• Structural Engineering and Mechanics
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• v.14 no.6
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.160-165
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• 2008

Kriging interpolation technique has been proposed by Danny Krige of South Africa to find the mineral distribution grade from information of geography and space. It is one of the generally used prediction technique for the mineral distribution grade and underground water level in wide scope also used in computer graphics fields by the ability for the surface regeneration This paper comprises two specific objectives. The first is to examine the applicability of Ordinary Kriging interpolation(OK) to finite element method that is based on variogram modeling in conjunction with different allowable limits of separation distance. The second is to investigate the accuracy according to theoretical variogram such as polynomial, Gauss, and spherical models.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.849-856
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• 2006

This paper is to examine the applicability of ordinary Kriging interpolation(OK) to the p-adaptivity of the finite element analysis that is based on variogram. In the p-refinement, the analytical domain has to be refined automatically to obtain an acceptable level of accuracy by increasing the p-level non-uniformly or selectively. In case of non-uniform p-distribution, the continuity between elements with different polynomial orders is achieved by assigning zero higher-order derivatives associated with the edge in common with the lower-order derivatives. It is demonstrated that the validity of the proposed approach by analyzing results for stress singularity problem.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.495-500
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• 2007

A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity. Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.75-82
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• 1997

An algorithm for computing the cubic spline interpolation coefficients for polynomials is presented in this paper. The matrix equation involved is solved analytically so that numerical inversion of the coefficient matrix is not required. For $f(t)=t^m$, a set of constants along with the degree of polynomial m are used to compute the coefficients so that they satisfy the interpolation constraints but not necessarily the derivative constraints. Then, another matrix equation is solved analytically to take care of the derivative constraints. The results are combined linearly to obtain the unique solution of the original matrix equation. This algorithm is tested and verified numerically for various examples.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.805-823
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• 2019

We introduce polynomial PH-MPH transitive mappings which transform planar PH curves to MPH curves in ${\mathbb{R}}^{2,1}$, and prove that parameterizations of Enneper surfaces of the 1st and the 2nd kind and conjugates of Enneper surfaces of the 2nd kind are PH-MPH transitive. We show how to solve $C^1$ Hermite interpolation problems in ${\mathbb{R}}^{2,1}$, for an admissible $C^1$ Hermite data-set, by using the parametrization of Enneper surfaces of the 1st kind. We also show that we can obtain interpolants for at least some inadmissible data-sets by using MPH biarcs on Enneper surfaces of the 1st kind.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1184-1193
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• 2006

Image interpolation has been widely used and studied in the various fields of image processing. There are many approaches of varying complexity and robustness. In this paper, a new distance weight is proposed for the conventional linear interpolation. In comparison with the conventional linear weight, the new distance weight uses a quadratic or cubic polynomial equation to reflect that the interpolated value should be influenced more by the value of closer pixels in an input image. In this paper, the new adaptive linear (NAL) interpolation, which considers patterns near the interpolated value, is also proposed. This algorithm requires a pattern weight, which is used to determine the ratio of reflection on local patterns, to obtain an interpolated image that exhibits better quality at various magnification factors (MF). In the computer simulation, not only did the NAL interpolation exhibit much lower computational complexity than conventional bicubic interpolation, it also improved peak signal-to-noise ratios (PSNR).

• Current Optics and Photonics
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• v.4 no.5
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• pp.411-420
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• 2020

Non-contact three-dimensional (3D) measuring technology is used to identify defects in miniature products, such as optics, polymers, and semiconductors. Hence, this technology has garnered significant attention in computer vision research. In this paper, we focus on shape from focus (SFF), which is an optical passive method for 3D shape recovery. In existing SFF techniques using interpolation, all datasets of the focus volume are approximated using one model. However, these methods cannot demonstrate how a predefined model fits all image points of an object. Moreover, it is not reasonable to explain various shapes of datasets using one model. Furthermore, if noise is present in the dataset, an error will be generated. Therefore, we propose an algorithm based on polynomial regression analysis to address these disadvantages. Our experimental results indicate that the proposed method is more accurate than existing methods.

• Journal of Information Processing Systems
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• v.10 no.3
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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 Korean Society for Geospatial Information Science
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• v.10 no.5 s.23
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• pp.75-80
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• 2002

Depending upon geographical features and surrounding errors in the survey field, inaccurate positioning is inevitable in a kinematic DGPs survey. Therefore, a data inaccuracy detection algorithm and an interpolation algorithm are essential to meet the requirement of a digital map. In this study, GPS characteristics are taken into account to develop the data inaccuracy detection algorithm. Then, the data interpolation algothim is obtained, based on the feature type of the survey. A digital map for 20km of a rural highway is produced by the kinematic DGPS survey and the features of interests are lines associated with the road. Since the vertical variation of GPS data is relatively higher, the trimmed mean of vertical variation is used as criteria of the inaccuracy detection. Four cases of 0.5%, 1%, 2.5% and 5% trimmings have been experimented. Criteria of four cases are 69cm, 65cm, 61cm and 42cm, respectively. For the feature of a curved line, cublic spine interpolation is used to correct the inaccurate data. When the feature is more or less a straight line, the interpolation has been done by a linear polynomial. Difference between the actual distance and the interpolated distance are few centimeters in RMS.