• Journal of Korean Institute of Industrial Engineers
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• v.20 no.1
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• pp.87-98
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• 1994

This paper describes a method of constructing VC2 Chord-length spline surface from semi-evenly spaced 3D point array. The suface uses Hermite interpolant as Ferguson surface, and it is an extention of chord-length spline curve to surface The proposed surface may be widely used in interpolating smoothly 3D point data obtaind by measurement or engineering design.

• 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.

• East Asian mathematical journal
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• v.13 no.1
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• pp.1-10
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• 1997

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.129-140
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• 1998

A numerical method is proposed to optimize automotive cam profiles. An acceleration curve of a cam follower motion is described by Hermite spline curves. Because of the intrinsic characteristics of the Hermite curve, it is possible to design an acceleration curve with arbitrary shape. Design variables in the optimization problem are location of control points which define the acceleration curve. Objective function includes dynamic performances as well as kinematic properties of a valve train. Similar optimization procedure was also performed using Polydyne cam profile synthesis method. Optimized profiles using the Hermite curve are proved to be superior to those using the Polydyne method.

• 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.

• Journal of Environmental Science International
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• v.11 no.9
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.331-347
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• 2002

We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

• 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.

• 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.

• Earthquakes and Structures
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• v.2 no.4
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• pp.323-336
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• 2011

The problem of reconstruction of complete building response from a limited number of response measurements is considered. The response at the intermediate degrees of freedom is reconstructed by using piecewise cubic Hermite polynomial interpolation in time domain. The piecewise cubic Hermite polynomial interpolation is preferred over the spline interpolation due to its trend preserving character. It has been shown that factorization of response data in variable separable form via singular value decomposition can be used to derive the complete set of normal modes of the structural system. The time domain principal components can be used to derive empirical transfer functions from which the natural frequencies of the structural system can be identified by peak-picking technique. A reduced-rank approximation for the system flexibility matrix can be readily constructed from the identified mass-orthonormal mode shapes and natural frequencies.