• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.93-100
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• 2001

The three dimensional(3D) reconstruction from two dimensional(2D) image data is using in many fields such as RPD(Rapid Product Development) and reverse engineering. In this paper, the main step of 3D reconstruction is comprised of two steps : image processing step and B-spline surface approximation step. In the image processing step, feature points of each cross-section are obtained by means of several image processing technologies. In the B-spline surface approximation step, using the data of feature points obtained in the image processing step, the control points of B-spline surface are obtained, which are used for IGES file of 3D CAD model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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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.

• 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.

• 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.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.473-478
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• 2002

Reverse Engineering is to find CAD model through measured data of a physical model which is not available in CAD model. The measured data are obtained from measuring with Coordinate Measuring Machine or Laser Scanner This paper introduces efficient methods of reconstruction through the application of the Reverse Engineering using Modified B-spline approximation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.171-179
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• 2013

In this paper we present a method of circular arc approximation by quartic B$\acute{e}$zier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvature-continuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.435-438
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• 1997

This paper presents the process generating a SAC(Sectional Area Cure) by using ASMOD(Adaptive Spline Modeling of Observation Data). That is, we define SACs of real ships as B-spline curves by a hybrid cure approximation(which is the combination method of a B-spline fitting method and a genetic algorithm) and accumulate a database of control points. Then we let ASMOD learn from the correlation principal dimensions with control points.

• Journal of Ocean Engineering and Technology
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• v.12 no.3 s.29
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• pp.96-102
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• 1998

This paper presents to create a SAC(Sectional Area Curve) using an ANFIS(Adaptive-Network-based Fuzzy Inference System). First, it defines SACs of parent ships by using a B-spline approximation and a genetic algorithm and accumulates a database about SAC's control points. Second, it learns an ANFIS from parent ship data, which are related with principal dimensions and SAC's control points. This process is to model an ANFIS for SAC inferreice. When an ANFIS modeling is completed, we can determine a SAC through an ANFIS inferring.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.683-686
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• 1988

In the recognition of similar patterns like profile contours of human faces, feature measure plays important role. We extracted effective and general feature by B-spline approximation. The nodes and vertices of the approximated curve are normalized and used as features. Since the features have both local property of curvature extrema and global property by B-spline approximation, they are superior to those of curvature extrema of the profile contour. For the image data of six sets of 56 persons, some of which are ill-made, averaged accuracy rate of 97.6 % is obtained in recognizing combinational 333 test samples.

• Journal of the Korea Computer Graphics Society
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• v.17 no.3
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• pp.33-42
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• 2011

We present a new technique for removing interior knots of parametric B-spline curves. An initial curve is constructed by continuous $L_{\infty}$ approximation proposed by Eck and Hadenfeld. We employ Hausdorff distance to measure the shape difference between the original curve and the initial one. The final curve is obtained by minimizing their Hausdorff distance. We demonstrate the effectiveness of our technique with experimental results on various types of planar and spatial curves.