Topic
Interpolation
About: Interpolation is a research topic. Over the lifetime, 54021 publications have been published within this topic receiving 904265 citations. The topic is also known as: interpolation & numerical interpolation.
Papers published on a yearly basis
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TL;DR: In this article, a monotone piecewise bicubic interpolation algorithm was proposed for data on a rectangular mesh, where the first partial derivatives and first mixed partial derivatives are determined by the mesh points.
Abstract: In a 1980 paper [SIAM J. Numer. Anal., 17 (1980), pp. 238–246] the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone $\mathcal{C}^1 $ piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm.
2,174 citations
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07 Jul 2003TL;DR: In this paper, a radial basis function approximation on infinite grids is proposed, based on the wavelet method with radial basis functions (WBFF) with compact support, which is a general method for approximation and interpolation.
Abstract: Preface 1. Introduction 2. Summary of methods and applications 3. General methods for approximation and interpolation 4. Radial basis function approximation on infinite grids 5. Radial basis functions on scattered data 6. Radial basis functions with compact support 7. Implementations 8. Least squares methods 9. Wavelet methods with radial basis functions 10. Further results and open problems Appendix Bibliography Index.
2,128 citations
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21 Oct 2008
TL;DR: Hello, world: handling spatial data in R.
Abstract: Hello, world: handling spatial data in R.- Classes for spatial data in R.- Visualizing spatial data.- Spatial data import and export.- Further methods for handling spatial data.- Customising spatial data classes and methods.- Spatial point pattern analysis.- Interpolation and geostatistics.- Areal data and spatial autocorrelation.- Modelling areal data.- Disease mapping.- Afterword.- References.
2,105 citations
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TL;DR: In this article, the authors analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials, and derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design.
Abstract: In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the so-called artificial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.
2,088 citations
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TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.
Abstract: Absract. This paper is concerned with the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods. The process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation. To indicate the flavor of the type of results obtained, we give a summary table and representative perspective plots of several surfaces.
2,087 citations