• Journal of Korean Institute of Industrial Engineers
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• v.19 no.2
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• pp.75-82
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• 1993

This paper deals with a systematic procedure for constructing a triangular composite surface which is interpolated from given scattered 3-D points. The procedure consists of a triangulation, construction of curve net, and interpolation of triangular patches. An obtained surface is composed of cubic triangular patches, which are $G^1$ continuous to adjacent other patches.

• 연구논문집
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• s.28
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• pp.123-135
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• 1998

A shape function for element free Galerkin method is carved from Shepard interpolant of singular weight and consistency condition. Thus present shape function is an interpolation and has no singularities. The shape function is applied to cantilever bending problems and gives good results in comparison with beam theory. Finally it is shown that the coupling with finite element method is made easily without any additional treaties.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.435-443
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• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.1-28
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• 2021

We study a continuous data assimilation algorithm for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field. Under suitable conditions on the relaxation (nudging) parameter and the spatial mesh resolution, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to zero.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.381-393
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• 2012

In this paper, we show two ways of the time reparametrization of piecewise Pythagorean-hodograph $C^1$ Hermite interpolants. One is the time reparametrization with no shape change, and the other is that with shape change. We show that the first reparametrization does not depend on the boundary data and that it is uniquely determined by the size of parameter domain, up to the general cases. We empirically show that the second parametrization can cause the change of the shape of interpolant.

• 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 applied mathematics & informatics
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• v.23 no.1_2
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• pp.73-86
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• 2007

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatial $C^1$ Hermite data, we construct a spatial PH curve on a sphere that is a $C^1$ Hermite interpolant of the given data as follows: First, we solve $C^1$ Hermite interpolation problem for the stereographically projected planar data of the given data in $\mathbb{R}^3$ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in $\mathbb{R}^3$ using the inverse general stereographic projection.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.4
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• pp.529-540
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• 1995

The paper deals with a procedure for constructing a composite surface interpolating a polygonal curve mesh defined from 3D scattered points. The procedure consists of a poly-angulation, construction of a curve net, and interpolation of the curve net. The poly-angulation contains a stage that changes a triangular edge net obtained from a triangulation into a poly-angular edge net. A curve net is constructed by replacing edges on the edge net with cubic Bezier curves. Finally, inside of an n-sided polygon is interpolated by n subdivided triangular subpatches. The method interpolates given point data with relatively few triangular subpatches. For an n-sided polygon, our method constructs an interpolant with n subdivided triangular subpatches while the existing triangular surface modeling needs 3(n-2) subpatches. The obtained surface is composed of quartic triangular patches which are $G^1$-continuous to adjacent patches.

• Journal of Korea Multimedia Society
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• v.11 no.6
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• pp.869-874
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• 2008

The work of creating character motion needs the higher professional technology and sense and the creating work of realistic and natural motion possess the most part of production term. In this paper we introduce the easy and convenient 3D animation authoring tool which makes the motion based on whole-body inverse kinematics and motion editing function. The proposed 3D animation authoring tool uses the forward kinematics using quaternion and whole-body inverse kinematics to determine the rotation and displacement of skeleton. Also, it provides the motion editing function using multi-level B-spline with quasi-interpolant. By using the proposed tool, we can make 3D animation easily and conveniently.

• The KIPS Transactions:PartA
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• v.13A no.3 s.100
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• pp.267-274
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• 2006

This paper describes a method to achieve different level of detail for the given volumetric data by assigning weight for the given data points. The relation between wavelet transformation and alpha shape was investigated to define the different level of resolution. Scattered data are defined as a collection of data that have little specified connectivity between data points. The quality of interpolant in volumetric trivariate space depends not only on the distribution of the data points in ${\Re}^3$, but also on the data value (intensity). We can improve the quality of an approximation by using wavelet coefficient as weight for the corresponding data points.