• East Asian mathematical journal
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• v.28 no.1
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• pp.13-23
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• 2012

In this paper, we present the geometric Hermite interpolation for planar Pythagorean-hodograph cubics for some general Hermite data.

• East Asian mathematical journal
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• v.29 no.1
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• pp.53-68
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• 2013

We solve the geometric Hermite interpolation problem with planar Pythagorean-hodograph cubics. For every Hermite data, we determine the exact number of the geometric Hermite interpolants and represent the interpolants explicitly. We also present a simple criterion for determining whether the interpolants have a loop or not.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.575-584
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• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.2
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• pp.59-70
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• 2024

In this paper we present the approximation method of the circular helix by G² cubic polynomial curves. The approximants are G¹ Hermite interpolation of the circular helix and their approximation order is four. We obtain numerical examples to illustrate the geometric continuity and the approximation order of the approximants. The method presented in this paper can be extended to approximating the elliptical helix. Using the property of affine transformation invariance we show that the approximant has G² continuity and the approximation order four. The numerical examples are also presented to illustrate our assertions.

• 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.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.4
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• pp.32-40
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• 1994

This paper describes a smooth surface interpolating method of ship hull using a three-dimensional currie net that comes from the mesh curve fairing process. Geometric continuity(($GC^1$) is preserved across the boundary curve between patches. The three-dimensional curve net can have nonrectangular topologies, such as triangular and pentagonal topology. Among the boundary curve interpolation methods, Hermite blended Coons patch, Convex combination, and Gregory patch interpolation method are used to generate the ship hull surface. To check the fairness of the surface, the numerical method of surface/surface intersection problem is adopted. An application to an actual ship hull is given as an example.

• 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 the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.21-30
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• 2004

This study deals with free vibrations of laminated composite structures with a channel section using finite element method. In this paper, the mixed finite element method using Lagrangian and Hermite interpolation functions is adopted and a high-order plate theory is used to analyze laminated composite non-prismatic folded plates with a channel section more accurately for free vibration. The theory accounts for parabolic distribution of the transverse shear stress and requires no shear correction factors supposed in the first-order plate theory. An 32×32 matrix is assembled to transform the system element matrices from the local to global coordinates using a coordinate transformation matrix, in which an eighth drilling degree of freedom (DOF) per node is appended to the existing 7-DOF system. The results in this study are compared with those of available literatures for the conventional and first-order plate theory. Sample studies are carried out for various layup configurations and length-thickness ratio, and geometric shapes of plates. The significance of the high-order plate theory in analyzing complex composite structures with a channel section is enunciated in this paper.