• Title/Summary/Keyword: Scattered Data Interpolation

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The Generation of Free-Form Surface using Scattered Data Interpolation (분산 데이터 보간을 이용한 자유 형태 곡면 생성방법)

  • Lee, A-Ri;Park, Cheol-Ho;Sim, Jae-Hong
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.9
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    • pp.2504-2511
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    • 1999
  • This paper proposes the scattered data interpolation as an efficient method that is designed for free-form surface. Data interpolation is an essential method of designing for various objects. For the generating free-form surface of complexity construction, the existing method had problems to represent flat area and sharp corner edge, in presenting objects with computing the weight of control points. For solving this problem, we proposes the generating method of new approximation surfaces, using scattered data interpolation. This method obtains B-Spline basis function which calculates main curvature, having optimized value in variable area, on given control points and changed objects, and then computes the changing rate the approximating data, using it's value. We also present this method that generates smoother free-form surface, using the scattered data interpolation with minimum weight.

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QUASI-INTERPOLATORY APPROXIMATION SCHEME FOR MULTIVARIATE SCATTERED DATA

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

Refinement of DEM boundaries using Point Distribution Criteria in Scattered Data Interpolation

  • KIM Seung-Bum
    • Proceedings of the KSRS Conference
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    • 2004.10a
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    • pp.103-106
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    • 2004
  • Extrapolation off the boundaries of scattered data is an intrinsic feature of interpolation. However, extrapolation causes serious problems in stereo-vision and mapping, which has not been investigated carefully. In this paper, we present novel schemes to eliminate the extrapolation effects for the generation of a digital elevation model (DEM). As a first step, we devise point distribution criteria, namely COG (Center of Gravity) and ECI (Empty Center Index), and apply rigorous and robust elimination based on the criteria. Compared with other methods, the proposed schemes are computationally fast and applicable to a wide range of interpolation techniques.

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SINGULARITY OF A COEFFICIENT MATRIX

  • Lee, Joon-Sook
    • Communications of the Korean Mathematical Society
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    • v.10 no.4
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    • pp.849-854
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    • 1995
  • The interpolation of scattered data with radial basis functions is knwon for its good fitting. But if data get large, the coefficient matrix becomes almost singular. We introduce different knots and nodes to improve condition number of coefficient matrix. The singulaity of new coefficient matrix is investigated here.

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Volumetric NURBS Representation of Multidimensional and Heterogeneous Objects: Modeling and Applications (VNURBS기반의 다차원 불균질 볼륨 객체의 표현: 모델링 및 응용)

  • Park S. K.
    • Korean Journal of Computational Design and Engineering
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    • v.10 no.5
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    • pp.314-327
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    • 2005
  • This paper describes the volumetric data modeling and analysis methods that employ volumetric NURBS or VNURBS that represents heterogeneous objects or fields in multidimensional space. For volumetric data modeling, we formulate the construction algorithms involving the scattered data approximation and the curvilinear grid data interpolation. And then the computational algorithms are presented for the geometric and mathematical analysis of the volume data set with the VNURBS model. Finally, we apply the modeling and analysis methods to various field applications including grid generation, flow visualization, implicit surface modeling, and image morphing. Those application examples verify the usefulness and extensibility of our VNUBRS representation in the context of volume modeling and analysis.

Comparative analysis of spatial interpolation methods of PM10 observation data in South Korea (남한지역 PM10 관측자료의 공간 보간법에 대한 비교 분석)

  • Kang, Jung-Hyuk;Lee, Seoyeon;Lee, Seung-Jae;Lee, Jae-Han
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.24 no.2
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    • pp.124-132
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    • 2022
  • This study was aimed to visualize the spatial distribution of PM10 data measured at non-uniformly distributed observation sites in South Korea. Different spatial interpolation methods were applied to irregularly distributed PM10 observation data from January, 2019, when the concentration was the highest and in July, 2019, when the concentration was the lowest. Four interpolation methods with different parameters were used: Inverse Distance Weighted (IDW), Ordinary Kriging (OK), radial base function, and scattered interpolation. Six cases were cross-validated and the normalized root-mean-square error for each case was compared. The results showed that IDW using smoothing-related factors was the most appropriate method, while the OK method was least appropriate. Our results are expected to help users select the proper spatial interpolation method for PM10 data analysis with comparative reliability and effectiveness.

A New Method of the Global Interpolation in NURBS Surface: II (NURBS Surface Global Interpolation에 대한 한 방법: II)

  • 정형배
    • Korean Journal of Computational Design and Engineering
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    • v.3 no.4
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    • pp.243-250
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    • 1998
  • In parametric surface interpolation, the choice of the parameter values to the set of scattered points makes a great deal of difference in the resulting surface. A new method is developed and tested for the parametrization in NURBS surface global interpolation. This method uses the parameter value at the maximal value of relevant rational basis function, to assign the parameter values to the arbitrary set of design data. This method gives us several important advantages in geometric modeling, the freedom of the selection of knot values, the feasible transformation of the data set to the matrix, the possibility of affinite transformation between the design data and generated surface, etc.

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Visualization of Trivariate Scattered Data Interpolation (트라이 베리에이트 산포된 자료 보간의 가시화)

  • Lee, Kun
    • Journal of the Korea Computer Graphics Society
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    • v.2 no.2
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    • pp.11-20
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    • 1996
  • The numerous application of scattered data include the modeling and visualization of physical phenomena. A tetrahedrization is one of pre-processing steps for 4-D surface interpolation. In this paper, various tetrahedrization methods are discussed including, Delaunay, least squares fitting, gradient difference, and jump in normal direction derivatives. This paper discriminates the characteristics of tetrahedrization through visualizing tetrahedral domain. This paper also, provides the tool that can compare and analyze the quality of 4-D space approximation over tetrahedral domain numerically, as well as graphically.

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APPROXIMATION METHOD FOR SCATTERED DATA FROM SHIFTS OF A RADIAL BASIS FUNCTION

  • Yoon, Jung-Ho
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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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.

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A Study on the Interpolation Characteristics of the Scattered Geographic Data according to the Gridding methods (격자화 기법에 따른 이산지형정보의 보간특성 연구)

  • Lee, Yong-Chang
    • Journal of Korean Society for Geospatial Information Science
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    • v.4 no.2 s.8
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    • pp.173-180
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    • 1996
  • In a grid based data transformation, the different gridding methods provide different interpretations of scattered data because each method calculate grid node values using a different weighted mathematical algorithms. Therefore, it is necessary to review the interpolated characteristics of some gridding methods according to search distance, search area and search options before determing the best method with a data set. For this, in this paper, six different gridding methods with the same search conditions are applied to a scattered data obtained from sterro-plotter. The interpolated characteristics of the scattered geographic data considered through comparison of coincidence between the data point and the grid node being interpolated. And also, shows the real application of gridding methods through calculating volumes and creating cross sections.

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