• Journal of computational fluids engineering
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• v.3 no.2
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• pp.1-8
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• 1998

We make use of cubic B-spline interpolation function in two cases: heat conduction and fluid flow problems. Cubic B-spline test function is employed because it is superior to approximation of linear and non-linear problems. We investigated the accuracy of the numerical formulation and focused on the position of the breakpoints within the computational domain. When the domain is divided by partitions of equal space, the results show poor accuracy. For the case of a heat conduction problem this partition can not reflect the temperature gradient which is rapidly changed near the wall. To correct the problem, we have more grid points near the wall or the region which has a rapid change of variables. When we applied the unequally spaced breakpoints, the results show high accuracy. Based on the comparison of the linear problem, we extended to the highly non-linear fluid flow problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.99-106
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• 1999

In this paper, the spline hazard rate model to the randomly censored data is introduced. The unknown hazard rate function is expressed as a linear combination of B-splines which is constrained to be linear(or constant) in tails. We determine the coefficients of the linear combination by maximizing the likelihood function. The number of knots are determined by Bayesian Information Criterion. Examples using simulated data are used to illustrate the performance of this method under presenting the random censoring.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.211-229
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• 2011

In this paper, we present a new explicit procedure using periodic cubic B-spline interpolation polynomials to solve linear and nonlinear dynamic equation of motion governing single degree of freedom (SDOF) systems. In the proposed approach, a straightforward formulation was derived from the approximation of displacement with B-spline basis in a fluent manner. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. Actually, this method lies in the case of conditionally stable methods. A simple step-by-step algorithm is implemented and presented to calculate dynamic response of SDOF systems. The validity and effectiveness of the proposed method is demonstrated with four examples. The results were compared with those from the numerical methods such as Duhamel integration, Linear Acceleration and also Exact method. The comparison shows that the proposed method is a fast and simple procedure with trivial computational effort and acceptable accuracy exactly like the Linear Acceleration method. But its power point is that its time consumption is notably less than the Linear Acceleration method especially in the nonlinear analysis.

• Korean Journal of Computational Design and Engineering
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• v.5 no.3
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• pp.276-284
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• 2000

Usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in a power form is done by either a knot refinement followed by basis conversions or applying a Taylor expansion on the B-spline curve for each knot span. Presented in this paper is a new algorithm, called a direct expansion algorithm, for the problem. The algorithm first locates the coefficients of all the linear terms that make up the basis functions in a knot span, and then the algorithm directly obtains the power form representation of basis functions by expanding the summation of products of appropriate linear terms. Then, a polynomial segment of a knot span can be easily obtained by the summation of products of the basis functions within the knot span with corresponding control points. Repeating this operation for each knot span, all of the polynomials of the B-spline curve can be transformed into a power form. The algorithm has been applied to both static and dynamic curves. It turns out that the proposed algorithm outperforms the existing algorithms for the conversion for both types of curves. Especially, the proposed algorithm shows significantly fast performance for the dynamic curves.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.474-479
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• 2003

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional lofting approach creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion, and performs B-spline surface lofting to get a B-spline surface interpolating them. The approach tends to result in an astonishing number of control points in the resulting B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for avoiding this troublesome situation. The approach includes a novel process of getting a set of compatible B-spline curves from the given contours. The process is based on the universal parameterization [1,2] allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realize efficient data reduction and provide a compact representation of a B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.867-880
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• 1996

Numerical approximations to the linear elasticity are traditionally based on the finite element method. In this paper we propose a new formulation based on the cubic spline collocation method for linear elastic problem on the unit square. We present several numerical results for the eigenvalues of the matrix represented by cubic collocation method and preconditioner matrix which is preconditioned by FEM and FDM. Finally we present the numerical solution for some example equation.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.1-10
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• 2001

In the reverse engineering, surfaces are modeled for new products by interpolating the digitized data points obtained by measuring the existing shapes. However, many measuring or deviation errors are happened during the measuring process. If these errors are ignored, designers could get undesirable results. Therefore, it is important to handle such errors and fairing procedure with the esthetics criteria is needed during surface modeling process. This paper presents algorithms for the fairing of B-spline surfaces. The algorithms are based on automatic repositioning of control points for B-spline surfaces. New positions of the control points are determined by solving a non-linear programming of which the objective functions are derived variously using derived surfaces and constraints are established by distance measures between the original and the modified control points. Changes in surface shapes are analyzed by illustrations of their shapes and continuous plotting of gaussian and mean curvatures.

• Journal of Korea Multimedia Society
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• v.13 no.9
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• pp.1373-1381
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• 2010

Current flight maneuver diagram used by pilots is based on 2D spatial presentation, so it has limitation on display 3D flight information and hard to understand it instinctively. Flight animation authoring tools for this diagram are complex to use and lack useful features like non-linear editing of flight path and real-time interactivity on multiple aircrafts. This research focuses on 3D flight path generation method in the animation system for flight maneuver education. This research combines initial sketch input on 2D diagram with the thrust of an aircraft to generate 3D linear spline as close as to real flight. Using suggested linear spline creation method, the flight path can be visualized, edited, and animated in real-time at the flight maneuver briefing and debriefing.

• Proceedings of the Acoustical Society of Korea Conference
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• 1995.06a
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• pp.225-227
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• 1995

This paper compared waveform, cepstrum, and spline wavelet features with nonlinear discriminant analysis. This measure shows efficiency of speech parametrization better than old linear separability criteria and can be used to measure the efficiency of each layer of certain system. Spline wavelet transform has larger gap among classes and cepstrum is clustered better than the spline wavelet feature. Both features do not have good property for classification and we will compare Gabor wavelet transform, Mel cepstrum, delta cepstrum, etc.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.77-88
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• 1998

Smoothing spline estimators are modified to remove boundary bias effects using the technique proposed in Eubank and Speckman (1991). An O(n) algorithm is developed for the computation of the resulting estimator as well as associated generalized cross-validation criteria, etc. The asymptotic properties of the estimator are studied for the case of a linear smoothing spline and the upper bound for the average mean squared error of the estimator given in Eubank and Speckman (1991) is shown to be asymptotically sharp in this case.