• Journal of the Korean Society of Manufacturing Process Engineers
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• v.7 no.3
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• pp.81-86
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• 2008

I present a 3-D profiler specially devised for the profile measurement of specular surfaces that requires precision shape accuracy up to a few nanometer. A profile is reconstructed from the curvature of a test part of the surface at several locations along a line. The local curvature data are acquired with White-light Scanning Interferometry. Test measurement proves that the proposed profiler is well suited for the specular surface inspection like precision mirror.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.151-167
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• 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 $L^3$.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.4
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• pp.455-461
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• 2010

Automated magnetic abrasive polishing which can be applied after machining of the mold on a machine tool without unloading is very effective for finishing a complicated injection mold surface. This study aims to realize one step polishing of free form surface with the same machine tool. For this purpose, magnetic flux density according to the change of curvature radii was simulated for selecting polishing conditions and experimental verification was performed with a complicated mold of aluminum alloy. As a result, it was seen by the simulation that the magnetic flux density at a gradual curvature of the mold was higher than at a steep curvature and the higher magnetic flux density produced the better surface roughness in the experimentation. The deviation for the surface roughness of the mold decreased on the whole and the uniform mold surface was obtained after the automated magnetic abrasive polishing.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.5
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• pp.691-699
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• 1997

The effects of concave hemispherical surface curvature on the local heat transfer from a turbulent round impinging jet were experimentally investigated. The liquid crystal transient method was used for these measurements. This method, which is a variation on the transient method, suddenly exposes a preheated wall to an impinging jet while video recording the response of liquid crystals for the measurement of the surface temperature. The Reynolds number ranges from Re=11,000 to 50,000, the nozzle-to- surface distance from L/d=2 to 10, and the surface curvature from D/d=6 to 12.The present results are also compared to those for the flat plate case. In the experiment, the local Nusselt numbers tend to increase in all regions with an increasing surface curvature. The maximum Nusselt number for all Reynolds numbers occurred at L/d .ident. 6 and a second maximum in the Nusselt number occurred at R/d .ident. 2 for both Re=23,000 and Re=50,000 in the case of L/d=2 and for Re=50,000 only in the case of L/d=4. Meanwhile, as the surface curvature increases, the value of the secondary maximum Nusselt number decreases. All the other cases exhibit monotonically decreasing values of the Nusselt number along the curved surface. The stagnation point Nusselt numbers are well correlated with Re, L/d, and D/d.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.677-683
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• 2008

On a compact n-dimensional manifold M, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of volume 1, should be Einstein. The purpose of the present paper is to prove that a 3-dimensional manifold (M,g) is isometric to a standard sphere if ker $s^*_g{{\neq}}0$ and there is a lower Ricci curvature bound. We also study the structure of a compact oriented stable minimal surface in M.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.159-162
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• 2008

This paper presents a modified mean curvature diffusion filter to smooth speckle noise in images. Mean curvature diffusion filter has already shown good results in reducing noise in images while preserving fine details. In the mean curvature diffusion, the rate of smoothing is controlled by the local value of the diffusion coefficient chosen to be a function of the local image gradient magnitude. In this paper, the diffusion coefficient is modified to be controlled adaptively by local image surface slope and heterogeneity. The local surface slope contributes to preserving details (e.g.edges) in image and the local surface heterogeneity helps the smoothing filter consider the amount of noise in both edge and non-edge area. The proposed filter's performance is demonstrated by quantitative experiments using speckle noised aerial image and TerraSAR-X satellite image.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.401-419
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• 2024

Let K, H, K_II and H_II be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface T_γ(α) with the radius γ along a timelike curve α(s) in Minkowski 3-space E³₁. We prove that T_γ(α) must be a (K, H)-Weingarten surface and a (K, H)-linear Weingarten surface. We also show that T_γ(α) is (X, Y)-Weingarten type if and only if its central curve is a circle or a helix, where (X, Y) ∈ {(K, K_II), (K, H_II), (H, K_II), (H, H_II), (K_II , H_II)}. Furthermore, we prove that there exist no timelike tubular surfaces of (X, Y)-linear Weingarten type, (X, Y, Z)-linear Weingarten type and (K, H, K_II, H_II)-linear Weingarten type along a timelike curve in E³₁, where (X, Y, Z) ∈ {(K, H, K_II), (K, H, H_II), (K, K_II, H_II), (H, K_II, H_II)}.

• Journal of Korea Multimedia Society
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• v.6 no.6
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• pp.985-990
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• 2003

This paper presents the representation and its shape analysis of face by features based on surface curvature estimation and proposed rotation vector of the human face. Curvature-based surface features are well suited to use for experimenting the 3D human face segmentation. Human surfaces are exactly extracted and computed with parameters and rotated by using active surface mesh model. The estimated features were tested and segmented by reconstructing surfaces from the face surface and analytically computing Gaussian (K) and mean (H) curvatures without threshold.

• Journal of the Korean Society of Clothing and Textiles
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• v.33 no.1
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• pp.68-79
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• 2009

It is inevitable to have cutting line to get the 2D pattern from 3D body surface. In this paper the efficiency of curvature plot as a cutting line in the process of flattening 3D surface was investigated. As reference, basic clothing construction line was adopted to divide the 3D surface into small blocks to make the flattening process easy. Female dummy as well as human body were scanned and surface of the upper body was segmented using curvature plot and basic constructing line. 2D tight-fit pattern was developed using three software, the RapidForm 2004, 2C-AN and Yuka CAD. Gap between clothes and body, and the clothing pressure on the body was observed to determine the fit of the clothes. As results, clothes constructed with blocks divided by curvature plot displayed a similar level of tight fit as compared with those by basic construction line. It was found that curvature plot is effective method as a segmentation of the 3D surface even for the actual body which does not have any previous reference line. It is expected that application of curvature plot will be expanded in 3D apparel technology.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.4
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• pp.39-47
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• 2004

In mold machining, there are many concave machining regions where chatter and tool deflection occur since MRR(material removal rate) increases as curvature increases even though cutting speed and depth of cut are constant. Boolean operation between stock and tool model is widely used to compute MRR in NC milling simulation. In finish cutting, the side step is reduced to about 0.3mm and tool path length is sometimes over loom, so Boolean operation takes long computation time and includes much error if the resolution of stock and tool model is larger than the side step. In this paper, curvature of CL (cutter location) surface and side step of tool path is used to compute the feedrate for constant MRR machining. The data structure of CL surface is Z-map generated from NC tool path. The algorithm to get local curvature from discrete data was developed and applied to compute local curvature of CL surface. The side step of tool path was computed by point density map which includes cutter location point density at each grid element. The feedrate computed from curvature and side step is inserted to new tool path to regulate MRR. The resultants were applied to feedrate optimization system which generates new tool path with feedrate from NC codes for finish cutting. The system was applied to the machining of speaker and cellular phone mold. The finishing time was reduced to 12.6%, tool wear was reduced from 2mm to 1.1mm and chatter marks and over cut on corner were reduced, compared to the machining by constant feedrate. The machining time was shorter to 17% and surface quality and tool was also better than the conventional federate regulation using curvature of the tool path.