• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.151-161
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• 2016

In this paper, we present a $C^3$ quartic B-spline approximation of circular arcs. The Hausdorff distance between the $C^3$ quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the $C^3$ quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the $C^3$ quartic B-spline approximation of a circular arc is also presented.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.679-682
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• 1988

From the viewpoint of general recognition system, B-spline is introduced for the approximation and recognition of human profile contours. Profile contour is approximated to the cublic B-spline curve by least square fitting so that B-Spline nodes nearly correspond with the curvature extrema of the contour. This method is designed for the spline to be good features in recognition, and also showed good approximation compared with the variants of B-spline appraximation.

• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.157-169
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• 2006

We study properties concerning approximation of fuzzy-number-valued functions by fuzzy B-spline series. Error bounds in approximation by fuzzy B-spine series are obtained in terms of the modulus of continuity. Particularly simple error bounds are obtained for fuzzy splines of Schoenberg type. We compare fuzzy B-spline series with existing fuzzy concepts of splines.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.5
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• pp.653-659
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• 2011

In general, electrocardiogram(ECG) signals are sampled with a frequency over 200Hz and stored for a long time. It is required to compress data efficiently for storing and transmitting them. In this paper, a method for compression of ECG data is proposed, using by Non Uniform B-spline approximation, which has been widely used to approximation theory of applied mathematics and geometric modeling. ECG signals are compressed and reconstructed using B-spline basis function which curve has local controllability and control a shape and curve in part. The proposed method selected additional knot with each step for minimizing reconstruction error and reduced time complexity. It is established that the proposed method using B-spline approximation has good compression ratio and reconstruct besides preserving all feature point of ECG signals, through the experimental results from MIT-BIH Arrhythmia database.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.4
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• pp.118-125
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• 1998

This paper presents the hybrid curve approximation with geometric boundary conditions as position vector and tangent vector of start and end point using a B-spline approximation and a genetic algorithm First, H-spline approximation generates control points to fit B-spline curries through specified data points. Second, these control points are modified by genetic algorithm(with floating point representation) under geometric boundary conditions. This method would be able to execute the efficient design work without fairing.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.741-754
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• 2002

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater [1]. The error estimating function proposed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the midpoint.

• 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.