an FFRM, a 7-piece co-axis relay lens, and an OLED. This structure can be applied to offset distortion, reach even relative illumination, and correct the off-axis aberrations. The HMD we finally have realized has a near 3% low distortion, a higher than 80% relative illumination, and a 40°×30° field of view (FOV).

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.12 no.1
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• pp.69-76
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• 1994

In this paper, the characteristics of coordinate transformation between the WGS84 and the Bessel ellipsoids according to the assumed values of the geoidal height on Bessel ellipsoid at the geodetic datum origin of Korea were investigated. For this, based on GPS data of 11 control points in Chungnam and Chungbuk province, the mean shift values between ellipsoids were calculated in each case. The geoidal heights on the Bessel ellipsoid were modelled in the area and the coordinate transformation coefficients were derived, and then the accuracy of the transformed coordinates according to fluctuations in geoidal heights were studied.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.726-729
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• 1996

A weighted impact ellipsoid normalized by maximum allowable angular velocity changes is defined and compared with conventional impact ellipsoids and impact polytopes. The results shows that the conventional impact ellipsoid may give false solution as far as the optimal direction of motion is concerned.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1291-1308
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• 2016

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids {$z{\in}\mathbb{C}^3:{\mid}z_1{\mid}^p+{\mid}z_2{\mid}^q$ < 1, ${\mid}z_1{\mid}^p+{\mid}z_3{\mid}^r$ < 1}. We consider cases p = 6, q = r = 2 and p = q = r = 2. We also investigate the Lu Qi-Keng problem for p = q = r = 2.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.451-456
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• 2010

In this paper, we construct explicitly K$\ddot{a}$hler metrics on the ellipsoids and calculate their sectional curvatures. Using MAPLE [3], we obtain some geodesic curves on an ellipsoid so that if some conditions are dropped in Question 2.1 [4], then Question 2.1 is not true.