• Title/Summary/Keyword: Local Polynomial Interpolation

Search Result 11, Processing Time 0.018 seconds

A local point interpolation method for stress analysis of two-dimensional solids

  • Liu, G.R.;Gu, Y.T.
    • Structural Engineering and Mechanics
    • /
    • v.11 no.2
    • /
    • pp.221-236
    • /
    • 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.

Point interpolation method based on local residual formulation using radial basis functions

  • Liu, G.R.;Yan, L.;Wang, J.G.;Gu, Y.T.
    • Structural Engineering and Mechanics
    • /
    • v.14 no.6
    • /
    • pp.713-732
    • /
    • 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.

Comparison and Evaluation of Root Mean Square for Parameter Settings of Spatial Interpolation Method (공간보간법의 매개변수 설정에 따른 평균제곱근 비교 및 평가)

  • Lee, Hyung-Seok
    • Journal of the Korean Association of Geographic Information Studies
    • /
    • v.13 no.3
    • /
    • pp.29-41
    • /
    • 2010
  • In this study, the prediction errors of various spatial interpolation methods used to model values at unmeasured locations was compared and the accuracy of these predictions was evaluated. The root mean square (RMS) was calculated by processing different parameters associated with spatial interpolation by using techniques such as inverse distance weighting, kriging, local polynomial interpolation and radial basis function to known elevation data of the east coastal area under the same condition. As a result, a circular model of simple kriging reached the smallest RMS value. Prediction map using the multiquadric method of a radial basis function was coincident with the spatial distribution obtained by constructing a triangulated irregular network of the study area through the raster mathematics. In addition, better interpolation results can be obtained by setting the optimal power value provided under the selected condition.

Adaptive Linear Interpolation Using the New Distance Weight and Local Patterns (새로운 거리 가중치와 지역적 패턴을 고려한 적응적 선형보간법)

  • Kim, Tae-Yang;Jeon, Yeong-Gyun;Jeong, Je-Chang
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.31 no.12C
    • /
    • pp.1184-1193
    • /
    • 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).

Correction of Antenna Position for Projection Center Coordinates by Kinematic DGPS-Positioning (동적 DGPS 측위에 의한 투영중심좌표 결정을 위한 수신기 위치의 보간)

  • 이종출;문두열;신상철
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
    • /
    • v.15 no.2
    • /
    • pp.165-173
    • /
    • 1997
  • The combined bundle block adjustment with projection center coordinates determined by kinematic DGPS-positioning has reached a high level of accuracy. Standard deviations of the ground coordinates of $\pm{10cm}$ or even better can be reached. On this accuracy level also smaller error components are becoming more important. One major point of this is the interpolation of the projection centers as a function of time between the GPS-antenna locations. A just linear interpolation is not respecting the not linear movement of the aircraft. Based on a least squares polynomial fitting the aircraft maneuver can be estimated more accurate and blunders of the GPS-positions caused by loss of satellite and cycle slips are determinable. The interpolation with a time interval of 3sec in the study area RHEINKAMP is quite different to the interpolation with a time interval of 6-7sec in the study area MAAS. The GPS-positions of the study area are identified as blunders based on a local polynomial regression. This cannot be neglected for precise block adjustment.

  • PDF

Imputation of Medical Data Using Subspace Condition Order Degree Polynomials

  • Silachan, Klaokanlaya;Tantatsanawong, Panjai
    • Journal of Information Processing Systems
    • /
    • v.10 no.3
    • /
    • pp.395-411
    • /
    • 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.

QUASI-INTERPOLATORY APPROXIMATION SCHEME FOR MULTIVARIATE SCATTERED DATA

  • Yoon, Jung-Ho
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.3_4
    • /
    • pp.713-719
    • /
    • 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.

Automatic Generation of the Input Data for Rapid Prototyping from Unorganized Point Cloud Data (임의의 점 군 데이터로부터 쾌속조형을 위한 입력데이터의 자동생성)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.24 no.11
    • /
    • pp.144-153
    • /
    • 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.

Method of Numerical Simulation by Using the Local Harmonic Functions in the Cylindrical Coordinates (국소적 조화함수를 사용한 원통좌표계에서의 유동 해석)

  • Suh, Yong-Kweon
    • Transactions of the Korean Society of Mechanical Engineers B
    • /
    • v.31 no.3 s.258
    • /
    • pp.300-305
    • /
    • 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.

Construction of Cubic Triangular Patches with $C^1$ Continuity around a Corner

  • Zhang, Renjiang;Liu, Ligang;Wang, Guojin;Ma, Weiyin
    • International Journal of CAD/CAM
    • /
    • v.6 no.1
    • /
    • pp.149-156
    • /
    • 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.