• Journal of KIISE:Computer Systems and Theory
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• v.31 no.5_6
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• pp.288-296
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• 2004

This paper proposes a new mesh simplification algorithm using differential error metric. Many simplification algorithms make use of a distance error metric, but it is hard to measure an accurate geometric error for the high-curvature region even though it has a small distance error measured in distance error metric. This paper proposes a new differential error metric that results in unifying a distance metric and its first and second order differentials, which become tangent vector and curvature metric. Since discrete surfaces may be considered as piecewise linear approximation of unknown smooth surfaces, theses differentials can be estimated and we can construct new concept of differential error metric for discrete surfaces with them. For our simplification algorithm based on iterative edge collapses, this differential error metric can assign the new vertex position maintaining the geometry of an original appearance. In this paper, we clearly show that our simplified results have better quality and smaller geometry error than others.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.441-460
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• 2016

We introduce the notions of h-v-semi-slant submersions and almost h-v-semi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations, investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. We find a condition for such submersions to be totally geodesic. We also obtain an inequality of a h-v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and h-v-semi-slant angle. Finally, we give examples of such maps.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.547-552
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• 2003

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 300m. 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 wire applied to feedrate optimization system which generates new tool path with feedrate from NC codes for finish cutting. The system was applied to speaker mold machining. 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 removed.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1361-1371
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• 2017

In this paper, we introduce a framework of (${\alpha},{\beta}$)-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.

• Journal of Digital Convergence
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• v.11 no.8
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• pp.205-212
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• 2013

In this paper, we present a procedural modeling algorithms to create Korean traditional stone fence using the fractal subdivision. The main process of the algorithm is to get the next step mesh by subdividing each triangle in the previous step triangular mesh. This process is repeated recursively. Dividing each triangle into four sub-triangles after choosing a random point on each side of the triangle and moving each vertices in the normal direction with random perturbations make the bumpy appearance of stone fences. In each step we remove flat vertices which does not influence the shape of the stone. The discrete curvature determines the flatness of a vertex. New triangles whose vertices are the vertices around the removed vertex are added to make a triangular mesh.

• 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.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.1 no.1
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• Tribology and Lubricants
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• v.36 no.6
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• pp.359-364
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• 2020

Numerical investigation of the groove trap effect with variation in the groove-edge radius of curvature is presented here. The trap effect is evaluated in a two-dimensional sliding bearing using computational fluid dynamics (CFD). This simulation is based on the discrete phase model (DPM) and standard k - ε turbulence model using commercial CFD software, FLUENT. The numerical results are evaluated by comparisons with streamlines and particle trajectories in the grooves. Grooves are applied to various lubrication systems to improve their lubrication characteristics, such as load carrying capacity increment, leakage reduction, frictional loss reduction, and preventing three-body abrasive wear due to trapping effect. This study investigates the grove trapping effect for various groove-edge radius of curvature values and Reynolds numbers. The particle is assumed to be made of steel, with a circular shape, and is injected as a single particle in various positions. One-way coupling is used in the DPM model because the single particle injection condition is applied. Further, the "reflect" condition is applied to the wall boundary and "escape" condition is used for the "pressure inlet" and "pressure outlet" boundaries. From the numerical results, the groove edge radius is found to influence the groove trap effect. Moreover, the groove trap effect is more effective when applying the groove edge radius.

• Journal of the Korean Society for Railway
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• v.9 no.4 s.35
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• pp.467-472
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• 2006

This paper deals with the applicability of long-gauge deformation fiber optic sensors (FOS) to prestressed concrete structures. A main motivation is the desire to monitor the deflection of the railway bridges without intervenes of the signal intensity fluctuations. A 25 m long, 1.8 m deep PSC girder was fabricated compositely with 22 cm thick reinforced concrete deck. Two pairs of 3 m long-gauge sensors are attached to the prestressed concrete girder with parallel topology. Using the relationship between curvature and vortical deflection and the quadratic regression of curvatures at the discrete point, it is possible to extrapolate the deflection curve of the girder. The estimated deflection based on the developed method is compared with the results using conventional strain gauges and LVDTS. It has been demonstrated that the proposed instrumentation technique is capable of estimating the vertical deflection and neutral axis position of the prestressed concrete girder up to weak nonlinear region.

• Journal of the Semiconductor & Display Technology
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• v.6 no.3
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• pp.65-70
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• 2007

A method to focus the object in camera system by applying the Hill climb algorithm from optical lens moving device (VCM; Voice coil motor) is proposed. The focusing algorithm from VCM is focus on the object but in these criteria is a well-known drawback; the focus is good only at same distance objects but the focus is bad (blur image) at different distance objects because of the DOF (Depth of focus) or DOF (Depth of field) at the optical characteristic. Here, the new camera system that describes the Reflector of free curvature systems (or Diffractive Fresnel lens) and the partition of focusing window area is proposed. The method to improve the focus in all areas (different distance objects) is proposed by new optical system (discrete auto in-focus) using the Reflector of free curvature systems (or Diffractive Fresnel lens) and by applying the partition of all areas. The proposal is able to obtain good focus in all areas.