• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.957-960
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• 1995

A new method is introduced for the parametrization in B-spline surface interpolation. THis method uses the basis function to assign the parameter values to the arbitrary set of geometric data. This method gives us several important advantages in geometric modeling.

• Structural Engineering and Mechanics
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• v.18 no.2
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• pp.247-262
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• 2004

In the earlier application of the spline finite strip method(FSM), the uniform B3-spline functions were used in the longitudinal direction while the conventional interpolation functions were used in the transverse direction to construct the displacement filed in a strip. To overcome the shortcoming of the uniform B3-spline, non-periodic B-spline was developed as the displacement function. The use of non-periodic B3-spline function requires no tangential vectors at both ends to interpolate the geometry of shell and the Kronecker delta property is also satisfied at the end boundaries. Recently, non-periodic spline FSM which was modified to have a multiple knots at the boundary was developed for the shell analysis and applied to the analysis of bridges. In the formulation of a non-symmetric spline finite strip method, the concepts of non-periodic B3-spline and a stress-resultant finite strip with drilling degrees of freedom for a shell are used. The introduction of non-symmetrically spaced knots in the longitudinal direction allows the selective local refinement to improve the accuracy of solution at the connections or at the location of concentrated load. A number of numerical tests were performed to prove the accuracy and efficiency of the present study.

• 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.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.281-294
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• 2016

The paper is devoted to study a mesh-free analysis method of structural elements of engineering structures based on B-spline Wavelet Basis Function. First, by employing the moving-least square method and the weighted residual method to solve the structural displacement field, the control equations and the stiffness equations are obtained. And then constructs the displacement field of the structure by using the m-order B-spline wavelet basis function as a weight function. In the end, the paper selects the plane beam structure and the structure with opening hole to carry out numerical analysis of deformation and stress. The Finite Element Method calculation results are compared with the results of the method proposed, and the calculation results of the relative error norm is compared with Gauss weight function as weight function. Therefore, the clarification verified the validity and accuracy of the proposed method.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.671-690
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• 2004

An assumed strain finite strip method(FSM) using the non-periodic B-spline for a shell is presented. In the present method, the shape function based on the non-periodic B-splines satisfies the Kronecker delta properties at the boundaries and allows to introduce interior supports in much the same way as in a conventional finite element formulation. In the formulation for a shell, the geometry of the shell is defined by non-periodic B3-splines without any tangential vectors at the ends and the penalty function method is used to incorporate the drilling degrees of freedom. In this study, new assumed strain fields using the non-periodic B-spline function are proposed to overcome the locking problems. The strip formulated in this way does not posses any spurious zero energy modes. The versatility and accuracy of the new approach are demonstrated through a series of numerical examples.

• Journal of Computational Design and Engineering
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• v.2 no.1
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• pp.1-15
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• 2015

Measured bidirectional reflectance distribution function (BRDF) data have been used to represent complex interaction between lights and surface materials for photorealistic rendering. However, their massive size makes it hard to adopt them in practical rendering applications. In this paper, we propose an adaptive method for B-spline volume representation of measured BRDF data. It basically performs approximate B-spline volume lofting, which decomposes the problem into three sub-problems of multiple B-spline curve fitting along u-, v-, and w-parametric directions. Especially, it makes the efficient use of knots in the multiple B-spline curve fitting and thereby accomplishes adaptive knot placement along each parametric direction of a resulting B-spline volume. The proposed method is quite useful to realize efficient data reduction while smoothing out the noises and keeping the overall features of BRDF data well. By applying the B-spline volume models of real materials for rendering, we show that the B-spline volume models are effective in preserving the features of material appearance and are suitable for representing BRDF data.

• Journal of Broadcast Engineering
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• v.8 no.1
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• pp.37-44
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• 2003

The standard approach to signal resampling is to fit the original image to a continuous model and resample the function at a desired rate. We used the compact B-spline function as the continuous model which produces less oscillatory behavior than other tails functions. In the case of nonuniform resampling based on a B-spline model, the digital signal is fitted to a spline model, and then the fitted signal is resampled at a space varying rate determined by the transformation function. It is simple to implement but may suffer from artifacts due to data loss. The main purpose of this paper is the derivation of optimal nonuniform resampling algorithm. For the optimal nonuniform formulation, the resampled signal is represented by a combination of shift varying splines determined by the transformation function. This optimal nonuniform resampling algorithm can be verified from the experiments that It produces less errors.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.979-983
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• 2001

We develop a new method of simultaneous optimization of trajectory and shape of redundant flexible manipulators for collision-free utilizing the B-spline function and a mathematical programming method We adopt an approximate flexible manipulator model which consists of rigid bar elements and spring elements. We use B-spline function for determining the approximate trajectory and the expressions of the outline of obstacles. The used total performance index consists of 2 performance indices. The first is the driving energy, and the second is the trajectory deviation which is caused by the approximate modeling for the flexible manipulator. We design optimal collision-free trajectory of flexible manipulators by searching optimum positions of the control points for B-spline approximation which minimize the performance index subject to constraint condition for collision-free. Some examinations through numerical examples show the effectiveness of the method

• Structural Engineering and Mechanics
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• v.12 no.3
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• pp.313-328
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• 2001

A multi-span bridge has the peak value of resultant girder moment or membrane stress at the interior support. In this paper, the spline finite strip method (FSM) is modified to obtain the more appropriate solution at the interior support where the peak values of solution exist. The modification has been achieved by expressing the shape function with non-periodic B-splines which have multiple knots at the boundary. The modified B-splines have the useful feature for interpolating the curve with sudden change in curvature. Moreover, the modified spline FSM is very efficient in analyzing multi-span box girder bridges, since a bridge can be modeled by an assembly of strips extended along the entire bridge length. Numerical examples of the bridge analysis have been performed to verify the efficiency and accuracy of the new spline FSM.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.729-738
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• 2013

In this paper, we investigate a localized approximation of a continuously differentiable function by neural networks. To do this, we first approximate a continuously differentiable function by B-spline functions and then approximate B-spline functions by neural networks. Our proofs are constructive and we give numerical results to support our theory.