• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.21-27
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• 1991

This paper outlines the method of formulating the bi-cubic B-spline surface of ship hull, employing the open uniform knot vector as well as the periodic uniform knot vector. An appropriate set of B-spline control vertices to generate the B-spline surface is determined by obtaining the pseudoinverse matrix of basis functions. The comparison between the given offsets and the resulting coordinates from the generated ship hull surface shows a good agreement. To check the fairness of the surface Gaussian curvature is calculated on many small subpatches and displayed on the black-and-white plot of the isoparametric net of the surface.

• Industrial Engineering and Management Systems
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• v.9 no.4
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• pp.323-338
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• 2010

In this paper, we introduce the implied volatility from Black-Scholes model and suggest a model for constructing implied volatility surfaces by using the two-dimensional cubic (bi-cubic) spline. In order to utilize a spline method, we acquire grid (knot) points. To this end, we first extract implied volatility curves weighted by trading contracts from market option data and calculate grid points from the extracted curves. At this time, we consider several conditions to avoid arbitrage opportunity. Then, we establish an implied volatility surface, making use of the two-dimensional cubic spline method with previously estimated grid points. The method is shown to satisfy several properties of the implied volatility surface (smile, skew, and flattening) as well as avoid the arbitrage opportunity caused by simple match with market data. To show the merits of our proposed method, we conduct simulations on market data of S&P500 index European options with reasonable and acceptable results.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.31-37
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• 1994

When a lot of input data are not distributed uniformly n a chord-span direction or when the given shape is complicated, it is very difficult to obtain an inverse matrix which represents the smooth Bi-cubic B-spline surface of the initial shape. To overcome this problem, we suggest image Surface Expansion Method(ISE Method) which is suggested for vertex creation of B-spline curves and surfaces. Its basic concept, convergency and verification are shown. Also B-spline curves and Surfaces represented by ISE Method were compared with those represented by the existing method which is based on the inverse matrix method, the pseudoinverse matrix method and the chord length approximation method for vertex yielding. Ship Hull Forms which have Knuckle, Bulbous Bow, Transom and Stern frame were represented by the ISE Method.

• Journal of Mechanical Science and Technology
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• v.14 no.5
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• pp.518-529
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• 2000

A detailed and thorough parametric study of digital image correlation method is presented. A theoretical background and development of the method were introduced and the effects of various parameters on the determination of displacement outputs from the raw original and deformed image information were examined. Use of the normalized correlation coefficient, the use of 20 to 40 pixels for a searching window side, 6 variables searching, bi-cubic spline sub pixel interpolations and the use of coarse-fine search are some of the key choices among the results of parametric studies. The displacement outputs can be further processed with two dimensional curve fitting for the data noise reduction as well as displacement gradient calculation.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.15-20
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• 1992

This paper outlines the methods of visualizing 3-dimensional free form surfaces employing the Painter's algorithm, especially for the ship hull forms which are defined as open uniform Bi-cubic B-spline surfaces. The computer graphic codes are developed for the transparent wire-frame, the hidden surface removal and the shading visualization techniques, The codes are applied to the ship hull 3-dimensional surface visualization and the color graphic figures are displayed. Also Gaussian curvature is displayed on the color plots of the isoparametric net of the ship hull surface.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.1-11
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• 1991

When a geometric modeling of a hull form for ship design and hull production is done, a hull fairing is a tedious process which wastes a lot of time, but it is unavoidable because hull consist of the sculptured surfaces. This paper presents the mathematical method of the direct fairing to overcome the tediousness of cross fairing. Bi-cubic B-spline surface description was adopted for the representation of the hull surface. The fairing process was executed by minimizing the strain energy in a shell plate. The color-encoded Gaussian curvature and strain energy were visualized on the screen to illustrate the fairness of the surface. The geometric information generated from the faired hull surface model was interfaced with the basic design calculation package and the hull production system.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.78-85
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• 1994

Impact forces are acting on the fore part of a body entering water and those are function o the shape of the fore part and entrance angle. In this paper, impact forces are computed for the flat faced body with arbitrary entrance angle The geometric characteristics of the wetted surface of the body are complicated. The surface is divided into several smooth parts and each of them is represented by a bi-cubic B-spline. The free surface condition, $\phi=0$, is applied at the undisturbed free surface and he boundary value problem is analized by using Green's function.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.4
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• pp.17-22
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• 1993

The intersection problem of three-dimensional free form surfaces can be solved by geometrical and numerical methods. Up to now, the subdivision technique, which is classified under the former, has been largely employed to find the cross section of ship hull form. In this paper, an algorithm is presented for intersecting ship hull form in high speed. The high speed calculation algorithm is based on simple numerical methods, such as the secant method, false position method and bisection method. The algorithm is directly applicable to depicting arbitrary ship cross sections, drawing ship lines and constructing the offset table.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.38-52
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• 1991

In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of $\phi$ and $\frac{\partial{\phi}}{\partial{n}}$ are assumed to be bilinear on the subdivided surface. The singular part proportional to $\frac{1}{R}$ are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

• Journal of the Korean earth science society
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• v.24 no.1
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• pp.7-21
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• 2003

The state-of-art third generation wave prediction model WAM was applied to the Korean seas for a winter monsoon period of January 1997. The wind field used in the present study is the global NSCAT-ERS/NCEP blended winds, which was further interpolated using a bi-cubic spline interpolator to fine grid limited area shallow water regime surrounding the Korean seas. To evaluate and investigate the accuracy of WAM, the hindcasted wave heights are compared with observed data from two shallow water buoys off Chil-Bal and Duk-Juk. A detailed study has been carried with the various meteorological parameters in observed buoy data and its inter-dependency on model computed wave fields was also investigated. The RMS error between the observation and model computed wave heights results to 0.489 for Chil-Bal and 0.417 for Duk-Juk. A similar comparison between the observation and interpolated winds off Duk-Juk show RMS error of 2.28 which suggest a good estimate for wave modelling studies.