• Journal of the Korean Mathematical Society
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• v.57 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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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.

• Journal for History of Mathematics
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• v.34 no.3
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• pp.113-115
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• 2021

An elementary proof of the Catalan Theorem is given.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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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.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.1
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• pp.38-48
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• 2007

In this paper, we propose an image-based method for modeling 3D objects with curved surfaces based on the NURBS (Non-Uniform Rational B-Splines) representation. Starting from a few calibrated images, the user specifies the corresponding curves by means of an interactive user interface. Then, the 3D curves are reconstructed using stereo reconstruction. In order to fit the curves easily using the interactive user interface, NURBS curves and surfaces are employed. The proposed surface modeling techniques include surface building methods such as bilinear surfaces, ruled surfaces, generalized cylinders, and surfaces of revolution. In addition to these methods, we also propose various advanced surface modeling techniques, including skinned surfaces, swept surfaces, and boundary patches. Based on these surface modeling techniques, it is possible to build various types of 3D shape models with textured curved surfaces without much effort. Also, it is possible to reconstruct more realistic surfaces by using proposed view-dependent texture acquisition algorithm. Constructed 3D shape model with curves and curved surfaces can be exported in VRML format, making it possible to be used in different 3D graphics softwares.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.4
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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.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.6
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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.

• Journal of computational fluids engineering
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• v.18 no.4
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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.

• Korean Journal of Computational Design and Engineering
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• v.6 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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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 ${\mathbb{R}}^3$.