• Communications of Mathematical Education
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• v.24 no.3
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• pp.659-689
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• 2010

Taxicab distance function is a practical distance notion which gives us information of real world pathway distance that really taxi can go through. As one of the non-Euclidean geometry, this study of an ideal city with all roads running horizontal or vertical, was introduced by the Russian Mathematician H. Minkowski and synthetically reported by the E. F. Kraus in 1986. After that, there were many reports and papers on this topic and still being researched. At this point of view, our research about taxicab geometry provides its differences from Euclidean plane geometry, and considers about several theorems on plane geometry using the taxicab distance function.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.175-184
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• 2013

In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $\mathbb{R}^2$ are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.227-245
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• 2016

A generalized constant ratio surface (GCR surface) is defined by the property that the tangential component of the position vector is a principal direction at each point on the surface, see [8] for details. In this paper, by solving some differential equations, a complete classification of Lorentz GCR surfaces in the three-dimensional Minkowski space is presented. Moreover, it turns out that a flat Lorentz GCR surface is an open part of a cylinder, apart from a plane and a CMC Lorentz GCR surface is a surface of revolution.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.301-312
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• 2015

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb{E}^4_1$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.885-899
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• 2013

In this paper, we study null helices, null slant helices and Cartan slant helices in $\mathb{E}^3_1$. Using some associated curves, we characterize the null helices and the Cartan slant helices and construct them. Also, we study a space-like curve with the principal normal vector field which is a degenerate plane curve.

• Journal of the Korea Computer Graphics Society
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• v.11 no.2
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• pp.1-8
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• 2005

하나의 치아가 일부 파손되어 수복되어야 할 보철물을 인레이/온레이(Inlay/Onlay)라 한다. 본 논문에서는 3차원 메쉬 기반 모델에서 보다 정확한 인레이/온레이를 효과적으로 모델링하기 위한 기법을 제안한다. 인레이/온레이는 지대치와 접하는 내면과 밖으로 들어나는 외면으로 구성된다. 인레이/온레이의 내면 모델링은 2차원 다각선상의 Minkowski Sum 알고리즘을 이용하여 지대치와의 접합력을 확보한다. 그리고 미리 데이터베이스에 저장된 표준 치아 모델, 치과의사에 의해 만들어진 FGP(functionally guided plane) 및 메쉬의 변형 기법인 DMFFD(direct manipulation free-form deformation) 기법[16]과 MWD(multiple wires deformation) 기법[24]을 이용하여 외면을 모델링한다. 데이터베이스에 저장된 표준 치아는 인레이/온레이 외면의 형태를 결정하기 위해 사용되며, FGP는 환자의 인접면과 교합면의 특성을 반영하기 위해 사용되었다. 마지막으로 3차원 메쉬의 두 변형 기법인 DMFFD와 MWD 기법은 환자의 인접면과 교합면을 반영한 치아의 형태를 만들어 내기 위해 사용된다. 본 논문에서 제안한 방법은 인레이/온레이의 내면과 외면을 설계할 때 필요한 정보를 미리 설정하여 처리하므로 기존의 방법에 비해 짧은 시간에 보다 정확한 인레이/온레이를 설계할 수 있었다.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.4
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• pp.85-95
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• 1998

In this paper, a new watermarking method for a copy protectionof images is proposed. The proposed method adaptively embeds a watermark in the frequency domain of images using human visual system model. For this purpose, the Just Noticeable Differences(JNDs) of each frequency coeffeicient value of a luminance plane is first found using Watson and Solomon's visual system model. An invisible maximum watermark value with is different in every position according to the characteristics of images is determined usig JND and Minkowski metric. A low frequency domain is divided into two sets based on a PN-sequence to protect thewatermark from the attack. The watermarks are added to one set of coefficients and detecting a watermark, the difference between the mean values of absolute coefficient values of both sets is calculated. The embedded watermark is tested using statistical hypothesis based on test static dertermined by the ean difference. To demonstrate the perfromance of the proposed method, the new watermarking method is applied to a high frequency image and low frequency images. Experimenatal results show the watermark is invisible and robust to JPEGlossy compression and noise.

• The KIPS Transactions:PartA
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• v.12A no.6 s.96
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• pp.515-522
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• 2005

This paper presents a method for effectively modeling inlay/onlay prostheses restoring a tooth that are partially destroyed. An inlay/onlay is composed of internal surface adhering to an abutment, and external surface revealed to the outside sight. Internal surfaces are modeled using Minkowski sum expanding the grinded surface parts of abutments so that the internal surfaces can adhere to the abutments with closer contact. In modeling external surfaces, we exploit 3D mesh deformation techniques: DMFFD(direct manipulation free-form deformation)[19] and MWD(multiple wires deformation)[17] with three kinds of informations: standard teeth models, mesh data obtained by scanning a plaster cast of a patient's tooth, FGP(functionally guided plane) measuring the occlusion of the patients's teeth. The standard teeth models are used for building up the basic shapes of external surfaces, while the plaster fast and FGP data are used for reflecting the unique properties of adjacent md occlusal surfaces of the patients's teeth, which are slightly different to each other but very important for correct functioning. With these informations as input data, the adjacent and occlusal surfaces are automatically generated as mesh data using the techniques of DMFFD and m, respectively. Our method was implemented so that inlay/onlay prostheses fan be designed more accurately by visualizing the generated mesh models with requirements by dentists.

• Journal of the Korean Institute of Telematics and Electronics
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• v.7 no.3
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• pp.12-18
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• 1970

In this paper, the radiation characteristics of a Circular Loop Antenna is studied in a moving homogeneous, isotropic and linear media with a constant velocity much less than the speed of light. In Stuffing the radiation characteristics, Srst vector potential on the loop antenna is derived in the moving media by appling Maxwell-Minkowaski's theory. Next, using the derived relations, the electric and magnetic Seld is calculated for the spec-i Sed wave length ana velocity of the media. The Seld patterns in the moving media are compared with those of stationary media. We find that the intensity of the field is reduced in the direction of the media velocity and increased in the opposite direction only for the component parallel with the plane of the antenna. The deviation from the stationary media is proportional to the velocity of the media and the frequency of source current.

• Journal of the Korea Computer Graphics Society
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• v.17 no.3
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• pp.9-19
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• 2011

Computing triangle-triangle intersections has been a fundamental task required for many 3D geometric problems. We propose a novel robust GPU algorithm to efficiently compute intersections in a large triangle set. The algorithm has three stages:k-d tree construction, triangle pair generation, and exact intersection computation. All three stages are executed on GPU except, for unsafe triangle pairs. Unsafe triangle pairs are robustly handled by CLP(controlled linear perturbation) on a CPU thread. They are identified by floating-point filtering while exact intersection is computed on GPU. Many triangles crossing a split plane are duplicated in k-d tree construction, which form a lot of redundant triangle pairs later. To eliminate them efficiently, we use a split index which can determine redundancy of a pair by a simple bitwise operation. We applied the proposed algorithm to computing 3D Minkowski sum boundaries to verify its efficiency and robustness.