• Structural Engineering and Mechanics
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• 제11권2호
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• pp.221-236
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• 2001

A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids. A local weak form is developed using the weighted residual method locally in two-dimensional solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions possess the Kronecker delta function property, the essential boundary condition can be implemented with ease as in the conventional finite element method (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration. The implementation procedure is as simple as strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency of the present LPIM formulation are demonstrated through example problems. It is found that the present LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired accuracy in solids.

• Structural Engineering and Mechanics
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• 제14권6호
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• pp.713-732
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• 2002

A local radial point interpolation method (LRPIM) based on local residual formulation is presented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by the radial point interpolation method (PIM) and establishes discrete equations through a local residual formulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial function and background mesh for integration is not necessary. Radial PIM is used for interpolation so that singularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by a straightforward and effective manner due to its Delta properties. Moreover, the approximation quality of the radial PIM is evaluated by the surface fitting of given functions. Numerical performance for this LRPIM method is further studied through several numerical examples of solid mechanics.

• 한국지리정보학회지
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• 제13권3호
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• pp.29-41
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• 2010

본 연구는 미측정점의 값을 모델링하기 위해 사용되는 여러 가지 공간보간방법들의 예측오차를 비교하고 정확성을 검증하였다. 동해안 해안 지역의 표고점을 대상으로 역거리가중법, 크리깅, 지역 다항식보간법, 방사기반함수의 공간보간법과 관련된 매개변수들을 동일한 조건하에서 실행하여 평균제곱근을 산출한 결과, 단순 크리깅 방법의 원형 모델이 가장 작은 값으로 나타났다. 래스터의 연산 결과, 방사기반함수의 다중방정식에 의한 예측 지도가 대상 지역의 불규칙삼각망 표현과 일치정도가 높았다. 또한 공간보간 실행시 선택된 조건하에서 제공되는 최적 파워값을 사용하는 것이 양호한 보간 결과를 얻을 수 있다.

• 한국통신학회논문지
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• 제31권12C호
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• pp.1184-1193
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• 2006

영상 보간은 영상 처리 분야에서 전통적으로 많이 연구되어 왔고 널리 사용되고 있다. 그에 따라 다양한 보간 능력과 계산 복잡도를 갖는 보간법들이 많이 시도되고 있다. 이 논문에서는 기존의 선형 보간법을 위한 새로운 거리 가중치 개념과 보간되는 값의 상하, 좌우 지역적 패턴을 고려하여 반영하는 적응적 선형 보간법(New Adaptive Linear Interpolation : NAL Interpolation)을 제안한다. 새로운 거리 가중치는 기존의 거리에 선형적으로 비례하는 가중치의 개념에서 벗어나 가까운 화소에 더욱 더 영향을 많이 받는 특성을 이용하여 거리 가중치를 2차, 3차 다항식으로 개선한 것이다. 또한 NAL 보간법은 보간되는 화소의 상하, 좌우 패턴을 고려하는 선형 보간법으로 MF(magnification factor)의 변화에 따라 보다 선명한 이미지를 쉽게 얻기 위해서 보간하기 전 MF에 따라 패턴을 반영하는 정도를 결정하는 패턴 가중치를 이용한다. 실험 결과에서 제안된 보간법은 계산 복잡도 면에서 기존의 bicubic 보간법 보다 훨씬 간단할 뿐만 아니라 더 좋은 PSNR(peak signal-to-noise ratio)를 갖고 보다 선명한 화질의 영상으로 보간하였다.

• 한국측량학회지
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• 제15권2호
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• pp.165-173
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• 1997

동적 DGPS 측위에 의해 결정된 투영중심 좌표를 이용한 결합 번들블럭조정은 높은 정확도를 가지게 되었으며, 지상좌표 표준편차가 $\pm$10cm 이내로 결정될 수 있다. 이러한 정확도 수준에서는 더 작은 오차 성분이 중요하게 되었으며, 이 가운데 중요한 것은 GPS-Antenna 위치 사이에서 시간의 함수로 투영중심을 보간하는 것이다. 선형보간은 비행기의 비선형 움직움을 고려하지 않는 반면 최소제곱 다항식에 의한 보간은 비행기의 거동이 더 정확하게 고려되고, 위성의 상실과 신호차단 등에 의한 GPS위치의 과대오차를 소거하여 준다. 본 연구대상지 RHEINKAMP에서 3초의 시간을 이용한 보간은 MAA의 6-7초의 시간간격을 이용한 보간과는 다르며, 이러한 GPS위치는 국부회귀 다항식에 의하여 과대오차로 확인되었고, 이것은 정확한 블럭조정을 위해서는 무시할 수 없다.

• Journal of Information Processing Systems
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• 제10권3호
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• pp.395-411
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• 2014

Temporal medical data is often collected during patient treatments that require personal analysis. Each observation recorded in the temporal medical data is associated with measurements and time treatments. A major problem in the analysis of temporal medical data are the missing values that are caused, for example, by patients dropping out of a study before completion. Therefore, the imputation of missing data is an important step during pre-processing and can provide useful information before the data is mined. For each patient and each variable, this imputation replaces the missing data with a value drawn from an estimated distribution of that variable. In this paper, we propose a new method, called Newton's finite divided difference polynomial interpolation with condition order degree, for dealing with missing values in temporal medical data related to obesity. We compared the new imputation method with three existing subspace estimation techniques, including the k-nearest neighbor, local least squares, and natural cubic spline approaches. The performance of each approach was then evaluated by using the normalized root mean square error and the statistically significant test results. The experimental results have demonstrated that the proposed method provides the best fit with the smallest error and is more accurate than the other methods.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.713-719
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• 2011

The problem of approximation from a set of scattered data arises in a wide range of applied mathematics and scientific applications. In this study, we present a quasi-interpolatory approximation scheme for scattered data approximation problem, which reproduces a certain space of polynomials. The proposed scheme is local in the sense that for an evaluation point, the contribution of a data value to the approximating value is decreasing rapidly as the distance between two data points is increasing.

• 한국정밀공학회지
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• 제24권11호
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• pp.144-153
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• 2007

In order to generate the input data for rapid prototyping, a new approach which is based on the implicit surface interpolation method is presented. In the method a surface is reconstructed by creating smooth implicit surface from unorganized cloud of points through which the surface should pass. In the method an implicit surface is defined by the adaptive local shape functions including quadratic polynomial function, cubic polynomial function and RBF(Radial Basis Function). By the reconstruction of a surface, various types of error in raw STL file including degenerated triangles, undesirable holes with complex shapes and overlaps between triangles can be eliminated automatically. In order to get the slicing data for rapid prototyping an efficient intersection algorithm between implicit surface and plane is developed. For the direct usage for rapid prototyping, a robust transformation algorithm for the generation of complete STL data of solid type is also suggested.

• 대한기계학회논문집B
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• 제31권3호
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• pp.300-305
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• 2007

Many practical flow problems are defined with the circular boundary. Fluid flows within a circular boundary are however susceptible to a singularity problem when the cylindrical coordinates are employed. To remove this singularity a method has been developed in this study which uses the local harmonic functions in discretization of derivatives as well as interpolation. This paper describes the basic reason for introducing the harmonic functions and the overall numerical methods. The numerical methods are evaluated in terms of the accuracy and the stability. The Lamb-dipole flow is selected as a test flow. We will see that the harmonic-function method indeed gives more accurate solutions than the conventional methods in which the polynomial functions are utilized.

• International Journal of CAD/CAM
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• 제6권1호
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• pp.149-156
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• 2006

This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with $C^1$ continuity around a common corner vertex. A $C^1$ continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with $C^1$ continuity around a corner is then developed. Our approach is easy and fast with the virtue of cubic reproduction, local shape controllability, $C^2$ continuous at the corner vertex. Some experimental results are presented to show the applicability and flexibility of the approach.