• 한국항행학회논문지
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• 제13권1호
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• pp.142-150
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• 2009

컴퓨터 게임에서 사용하는 복잡한 3차원 캐릭터 모델을 단순한 모델로 만드는 것은 매우 중요하다. 제안 방법은 3차원 게임 캐릭터에서 특징선을 추출하여 모델을 단순화 시키는 새로운 방법에 대해 제안한다. 주어진 3차원 캐릭터 모델은 텍스처 정보를 포함하고 있다. 3차원 캐릭터 모델에서의 텍스처 및 곡률의 변동을 이용해서 2차원 맵인 모델특징맵(Model Feature Map)을 생성한다. 모델특징맵은 곡률 맵(curvature map)과 텍스처 맵(texture map)으로부터 생성되며, 본 맵을 통해 에지 추출 기법을 이용하여 특징선을 추출한다. 모델특징맵은 표준 영상처리툴을 이용해 쉽게 편집할 수 있다. 실험을 통하여 본 알고리즘의 효율성을 보여주며, 실험은 얼굴 캐릭터에 한정하지 않는다.

• 대한수학회지
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• 제61권5호
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• pp.923-951
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• 2024

We consider a vector bundle map F : E₁ → E₂ between Lie algebroids E₁ and E₂ over arbitrary bases M₁ and M₂. We associate to it different notions of curvature which we call A-curvature, Q-curvature, P-curvature, and S-curvature using the different characterizations of Lie algebroid structure, namely Lie algebroid, Q-manifold, Poisson and Schouten structures. We will see that these curvatures generalize the ordinary notion of curvature defined for a vector bundle, and we will prove that these curvatures are equivalent, in the sense that F is a morphism of Lie algebroids if and only if one (and hence all) of these curvatures is null. In particular we get as a corollary that F is a morphism of Lie algebroids if and only if the corresponding map is a morphism of Poisson manifolds (resp. Schouten supermanifolds).

• 대한수학회지
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• 제41권2호
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• pp.379-396
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• 2004

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1461-1466
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• 2010

aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K < 0 and (N, $\bar{b}$) is a complete Riemannian manifold with sectional curvature bounded above by a constant $\mu$ > 0. Let u : $M{\times}[0,\;{\infty}]{\rightarrow}B_{\tau}(p)$ is a heat equation for harmonic map. We estimate the energy density of u.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2007년도 춘계학술발표대회
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• pp.731-734
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• 2007

본 연구는 구조광 기반의 깊이 에지를 이용하여 조명의 변화와 복잡한 배경에 상관없이 손 제스처의 외곽선 영상을 안정적으로 획득하였고, 제스처 영상을 표현하기 위하여 Curvature Scale Space(CSS) map을 이용하였다. 기존의 CSS map은 외곽선 영상의 깊은 굴곡과 완만한 굴곡을 잘 구분하지 못하는 문제점이 있었으나, 본 연구에서는 이러한 문제점을 분석하고, 이를 개선하기 위해서 각도 좌표를 이용한 CSS map 생성 방법을 제안하였다. 실험을 통해서 제안한 방법이 기존의 CSS map보다 우수한 인식 성능이 있음을 보였다.

• 대한수학회논문집
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• 제38권4호
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• 대한수학회논문집
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• 제11권3호
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• pp.789-796
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• 1996

A complete open manifold with nonnegative curvature is diffeomorphic to the normal bundle of the soul, and the projection map is a Riemannian submersion. Under certain circumstances, we prove that a harmonic map from a compact manifold followed by the projection is again harmonic. Therefore we obtain a harmonic map onto the soul when there is a harmonic map into an open manifold.

• Journal of Multimedia Information System
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• 제4권4호
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• pp.249-254
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• 2017

Digital vector maps must be compressed effectively for transmission or storage in Web GIS (geographic information system) and mobile GIS applications. This paper presents a polyline compression method that consists of polyline feature-based hybrid simplification and second derivative-based data compression. Experimental results verify that our method has higher simplification and compression efficiency than conventional methods and produces good quality compressed maps.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권1호
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• pp.43-53
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• 2021

We study translation surfaces in the Euclidean 3-space ��3 and the Gauss map N with respect to the so-called Cheng-Yau operator ☐. As a result, we prove that the only translation surfaces with Gauss map N satisfying ☐N = AN for some 3 × 3 matrix A are the flat ones. We also show that the only translation surfaces with Gauss map N satisfying ☐N = AN for some nonzero 3 × 3 matrix A are the cylindrical surfaces.

• 대한수학회보
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• 제50권3호
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• pp.935-949
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• 2013

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.