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Multivariate scattered data fitting

Alain Le Méhauté, Larry L. Schumaker, Leonardo Traversoni
1996 Journal of Computational and Applied Mathematics  
Many methods have been developed for solving the scattered data fitting problem, see [26] for an early survey, and [7] for a comparison of a number of methods available in the early 1980s.  ...  Although the paper [21] does not deal directly with scattered data interpolation, it nicely illustrates the idea of a multiresolution analysis.  ... 
doi:10.1016/0377-0427(96)00032-5 fatcat:n3q4yzeudjgbpm45s5bc37p3iq

New Spline Quasi-Interpolant for Fitting 3-D Data on the Sphere: Applications to Medical Imaging

El Bachir Ameur, Driss Sbibih, Ahmad Almhdie, Christophe Leger
2007 IEEE Signal Processing Letters  
In this paper, a new local spline quasi-interpolant is constructed for fitting 3-D data defined on the sphere-like surface .  ...  a new expression of the associated quasi-interpolant .  ...  In this paper, we propose a new method for fitting 3-D data by using a spline quasi-interpolant.  ... 
doi:10.1109/lsp.2006.888261 fatcat:vvk6y76uofar3b6ay43osemtzu

Hybrid Bézier patches on sphere-like surfaces

Xiaoyu Liu, Larry L. Schumaker
1996 Journal of Computational and Applied Mathematics  
We develop a method for interpolating scattered data on sphere-like surfaces based on a local triangular patch which is constructed from a blend of certain spherical Bernstein-Bkzier polynomials introduced  ...  We also show how the same approach can be used to construct a C2 quintic hybrid patch matching second derivative information as an analog of a planar method of Chang and Said (1995) .  ...  Estimating derivatives In the original interpolation problem (1.1) we are given only function values at scattered data points.  ... 
doi:10.1016/0377-0427(96)00041-6 fatcat:tbharweluvaz5obgcb2zbullji

Fitting scattered data on sphere-like surfaces using spherical splines

Peter Alfeld, Marian Neamtu, Larry L. Schumaker
1996 Journal of Computational and Applied Mathematics  
Spaces of polynomial splines defined on planar triangulations are very useful tools for fitting scattered data in the plane.  ...  For interpolation. we discuss macro-element methods and minimal energy splines. and for fitting, we consider discrete least squares and penalized least squares.  ...  Because of the structure of spherical spline spaces, virtually any spline interpolation or approximation method for the planar scattered data problem has a spherical analog.  ... 
doi:10.1016/0377-0427(96)00034-9 fatcat:rw5j6e4aonfxfim7pytfsmepyq

3D rotation estimation using discrete spherical harmonic oscillator transforms

Soo-Chang Pei, Chun-Lin Liu
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The phenomenon results from no interpolations in discrete SHOTs.  ...  Thus, the spherical harmonics related algorithms could be utilized to discrete SHOTs without modification.  ...  SHTs take C1N 2 pt steps for interpolation and approximately C2N 2 pt operations for 2D separable transforms, where C1 depends on interpolation methods and C2 denotes the number of F ℓ,m needed in (15  ... 
doi:10.1109/icassp.2014.6853701 dblp:conf/icassp/PeiL14 fatcat:u2icp5l3treg3ichrv2an4om5a

Weighted quadrature formulas and approximation by zonal function networks on the sphere

H.N. Mhaskar
2006 Journal of Complexity  
In the case of uniform approximation, our construction utilizes values of the target function at scattered sites.  ...  The approximation bounds are used to obtain error bounds on a very general class of quadrature formulas that are exact for the integration of high degree polynomials with respect to a weighted integral  ...  We would also like to thank Feng Dai for [5] , and the referees for their suggestions for improvement in the first submitted version of the paper.  ... 
doi:10.1016/j.jco.2005.10.003 fatcat:snek6rclargs7btamvqt3pb7ju

Locally Supported Kernels for Spherical Spline Interpolation

Michael Schreiner
1997 Journal of Approximation Theory  
By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is spread out since the resulting interpolation matrix is sparse and thus  ...  We show how spherical spline interpolation with polynomial precision can be managed with locally supported kernels, thus giving the possibility to combine approximation techniques based on spherical harmonic  ...  For G E C2 [-1, l] and F E L"(Q) we set Of particular importance is the convolution with a second zonal function: let H E ,C2 [-1, 11 .  ... 
doi:10.1006/jath.1997.3037 fatcat:5zmghaxak5eepa5shbzixtfnm4

Comparison of COSMIC and COSMIC-2 Radio Occultation Refractivity and Bending Angle Uncertainties in August 2006 and 2021

Richard Anthes, Jeremiah Sjoberg, Xuelei Feng, Stig Syndergaard
2022 Atmosphere  
However, a higher percentage of C2 profiles reach close to the surface in the moisture-rich tropics, an advantage of the higher signal-to-noise ratio (SNR) in C2.  ...  We compare the random error statistics (uncertainties) of COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate, C1) and COSMIC-2 (C2) radio occultation (RO) bending angles and  ...  Acknowledgments: We thank Sergey Sokolovskiy and Tae-Kwon Wee for their inciteful discussions and Eric DeWeaver (NSF) and Jack Kaye (NASA) for their long-term support of COSMIC.  ... 
doi:10.3390/atmos13050790 fatcat:jmc3svxtozabhfpilhamgp2lie

Physically-based simulation of rainbows

Iman Sadeghi, Adolfo Munoz, Philip Laven, Wojciech Jarosz, Francisco Seron, Diego Gutierrez, Henrik Wann Jensen
2012 ACM Transactions on Graphics  
However, as Lorenz-Mie theory is restricted to scattering by spherical particles, it cannot be applied to real raindrops which are non-spherical, especially for larger raindrops.  ...  We present the first comprehensive technique for simulating the interaction of a wavefront of light with a physically-based water drop shape.  ...  Thanks also to Mapi for the rainbow image in Figure 2d and Jurgen Schulze for referring us to the facility of Project GreenLight.  ... 
doi:10.1145/2077341.2077344 fatcat:x25scdpcjndhviljuffu6eayyu

Ultrasonic Heating Distribution in Lossy Cylinders and Spheres

L.A. Longley, W.D. O'Brien
1982 IEEE Transactions on Sonics and Ultrasonics  
The greatest spatial nonunifonnity and highest peaks of heat generation were found for maximum ka and impedance mismatch.  ...  Impedance mismatches of up to 20 percent are considered for 1 < ka < 40. Plots of typical heat generation distributions are presented, and apparent trends are summarized.  ...  A comparison of calculated (b), (d), ( f ) and published (a), (c), (e) plots of scattered intensity as in Fig. 7, but for a rigid sphere in this case.  ... 
doi:10.1109/t-su.1982.31310 fatcat:abbxfl3uzrai3klnxqudczpt7i

Three-dimensional reconstruction of the streamer belt and other large-scale structures of the solar corona

F. Saez, A. Llebaria, P. Lamy, D. Vibert
2007 Astronomy and Astrophysics  
The radiance of the synthetic images is calculated with a ray-tracing algorithm that incorporates the Thomson scattering.  ...  A systematic analysis of the LASCO data over almost a full solar cycle will be developed in forthcoming articles. Article published by EDP Sciences and available at  ...  Wang of the Naval Research Laboratory for his helpful advice on calculation of the magnetic field.  ... 
doi:10.1051/0004-6361:20066777 fatcat:qfsdzvvgp5gopo5loxjz3f2qsq

ElectromagneticN→ΔTransition and Neutron Form Factors

A. J. Buchmann
2004 Physical Review Letters  
The proposed relation holds with good accuracy for the entire range of momentum transfers where data are available.  ...  The C2/M1 ratio of the electromagnetic N->Delta(1232) transition, which is important for determining the geometric shape of the nucleon, is shown to be related to the neutron elastic form factor ratio  ...  A two-parameter fit of the experimental data for Rn using Eq.(8) with a = 0.9 and d = 2.8 [34] is also listed.  ... 
doi:10.1103/physrevlett.93.212301 pmid:15601000 fatcat:dzqksmgdzzasllaevz7p74tame

Effects of disorder on the superconducting properties of BaFe1.8Co0.2As2single crystals

M Eisterer, M Zehetmayer, H W Weber, J Jiang, J D Weiss, A Yamamoto, E E Hellstrom
2009 Superconductors Science and Technology  
Single crystals of superconducting BaFe_1.8Co_0.2As_2 were exposed to neutron irradiation in a fission reactor.  ...  introduced defects decrease the superconducting transition temperature (by about 0.3 K) and the upper critical field anisotropy (e.g. from 2.8 to 2.5 at 22 K) and enhance the critical current densities by a  ...  Larbalestier, A. Gurevich, M. Putti, D. V. Abraimov, C. Tarantini and F. Kametanni for discussions. Work at the NHMFL was supported by AFOSR, NSF, and the State of Florida.  ... 
doi:10.1088/0953-2048/22/9/095011 fatcat:vkkcuywrivacbj4vx5oepvkhiu

Three-dimensional local structure refinement using a full-potential XANES analysis

G. Smolentsev, A. V. Soldatov, M. C. Feiters
2007 Physical Review B  
The method is based on the fitting of experimental XANES using a multidimensional interpolation of spectra and ab-initio full potential calculations of XANES.  ...  Alternatively simultaneous analysis of EXAFS and XANES taking into account a limited number of multiple scattering paths sometimes gives information about angles in addition to distances4.  ...  C1-C2 1.39 Â and O-Ni-O angle 940.  ... 
doi:10.1103/physrevb.75.144106 fatcat:n7qgk4mxubb47djwjj6sgk7g3a

Brownian Coagulation of Aerosols in the Transition Regime

M. Kerker, A. Chatterjee, D. D. Cooke
1976 Pure and Applied Chemistry  
This was done by working with the same range of particle size as earlier, but at a reduced pressure.  ...  A number of modffications were made in the experimental technique, including the use of diethylhexylsebacate instead of dibutylphthalate in order to avoid the possibility of loss to the walls by evaporation  ...  Two light scattering cells, C1 and C2, each equipped with a flat entrance window and a Rayleigh horn, are attached by ground glass joints at the entrance and at the exit of the hold-up tube D.  ... 
doi:10.1351/pac197648040457 fatcat:e3nxysymzfg63nzoyunb4233pa
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