• 대한수학회지
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• 제57권4호
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• pp.957-971
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• 2020

In this paper, we introduce a new method to construct a parametric surface in terms of curves and points lying on Euclidean 3-space, called a C⁰-Hermite surface interpolation. We also prove the existence of a C⁰-Hermite interpolation of isoparametric surfaces with the so-called marching scale functions, and give some examples. Finally, we construct ruled surfaces and surfaces foliated by a circle as an isoparametric surface.

• 대한수학회보
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• 제33권1호
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• pp.97-106
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• 1996

The study of surface in a Euclidean space whose Gauss map G satisfies the condition : \DeltaG = AG(*)$ for some matrix A was studied by C. Baikoussis, D. E. Blair, B. Y. Chen, F. Dillen, L. Verstraelen ([1]1, [2], [7]) and so on.

• 한국수학사학회지
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• 제34권3호
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• pp.113-115
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• 2021

An elementary proof of the Catalan Theorem is given.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 춘계학술대회 논문집
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• pp.683-691
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• 1997

This paper presents a new robot trajectory generation method based on the curvatre theory of ruled surfacees. robot trajectory is represented as a ruled surface generated by the TCP (Tool center point ) and any one unit vector among the tool frame (usually denoted O, A,N). The curvature theory of ruled surfaces provides the robot control algorithm with the motion property oarameters. The proposed method eliminates the necessity of approximation technic of either joint or cartesian interpolation. This technic may give new methodology of precision robot control. Especially this is very efficient when the robot traces an analytical or form surface if the surface is geometrically modelled.

• 한국정보과학회논문지:시스템및이론
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• 제34권1호
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• pp.38-48
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• 2007

본 논문에서는 NURBS(Non-Uniform Rational B-Splines)로 표현된 3차원 곡면을 복원하기 위한 영상 기반 곡면 모델링 기법을 제안한다. 카메라 보정이 수행된 복수의 영상으로부터 사용자가 대응곡선을 지정하면 카메라의 정보를 이용하여 대응 곡선의 3차원 복원을 수행한다. 사용자 인터페이스에 의해 각 영상에서 곡선을 지정하기 위하여 본 논문에서는 NURBS 곡선을 이용하였으며 bilinear surface, ruled surface, generalized cylinder, surface of revolution등의 기본 곡면뿐 아니라 skinned surface, swept surface, boundary patch등의 고급 곡면 생성을 지원하여 다양한 모양의 곡면 물체를 모델링 할 수 있다. 또한 영상을 기반으로 view-dependent 텍스처 생성방법을 지원하여 좀더 사실적인 곡면의 복원을 수행한다. 생성된 3차원 곡선 또는 곡면은 VRML과 같은 표준 형식으로 출력하여 재사용할 수 있다.

• 한국생산제조학회지
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• 제6권4호
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• pp.19-26
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• 1997

The manufacture of an impeller typically requires the 5-axis CNC machining, since the impeller is usually under working conditions such as high speed, high temperature, and high pressure. Thus, this study contributes to development of an exclusive CAM system for effective 5-axis CNC machining of a ruled surface type impeller. In this study, the sampled impeller is made of blades and a body and the blade consists of ruled surfaces between hub curve and shroud curve. In the post processing for 5-axis NC part program, the cutter axis direction vector is the straighten vector on ruled surface. The position of ball center in ball end mill cutter is decided on the interference check between the cutter and body surface of impeller using with the modified z-map method that z-axis is the same of cutter axis direction vector. The exclusive CAM system for an impeller developed in this study was very effective for designs and 50-axis machining of a ruled surface type impeller.

• 한국공작기계학회논문집
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• 제10권6호
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• pp.71-77
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• 2001

We have developed the exclusive CAD/CAM system for the machining of impeller blades. This study is about the mod-eling method for the effective machining of impeller blades farmed by ruled surface. As the impeller is consisted of boss part and blade part, the boss is modeled by rotational surface of hub curve on z-axis and the blade is described by ruled- surfaces between hub curve and shroud curve. This modeling process can be carried out on the software developed in this study. And, the developed software can describe the impeller as a solid model through interface with Solid-Works soul- ware. The developed software containing the interface method proposed in this study was very effective fur impeller modeling.

• 한국전산유체공학회지
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• 제18권4호
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• pp.1-8
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• 2013

The performance of small-size impellers with ruled surfaces was investigated for flank milling over a wide speed range, using computational fluid dynamics analyses and gas bench tests. An impeller with a ruled surface was designed, manufactured, and tested to evaluate the effects of blade loading, the backsweep angle, and the relative velocity distribution on the compressor performance. The simulations and tests were completed using the same compressor cover with identical inlet and outlet channels to accurately compare the performance of the abovementioned impeller with a commercial impeller containing sculptured blades. Both impellers have the same number of blades, number of splitters, and shroud meridional profiles. The backsweep angles of the blades on the ruled impeller were selected to work with the same pinched diffuser as for a sculptured impeller. The inlet-to-exit relative velocity diffusion ratio and the blade loading were provided to maximize the flow rate and to minimize the surge flow rate. The design flow rate, rpm, were selected same for both impellers. Test results showed that for the compressor stage with a ruled impeller, the efficiency was increased by 0.32% with an extended surge margin without a reduction in the pressure ratio as compared to the impeller with the sculptured design. It was concluded that an increased relative velocity diffusion coupled with a large backsweep angle was an effective way to improve the compressor stage efficiency. Additionally, an appropriate blade loading distribution was important for achieving a wide operating range and higher efficiency.

• 한국CDE학회논문집
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• 제6권2호
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• pp.89-100
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• 2001

Swept volume is the sweeping region of moving objects. It is used in various applications such as interference detection in assembly design, visualization of manipulator motions in robotics, simulation of the volume removal by a cutter in NC machining. The shape of swept volume is defined by the envelope, which is determined by the boundary of moving objects and its direction of motion. In order to implement the generation of swept volume, researchers have taken much effort to develop the techniques how to generate the envelope. However, their results are confined to envelope generated only in simple shape objects, such as polyhedra or quadric surfaces. This study provided the envelope generation algorithm of NURBS objects. Characteristic points were obtained by applying the geometric conditions of envelope to NURBS equations, and then characteristic curves were created by means of interpolating those points. Silhouette edges were determined in the following procedures. First, two adjacent surfaces which have the same edge were found from B-Rep data. Then, by taking the scalar product of velocity vector of a point on that edge with each normal vector on two surfaces, silhouette edges were discriminated. Finally, envelope was generated along moving direction in the form of ruled surfaces by using both the partial information between initial and final position of objects affecting envelope along with characteristic curves and silhouette edge. Since this developed algorithm can be applied not only to NURBS objects but also to their Boolean objects, it can be used effectively in various applications.

• 대한수학회보
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• 제46권1호
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• pp.35-43
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• 2009

We say that an isometric immersed hypersurface x : $M^n\;{\rightarrow}\;{\mathbb{R}}^{n+1}$ is of $L_k$-finite type ($L_k$-f.t.) if $x\;=\;{\sum}^p_{i=0}x_i$ for some positive integer p < $\infty$, $x_i$ : $M{\rightarrow}{\mathbb{R}}^{n+1}$ is smooth and $L_kx_i={\lambda}_ix_i$, ${\lambda}_i\;{\in}\;{\mathbb{R}}$, $0{\leq}i{\leq}p$, $L_kf=trP_k\;{\circ}\;{\nabla}^2f$ for $f\;{\in}\'C^{\infty}(M)$, where $P_k$ is the kth Newton transformation, ${\nabla}^2f$ is the Hessian of f, $L_kx\;=\;(L_kx^1,\;{\ldots},\;L_kx^{n+1})$, $x=(x^1,\;{\ldots},\;x^{n+1})$. In this article we study the following(hyper)surfaces in ${\mathbb{R}}^{n+1}$ from the view point of $L_1$-finiteness type: totally umbilic ones, generalized cylinders $S^m(r){\times}{\mathbb{R}}^{n-m}$, ruled surfaces in ${\mathbb{R}}^{n+1}$ and some revolution surfaces in ${\mathbb{R}}^3$.