• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.4
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• pp.309-321
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• 1988

This paper proposes on the algorithm of axis equation & radius function for the G.C representation which describes the curved objects with circular cross section. Object combined with linear and nonlinear parts is detached by clustering from depth data & axis points is extracted by normal vecter of the surface mask patches. In ths case of nonlinear axis point, axis equation is described by Hermite curve & the effectiveness of this paper is demonstrated by serveral experiments.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.1
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• pp.92-98
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• 2014

This paper proposes a hermite spline based D* algorithm for effective path planning of mobile robot to improve the detecting speed. In conventional path planning research, a robot is supposed to pass through predetermined centers of grid partitions of area. However it doesn't guarantee the optimal path during its navigation. In addition, a robot is hard to avoid obstacles effectively. The proposed algorithm in this paper makes use of stochastic characteristics of nonholonomic mobile robot and estimation of shortest path to curvature movement of the robot. The performance evaluation of the improved spline D* algorithm performed through simulation shows its effectiveness. Moreover, the experiment verifies that a robot can find the shortest path by building the curve paths while it is moving on the path in spline.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.49 no.1
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• pp.16-22
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• 2012

In this paper, we proposed a method of baseline correction for analysis of Raman spectra of platelets from Alzheimer's disease (AD) transgenic mice. Measured Raman spectra include the meaningful information and unnecessary noise which is composed of baseline and additive noise. The Raman spectrum is divided into the local region including several peaks and the spectrum of the region is modeled by curve fitting using Gaussian model. The additive noise is clearly removed from the process of replacing the original spectrum with the fitted model. The baseline correction after interpolating the local minima of the fitted model with linear, piecewise cubic Hermite and cubic spline algorithm. The baseline corrected models extract the feature with principal component analysis (PCA). The classification result of support vector machine (SVM) and maximum $a$ posteriori probability (MAP) using linear interpolation method showed the good performance about overall number of principal components, especially SVM gave the best performance which is about 97.3% true classification average rate in case of piecewise cubic Hermite algorithm and 5 principal components. In addition, it confirmed that the proposed baseline correction method compared with the previous research result could be effectively applied in the analysis of the Raman spectra of platelet.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.4
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• pp.1005-1012
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• 1995

This paper proposes a new approach for modeling sweep surfaces. The overall modeling procedure consists of following steps : (1)remeshing the section curves based on the curve lengths ; (2)remeshing the guide curve and the boundary curves based on a given sweeping rule ; (3)obtaining intermediate section curves at the remeshed points of the guide curve by blending the initial section curves ; (4)compensation of the intermediate section curves ; (5)interpolating the initial and intermediate curves using Hermite interpolant. The resulting sweep surface is expressed in a G$^{2}$ bicubic parametric spline surface.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.55-60
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• 2010

Quadratic B$\acute{e}$zier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic B$\acute{e}$zier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing $G^1$ quadratic B$\acute{e}$zier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the $G^1$ quadratic B$\acute{e}$zier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.

• Proceedings of the Korean Society of Computer Information Conference
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• 2022.07a
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• pp.113-114
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• 2022

가상의 공간에 실제의 설비를 구현하는 시뮬레이션 기술은 스마트팩토리를 구성하는 필수 요소 중의 하나이다. 다만, 현업의 제조 설비 도면을 시뮬레이션 소프트웨어에 적용하는데 있어 자유 곡선을 가지는 공압 배관 등의 모델 데이터는 작업의 난해함 등의 이유로 기 설계 도면에 누락되어 있는 경우가 빈번하다. 본 연구에서는 시뮬레이션 툴 중에 하나인 유니티를 이용하여 내부에서 직접 스윕 곡선을 생성하는 과정을 구현하였다. 이를 통해 기 설계 데이터에 누락된 다양한 자유 곡선 모델을 신속하게 시뮬레이션에 적용하는데 효과가 있을 것으로 기대된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.22-32
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• 2024

In this paper we present a method of conic section approximation by hexic Bézier curves. The hexic Bézier approximants are G³ Hermite interpolations of conic sections. We show that there exists at least one hexic Bézier approximant for each weight of the conic section The hexic Bézier approximant depends one parameter and it can be obtained by solving a quartic polynomial, which is solvable algebraically. We present the explicit upper bound of the Hausdorff distance between the conic section and the hexic Bézier approximant. We also prove that our approximation method has the maximal order of approximation. The numerical examples for conic section approximation by hexic Bézier curves are given and illustrate our assertions.

• Journal of Navigation and Port Research
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• v.26 no.4
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• pp.473-479
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• 2002

The estimation of the volume of a pit excavation is often required in many surveying, soil mechanics, highway applications and transportation engineering situations. The calculation of earthwork plays a major role in plan or design of many civil engineering projects such as seashore reclamation, and thus it has become very important to improve the accuracy of earthwork calculation. In this paper the spot height method, proposed formulas(A, B, C), and chen and Line method are compared with the volumes of the pits in these examples. And we proposed an algorithm of finding a terrain surface with the free boundary conditions and both direction spline method drawback, i.e., the modeling curves form peak points at the joints. To avoid this drawback, the cubic spline polynomial was chosen as the methematical model of the new method. From the characteristics of the cubic spline polynomial, the modeling curve of the new method was smooth and matched the ground profile well. As a result of this study, algorithm of proposed three methods to estimate pit excavation volume provided a better accuracy than spot height, chamber, chen and Lin method. And the mathematical model mentioned makes is thought to give a maximum acccuracy in estimating the volume of a pit excavation.