• 한국컴퓨터그래픽스학회논문지
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• 제4권2호
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• pp.69-75
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• 1998

선직면은 곡선을 따라 움직이는 직선들의 궤적으로 정의된다는 점에서 비교적 간편하게 곡면을 모델링하는데 사용될 수 있는 개념이다. 본 논문에서는 선직면의 특수한 경우인 전개가능 곡면의 오프셋이 다시 전개가능 곡면이 됨을 증명하였다. 뿐만 아니라 전개가능 곡면이 아닌 선직면의 오프셋은 절대 선직면이 될 수 없음을 증명하였다.

• 대한수학회보
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• 제52권4호
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• pp.1339-1351
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• 2015

In this paper, using pseudo-spherical Frenet frame of pseudo-spherical curves in hyperbolic space, we define the notion of the structure functions on the non-developable ruled surfaces with timelike ruling. Then we obtain the properties of the structure functions and a complete classification of the non-developable ruled surfaces with timelike ruling in Minkowski 3-space by the theories of the structure functions.

• 오토저널
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• 제7권3호
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• pp.42-55
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• 1985

The study is concerned with the investigation of curved line folding of developable surface from flat sheets of metal. General geometric relations among folding line, folded surface, folded angle are derived. From the derived geometric relations, the required plastic work and punch force are derived for the first approximation. Five methods of forming are suggested and the experiment is carried out using two chosen methods for the prismatic developable surfaces of which cross-sections have 103.deg.arc, 180.deg.arc, sinusoidal shape. In the die design for the tolding of prismatic developable surfaces, a stack of sheets were used to form shapes of the dies by which acceptable folded surfaces were obtained. The computed plastic work and punch force turned out to be in reasonable agreement with the experimental result.

• Journal of Computational Design and Engineering
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• 제3권2호
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• pp.102-111
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• 2016

In this paper, we study the problem of computing smooth feature curves from CAD type point clouds models. The proposed method reconstructs feature curves from the intersections of developable strip pairs which approximate the regions along both sides of the features. The generation of developable surfaces is based on a linear approximation of the given point cloud through a variational shape approximation approach. A line segment sequencing algorithm is proposed for collecting feature line segments into different feature sequences as well as sequential groups of data points. A developable surface approximation procedure is employed to refine incident approximation planes of data points into developable strips. Some experimental results are included to demonstrate the performance of the proposed method.

• 호남수학학술지
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• 제40권4호
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• pp.701-718
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• 2018

In this paper, we will study the constant mean curvature (CMC) surfaces foliated by ellipses in three dimensional Euclidean space $E^3$. We prove that: (1): Surfaces foliated by ellipses are CMC surfaces if and only if it is a part of generalized cylinder. (2): All surfaces foliated by ellipses are not minimal surfaces. (3): CMC surfaces foliated by ellipses are developable surfaces. (4): CMC surfaces foliated by ellipses are translation surfaces generated by a straight line and plane curve.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.509-531
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• 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
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• 제44권4호
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• pp.594-617
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• 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.

• 대한수학회보
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• 제56권4호
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• pp.867-883
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• 2019

The canal surfaces foliated by pseudo spheres $\mathbb{S}_1^2$ along a space curve in Minkowski 3-space are studied. The geometric properties of such surfaces are shown by classifying the linear Weingarten canal surfaces, the developable, minimal and umbilical canal surfaces are discussed at the same time.

• 호남수학학술지
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• 제28권4호
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• pp.549-558
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• 2006

In this paper, we classify non-developable ruled surfaces in a Euclidean 3-spaces satisfying some algebraic equations in terms of the second mean curvature, the mean curvature and the Gaussian curvature.

• 호남수학학술지
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• 제46권1호
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• pp.12-37
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• 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.