• 호남수학학술지
• /
• 제36권1호
• /
• pp.113-129
• /
• 2014

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

• 호남수학학술지
• /
• 제38권3호
• /
• pp.467-477
• /
• 2016

In this paper, we study the timelike Bertrand curves in Minkowski 3-space. Since the principal normal vector of a timelike curve is spacelike, the Bertrand mate curve of this curve can be a timelike curve, a spacelike curve with spacelike principal normal or a Cartan null curve, respectively. Thus, by considering these three cases, we get the necessary and sufficient conditions for a timelike curve to be a Bertrand curve. Also we give the related examples.

• 대한수학회보
• /
• 제52권1호
• /
• pp.183-200
• /
• 2015

In this paper, we define the directional associated curve and the self-associated curve of a null curve in Minkowski 3-space. We study the properties and relations between the null curve, its directional associated curve and its self-associated curve. At the same time, by solving certain differential equations, we get the explicit representations of some null curves.

• 호남수학학술지
• /
• 제36권3호
• /
• pp.475-492
• /
• 2014

In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space $\mathbb{E}_1^3$ also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

• 대한수학회보
• /
• 제44권3호
• /
• pp.429-438
• /
• 2007

In this paper, we study the position vectors of a spacelike W-curve (or a helix), i.e., curve with constant curvatures, with spacelike, timelike and null principal normal in the Minkowski 3-space $\mathbb{E}_1^3$. We give some characterizations for spacelike W - curves whose image lies on the pseudohyperbolical space $\mathbb{H}_0^2$ and Lorentzian sphere $\mathbb{S}_1^2$ by using the positions vectors of the curve.

• 호남수학학술지
• /
• 제45권1호
• /
• pp.130-145
• /
• 2023

In this paper, we define some integral curves connected with a framed curve in Euclidean 3-space. These curves include framed generalized principal-direction curve, framed generalized binormal-direction curve, framed principal-donor curve and framed Darboux-direction curve. We obtain some relations between the framed curvatures of new defined framed curves and framed curvatures of given framed curve. By using the obtained relationships we give some characterizations for such curves. We also give methods for constructing framed helix and framed slant helix from planar curves.

• 한국항행학회논문지
• /
• 제13권6호
• /
• pp.984-990
• /
• 2009

하프토닝은 단색으로 다양한 계조의 색단계를 표현하는 방법으로 인쇄 매체와 같은 분야에서 제한된 색으로 다양한 톤을 표현할 수 있도록 해주는 매우 중요한 영상처리기법이다. 본 논문에서는 공간채움곡선 (Space-Filling Curve)에 의한 하프토닝 방법의 대안으로 미로 생성 알고리즘에 기반한 새로운 하프토닝 방법을 제안한다. 기존의 공간채움곡선에 의한 오류 확산방법은 규칙적인 스캔 패턴으로 인해 해프토닝의 결과에도 규칙적인 패턴이 발생한다. 이러한 부분을 개선하기 위해 공간채움곡선 대신 미로의 경로를 사용함으로써 규칙적인 패턴을 제거하였다.

• 대한수학회지
• /
• 제58권6호
• /
• pp.1485-1500
• /
• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• 호남수학학술지
• /
• 제44권3호
• /
• pp.391-401
• /
• 2022

In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.

• 디지털융복합연구
• /
• 제12권1호
• /
• pp.415-421
• /
• 2014

본 논문에서는 무작위 공간 채움 곡선을 스캐닝 경로로 사용하는 디지털 하프토닝 방법에 대한 문제점과 개선 방안에 관해 제시한다. 무작위 공간 채움 곡선은 공간 채움 곡선의 자기 유사성으로 인한 단점을 해소하기 위한 방법으로 제안되었다. 스캐닝 경로에 무작위성을 도입하여 일정한 밝기를 가진 영역에서 발생할 수 있는 규칙적인 패턴을 줄이기 위해 사용되었다. 그러나 무작위 공간 채움 곡선을 사용한 하프토닝에도 일부 영역에서 경로를 따라 밝기가 지나치게 밝아지는 결과를 보일 수 있는 문제점이 발생한다. 본 논문에서는 이러한 문제점의 원인을 제시하고 이를 해결할 수 있는 방법으로써 단일 화소로 제한된 확산 방식을 제시한다. 이러한 방식은 효과적으로 오차의 과다 누적을 막아주며 하프토닝에도 개선된 결과를 보여준다.