• 한국멀티미디어학회논문지
• /
• 제6권6호
• /
• pp.985-990
• /
• 2003

본 논문에서는 3차원 사람얼굴의 굴곡표면에 대하여 특징 값들을 추출하여 회전벡터를 이용하여 회전한 후 그들을 분석, 표현하는 방법을 제안한다. 또한 실험을 통하여 정확하게 추출된 굴곡표면의 특징 값들은 3차원 사람얼굴을 세그멘테이션 하는데 적용되었다 사람얼굴의 표면은 메쉬(mesh)모델을 사용하여 파라메타를 계산, 추출하였으며, 추출된 특징 값들은 얼굴표면을 Gaussian과 Mean 곡면 분류표(classification)를 사용하여 임계 값을 사용하지 않고 3D 얼굴표면을 세그멘테이션 하였다.

• Kyungpook Mathematical Journal
• /
• 제50권2호
• /
• pp.337-343
• /
• 2010

We study affine translation surfaces in $\mathbb{R}^3$ and get a complete classification of such surfaces with constant Gauss-Kronecker curvature.

• 대한수학회지
• /
• 제45권1호
• /
• pp.41-61
• /
• 2008

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

• Kyungpook Mathematical Journal
• /
• 제62권3호
• /
• pp.509-531
• /
• 2022

In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.

• 호남수학학술지
• /
• 제44권4호
• /
• pp.594-617
• /
• 2022

In this study, firstly Smarandache ruled surfaces whose base curves are Smarandache curves derived from Frenet vectors of the curve, and whose direction vectors are unit vectors plotting Smarandache curves, are created. Then, the Gaussian and mean curvatures of the obtained ruled surfaces are calculated separately, and the conditions to be developable or minimal for the surfaces are given. Finally, the examples are given for each surface and the graphs of these surfaces are drawn.

• 충청수학회지
• /
• 제27권3호
• /
• pp.403-404
• /
• 2014

• 호남수학학술지
• /
• 제46권1호
• /
• pp.12-37
• /
• 2024

The paper introduces a set of new ruled surfaces such that the base curve is taken to be the striction curve of N, C and W ruled surfaces from the alternative frame, and the generating line is taken to be one of the vectors of Sannia frame. The characterizations for each ruled surface such as fundamental forms, the Gaussian and mean curvature are also examined to provide the conditions for each surface to be developable or minimal.

• 한국수학사학회지
• /
• 제16권1호
• /
• pp.79-85
• /
• 2003

We define the second Gausssian curvature $K_{II}$ by using Brioschi's formula and shall disscuss the helicoidal surfaces satisfying $K_{II}$=Η.

• East Asian mathematical journal
• /
• 제21권1호
• /
• pp.113-122
• /
• 2005

Let $\mathbb{H}^3$ be the 3-dimensional Heisenberg group equipped with a left-invariant metric. In this paper, We characterize the Gaussian curvatures of the geodesic spheres on $\mathbb{H}^3$.

• 호남수학학술지
• /
• 제38권1호
• /
• pp.151-167
• /
• 2016

In Minkowskian 3-spacetime $L^3$ we find timelike or spacelike surface of revolution for the given Gauss curvature K = -1, 0, 1 and mean curvature H = 0. In fact, we set up the surface of revolution with the time axis for z-axis to be able to draw those surfaces on standard pictures in Minkowskian 3-spacetime $L^3$.