• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권3호
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1994년도 추계학술대회 논문집
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• pp.188-192
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• 1994

This paper presenta new method for tool interference acoidance using rectanguar approximation in NC machining of scuptured surface. The procedure of algorithm for approximation of sculptured surface to rectangular surface is described. Using this algorithm, we can check concave, convex, and side interference region and avoid these interferenes.

• 한국음향학회지
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• 제20권4호
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• pp.81-86
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• 2001

126-kHz양상태 해수면 음파산란 측정을 강원도 삼척시 연안에서 수행하였다. 수평입사각을38％, 52％로 고정시킨 상태에서 트랜스듀서와 청음기의 거리를 변화시키면서 산란각의 변화에 따른 전방산란 신호의 변화를 관찰하였다. 해저면 산란신호와는 달리 해수면 산란신호는 해수면 유동성에 의해서 도달시간 변이와 진폭의 변이를 나타내었으며 신호간의 상관관계도 불규칙적인 경향을 나타내었다. 전방산란강도를 계산하여 Kirchhoff approximation (KA)과 small slope approximation (SSA)을 비교한 결과 두 모델 모두 실측치와 잘 일치하였다.

• Journal of Mechanical Science and Technology
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• 제20권3호
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• pp.319-328
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• 2006

A simple approximation method for the stress intensity factor at the tip of the axial semielliptical cracks on the cylindrical vessel is developed. The approximation methods, incorporated in VINTIN (Vessel INTegrity analysis-INner flaws), utilizes the influence coefficients to calculate the stress intensity factor at the crack tip. This method has been compared with other solution methods including 3-D finite element analysis for internal pressure, cooldown, and pressurized thermal shock loading conditions. For these, 3-D finite-element analyses are performed to obtain the stress intensity factors for various surface cracks with t/R=0.1. The approximation solutions are within $\pm2.5%$ of the those of finite element analysis using symmetric model of one-forth of a vessel under pressure loading, and 1-3% higher under pressurized thermal shock condition. The analysis results confirm that the approximation method provides sufficiently accurate stress intensity factor values for the axial semi-elliptical flaws on the surface of the reactor pressure vessel.

• International Journal of CAD/CAM
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• 제13권1호
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• pp.1-11
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• 2013

Just by adjusting the control points iteratively, progressive iterative approximation (PIA) presents an intuitive and straightforward scheme such that the resulting limit curve (surface) can interpolate the original data points. In order to obtain more flexibility, adjusting only a subset of the control points, a new method called local progressive iterative approximation (LPIA) has also been proposed. But to this day, there are two problems about PIA and LPIA: (1) Only an approximation process is discussed, but the accurate convergence curves (surfaces) are not given. (2) In order to obtain an interpolating curve (surface) with high accuracy, recursion computations are needed time after time, which result in a large workload. To overcome these limitations, this paper gives an explicit matrix expression of the control points of the limit curve (surface) by the PIA or LPIA method, and proves that the column vector consisting of the control points of the PIA's limit curve (or surface) can be obtained by multiplying the column vector consisting of the original data points on the left by the inverse matrix of the collocation matrix (or the Kronecker product of the collocation matrices in two direction) of the blending basis at the parametric values chosen by the original data points. Analogously, the control points of the LPIA's limit curve (or surface) can also be calculated by one-step. Furthermore, the $G^1$ joining conditions between two adjacent limit curves obtained from two neighboring data points sets are derived. Finally, a simple LPIA method is given to make the given tangential conditions at the endpoints can be satisfied by the limit curve.

• 한국음향학회지
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• 제28권3호
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• pp.174-186
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• 2009

경계면이 존재하는 해양에서의 수중 음파 전달 모델링 시 일반적으로 평평한 경계면을 가정하고 Rayleigh가 제안했던 반사계수를 이용해 반사파를 계산할 수 있다. 하지만 해수면이나 해저면과 같은 실제 해양의 경계면은 불규칙적인 거칠기를 가진다. 이러한 경계면에서의 반사 손실은 실험식이나 산란 이론에 기반한 간섭 반사 계수를 계산하여 구할 수 있다. 본 논문에서는 섭동 이론, Kirchhoff 근사법, 작은 가지 근사법과 같은 산란 이론을 이용하여 유체-유체 경계면에 대한 간섭 반사 계수를 각각 유도한다. 이를 이용하여 임의의 거칠기를 가지는 해수면과 해저면에 대한 각 산란 이론의 간섭 반사계수를 계산하며, 이 결과를 Rayleigh 반사 계수와 비교하여 경계면의 거칠기에 따른 반사 손실을 분석한다. 또한, 섭동 이론과 Kirchhoff 근사법의 결과를 일반적으로 적용 범위가 넓은 작은 기울기 근사법의 결과와 비교하여 각 이론의 유효범위에 대해 고찰한다.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2006년도 International Symposium on GPS/GNSS Vol.2
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• pp.101-106
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• 2006

The geoidal undulations are needed for determining the orthometric heights from the Global Positioning System GPS-derived ellipsoidal heights. There are several methods for geoidal undulation determination. The paper presents a method employing a simple architecture Two Layer Multiquadric-Biharmonic Artificial Neural Network (TLMB-ANN) to approximate an area of 4200 square kilometres quasigeoid surface with GPS-levelling data. Hardy’s Multiquadric-Biharmonic functions is used as the hidden layer neurons’ activation function and Levenberg-Marquardt algorithm is used to train the artificial neural network. In numerical examples five surfaces were compared: the gravimetric geometry hybrid quasigeoid, Support Vector Machine (SVM) model, Hybrid Fuzzy Neural Network (HFNN) model, Traditional Three Layer Artificial Neural Network (ANN) with tanh activation function and TLMB-ANN surface approximation. The effectiveness of TLMB-ANN surface approximation depends on the number of control points. If the number of well-distributed control points is sufficiently large, the results are similar with those obtained by gravity and geometry hybrid method. Importantly, TLMB-ANN surface approximation model possesses good extrapolation performance with high precision.

• 한국정밀공학회지
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• 제16권5호통권98호
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• pp.160-168
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• 1999

This paper describes one method of reverse engineering that machines a free form shape without descriptive model. A portable five-axes 3D CMM was used to digitize point data from physical model. After approximation by rational B-spline curve from digitized point data of a geometric shape, a surface was constructed by the skinning method of the cross-sectional design technique. Since a surface patch was segmented by fifteen part, surface merging was also implemented to assure the surface boundary continuity. Finally, composite surface was transferred to commercial CAD/CAM system through IFES translation in order to machine the modeled geometric shape.

• Bulletin of the Korean Chemical Society
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• 제35권4호
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• pp.1061-1066
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• 2014

Time-dependent formulations of the reactive scattering theory based on the wavepacket correlation functions with the M${\phi}$ller wavepackets for the electronically nonadiabatic reactions are presented. The calculations of state-to-state reactive probabilities for the quasi-Jahn-Teller scattering model system were performed. The conical intersection (CI) effects are investigated by comparing the results of the two-surface nonadiabatic calculations and the single surface adiabatic approximation. It was found that the results of the two-surface nonadiabatic calculations show interesting features in the reaction probability due to the conical intersection. Single surface adiabatic calculations with extended Born-Oppenheimer approximation using simple wavepacket phase factor was found to be able to reproduce the CI effect semi-quantitatively, while the single surface calculations with the usual adiabatic approximation cannot describe the scattering process for the Jahn-Teller model correctly.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.81-98
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• 1999

In spite of the well developed theory and the practical use of the univariate B-spline, the theory of multivariate B-spline is very new and waits its practical use. We compare in this article the multivariate B-spline approximation with the polynomial approximation for the surface fitting. The graphical and numerical comparisons show that the multivariate B-spline approximation gives much better fitting than the polynomial one, especially for the surfaces which vary very rapidly.