• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권4호
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• pp.409-416
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• 2015

In many practical applications, we face the problem of reconstruction of an unknown function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in $\mathbb{R}^2$. The traditional proofs supporting the argument are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.321-332
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• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.

• 지구물리
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• 제8권1호
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• pp.23-33
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• 2005

The digital surface model (DSM) is used for several purposes in photogrammetry, remote sensing and laser scanned data such as orthoimage production, contours erivation, extraction of height information. Creation of a surface model from point-clouds (3-D sparse points) that can be derived from stereo imagery and range data (e.g. laser scanned data) can be done with several mathematical interpolation models. In this paper, thin-plate-spline (TPS) is used for digital surface modeling. Determination of suitable weight is an important problem in thin-plate function for a surface. The Voronoi algorithm has been proposed as a method for determination of the weight in thin-plate-spline. In this paper, methods has been tested for different surfaces. The results show that thin-plate-spline can be independent of weight.

• Steel and Composite Structures
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• 제44권5호
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• Geomechanics and Engineering
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• 제2권2호
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• pp.141-156
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• 2010

In the framework of meshfree methods, a new methodology is developed based on radial point interpolation method (RPIM). This methodology is applied to a one-dimensional contaminant transport modelling in the saturated porous media. The one-dimensional form of advection-dispersion equation involving reactive contaminant is considered in the analysis. The Galerkin weak form of the governing equation is formulated using 1D meshfree shape functions constructed using thin plate spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Numerical examples representing various phenomena, which occur during migration of contaminants, are presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the analytical and finite element solutions. The proposed RPIM has generated results with no oscillations and they are insensitive to Peclet constraints. In order to test the practical applicability and performance of the RPIM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the RPIM and the field investigation data.

• 정보처리학회논문지D
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• 제11D권6호
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• pp.1259-1268
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• 2004

제한된 훈련장안에서 실전에 대비한 훈련이 되려면, 다양한 전투상황이 부여된 현실감 있는 모의훈련이 필수적이다. 본 논문에서는 현실감 있는 모의훈련을 위해 가상영상이 아닌 지상기반 CCD 카메라영상에 지정된 시나리오대로 가상표적을 전시하는 방법을 제안한다. 이를 위해 고해상도 GeoTIFF(Geographic Tag Image File Format) 위성 영상과 DTED(Digital Terrain Elevation Data)를 이용하여 현실감 있는 3차원 모델을 생성(운용자용)하고, 입력된 CCD 영상(운용자, 훈련자용)으로부터 도로를 추출하였다. 위성영상과 지상기반 센서영상은 관측위치, 분해능, 스케일 등에 많은 차이가 있어 특징기반 정합이 어렵다. 따라서 본 논문에서는 영상 워핑함수인 TPS(Thin-Plate Spline) 보간 함수를 일치하는 두개의 제어점 집합에 적용하여 3차원 모델에 표시된 이동경로를 따라 CCD 영상에서도 표적이 전시되는 이동 동기화 방법을 제안하였다. 실험환경은 Pentium4 1.8MHz(RAM 512M)의 PC 2대를 사용하였으며, 실험 영상은 대전지역의 위성영상과 CCD 영상을 이용, 제안한 알고리즘의 유효성을 입증하였다.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1087-1095
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• 2009

In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

• 한국항해항만학회지
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• 제46권6호
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• pp.471-482
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• 2022

본 연구는 심해공학수조의 파 생성 특성을 규명하고, 심해공학수조의 기하학적 특성을 반영한 조파기 전달함수의 근사모델을 개발하는 것을 목적으로 한다. 심해공학수조의 기하학적 특성을 반영한 효율적인 해석을 위해 2차원 주파수영역 경계요소법이 적용되었다. 개발된 수치해석법은 해석해와 비교하여 검증되었다. 다양한 주기와 이동식 바닥판의 위치 변화에 대한 조파기의 경계치 문제의 수치해석이 수행되었다. 수치결과를 통해 심해공학수조의 기하학적 특성이 조파기의 전달함수에 미치는 영향을 조사하였고, 이동식 바닥판의 위치를 변화시켜 파도 생성에 대한 깊이 효과를 확인하였다. 경계요소법의 다양한 결과를 효율적으로 활용하기 위해 박판 스플라인 보간 모델 기반의 조파기 근사모델을 개발하였다. 개발된 근사 모델의 타당성은 모델 테스트 결과 비교를 통해 확인하였다.