For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon'...For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics.展开更多
We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improveme...We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.展开更多
Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficult...Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.展开更多
An analytic massive total cross section of photon proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive ...An analytic massive total cross section of photon proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive structure function F2 measured in lepton-hadron scattering experiments at small values of Bjorken x. It is shown that the descriptions of the inclusive structure function F2 and longitudinal structure function FL are improved with the massive analytic structure function, which may imply the gluon saturation effect dominating the parton evolution process at HERA. The inclusion of the heavy quarks prevent the divergence of the lepton-hadron cross section, which plays a significant role in the description of the photoproduction region.展开更多
We study the effects of running coupling and gluon number fluctuations in the latest diffractive deep inelastic scattering data. It is found that the description of the data is improved once the running coupling and g...We study the effects of running coupling and gluon number fluctuations in the latest diffractive deep inelastic scattering data. It is found that the description of the data is improved once the running coupling and gluon number fluctuations are included with x2/d.o.f. = 0.867, x2/d.o.f. = 0.923 and x2/d.o.f. = 0.878 for three different groups of experimental data. The values of diffusive coefficient subtracted from the fit are smaller than the ones obtained by considering only the gluon number fluctuations in our previous studies. The smaller values of the diffusive coefficient are in agreement with the theoretical predictions, where the gluon number fluctuations are suppressed by the running coupling which leads to smaller values of the diffusive coefficient.展开更多
Consider a kind of Hermit interpolation for scattered data of 3D by trivariate polynomial natural spline, such that the objective energy functional （with natural boundary conditions） is minimal. By the spline functi...Consider a kind of Hermit interpolation for scattered data of 3D by trivariate polynomial natural spline, such that the objective energy functional （with natural boundary conditions） is minimal. By the spline function methods in Hilbert space and variational theory of splines, the characters of the interpolation solution and how to construct it are studied. One can easily find that the interpolation solution is a trivariate polynomial natural spline. Its expression is simple and the coefficients can be decided by a linear system. Some numerical examples are presented to demonstrate our methods.展开更多
This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with C1 continuity everywhere.We derive the C1 condition on each adjacent triangle.On each triangular patch,we...This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with C1 continuity everywhere.We derive the C1 condition on each adjacent triangle.On each triangular patch,we employ convex combination method between three local schemes.The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets.We tested the proposed scheme with 36,65,and 100 data points for some well-known test functions.The scheme is also applied to interpolate the data for the electric potential.We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell–Sabin(PS)and Clough–Tocher(CT)by measuring the maximum error,root mean square error(RMSE)and coefficient of determination(R^(2)).From the results obtained,our proposed method is competent with cubic Bézier,cubic Ball,PS and CT triangles splitting schemes to interpolate scattered data surface.This is very significant since PS and CT requires that each triangle be splitting into several micro triangles.展开更多
In this paper,A MySAS package,which is verified on Windows XP,can easily convert two-dimensional data in small angle neutron and X-ray scattering analysis,operate individually and execute one particular operation as n...In this paper,A MySAS package,which is verified on Windows XP,can easily convert two-dimensional data in small angle neutron and X-ray scattering analysis,operate individually and execute one particular operation as numerical data reduction or analysis,and graphical visualization.This MySAS package can implement the input and output routines via scanning certain properties,thus recalling completely sets of repetition input and selecting the input files.On starting from the two-dimensional files,the MySAS package can correct the anisotropic or isotropic data for physical interpretation and select the relevant pixels.Over 50 model functions are fitted by the POWELL code using x^2 as the figure of merit function.展开更多
A method of 3D model reconstruction based on scattered point data in reverse engineering is presented here. The topological relationship of scattered points was established firstly, then the data set was triangulated ...A method of 3D model reconstruction based on scattered point data in reverse engineering is presented here. The topological relationship of scattered points was established firstly, then the data set was triangulated to reconstruct the mesh surface model. The curvatures of cloud data were calculated based on the mesh surface, and the point data were segmented by edge-based method; Every patch of data was fitted by quadric surface of freeform surface, and the type of quadric surface was decided by parameters automatically, at last the whole CAD model was created. An example of mouse model was employed to confirm the effect of the algorithm.展开更多
An assistant surface was constructed on the base of boundary that being auto-matically extracted from the scattered data.The parameters of every data point corre-sponding to the assistant surface and their applied fie...An assistant surface was constructed on the base of boundary that being auto-matically extracted from the scattered data.The parameters of every data point corre-sponding to the assistant surface and their applied fields were calculated respectively.Inevery applied region,a surface patch was constructed by a special Hermite interpolation.The final surface can be obtained by a piecewise bicubic Hermite interpolation in the ag-gregate of applied regions of metrical data.This method avoids the triangulation problem.Numerical results indicate that it is efficient and accurate.展开更多
This article describes the data processing and acquisition system for the HT-7 mul-tipulse Thomson scattering diagnostic. An eight-pulse laser is used in the Thomson scattering system to obtain electron temperature pr...This article describes the data processing and acquisition system for the HT-7 mul-tipulse Thomson scattering diagnostic. An eight-pulse laser is used in the Thomson scattering system to obtain electron temperature profiles at eight different times throughout an entire plasma discharge. The major components of the diagnostic system consist of a multipulse Nd-glass laser, a photodetector's subsystem, a calibration set and a CAMAC data processing and acquisition system. The data processing software along with LeCroy 2250L will perform the data acquisition. In order to simplify the operation and extend the capability of its compatibility with other math softwares, the processing software has been improved by the authors. The new software based on the VC++ easily utilizes some math softwares to calculate the electron temperature. The new software is simpler and more operational than the old one.展开更多
Fourier transform is a basis of the analysis. This paper presents a kind ofmethod of minimum sampling data determined profile of the inverted object ininverse scattering.
文摘For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics.
文摘We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.
基金Supported by National Natural Science Youth Foundation (10401021).
文摘Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11305040,11375071 and 11447203the Education Department of Guizhou Province Innovation Talent Fund under Grant No[2015]5508+2 种基金the Education Department of Guizhou Province Innovation Team Fund under Grant No[2014]35the Guizhou Province Science Technology Foundation under Grant No[2015]2114the Guizhou Province Innovation Talent Team Fund under Grant No[2015]4015
文摘An analytic massive total cross section of photon proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive structure function F2 measured in lepton-hadron scattering experiments at small values of Bjorken x. It is shown that the descriptions of the inclusive structure function F2 and longitudinal structure function FL are improved with the massive analytic structure function, which may imply the gluon saturation effect dominating the parton evolution process at HERA. The inclusion of the heavy quarks prevent the divergence of the lepton-hadron cross section, which plays a significant role in the description of the photoproduction region.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11305040,11505036 and 11447203the Education Department of Guizhou Province Talent Fund under Grant No[2015]5508the Science and Technology Department of Guizhou Province Fund under Grant Nos[2015]2114 and [2014]7053
文摘We study the effects of running coupling and gluon number fluctuations in the latest diffractive deep inelastic scattering data. It is found that the description of the data is improved once the running coupling and gluon number fluctuations are included with x2/d.o.f. = 0.867, x2/d.o.f. = 0.923 and x2/d.o.f. = 0.878 for three different groups of experimental data. The values of diffusive coefficient subtracted from the fit are smaller than the ones obtained by considering only the gluon number fluctuations in our previous studies. The smaller values of the diffusive coefficient are in agreement with the theoretical predictions, where the gluon number fluctuations are suppressed by the running coupling which leads to smaller values of the diffusive coefficient.
基金Ph.D.Programs Foundation (200805581022) of Ministry of Education of China
文摘Consider a kind of Hermit interpolation for scattered data of 3D by trivariate polynomial natural spline, such that the objective energy functional （with natural boundary conditions） is minimal. By the spline function methods in Hilbert space and variational theory of splines, the characters of the interpolation solution and how to construct it are studied. One can easily find that the interpolation solution is a trivariate polynomial natural spline. Its expression is simple and the coefficients can be decided by a linear system. Some numerical examples are presented to demonstrate our methods.
基金This research was fully supported by Universiti Teknologi PETRONAS(UTP)and Ministry of Education,Malaysia through research grant FRGS/1/2018/STG06/UTP/03/1/015 MA0-020(New rational quartic spline interpolation for image refinement)and UTP through a research grant YUTP:0153AA-H24(Spline Triangulation for Spatial Interpolation of Geophysical Data).
文摘This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with C1 continuity everywhere.We derive the C1 condition on each adjacent triangle.On each triangular patch,we employ convex combination method between three local schemes.The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets.We tested the proposed scheme with 36,65,and 100 data points for some well-known test functions.The scheme is also applied to interpolate the data for the electric potential.We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell–Sabin(PS)and Clough–Tocher(CT)by measuring the maximum error,root mean square error(RMSE)and coefficient of determination(R^(2)).From the results obtained,our proposed method is competent with cubic Bézier,cubic Ball,PS and CT triangles splitting schemes to interpolate scattered data surface.This is very significant since PS and CT requires that each triangle be splitting into several micro triangles.
基金Supported by Science and Technology Foundation of China Academy of Engineering Physics(No.2010A0103002)Innovation Foundation of Institute of Nuclear Physics and Chemistry,CAEP(No.2009CX01)
文摘In this paper,A MySAS package,which is verified on Windows XP,can easily convert two-dimensional data in small angle neutron and X-ray scattering analysis,operate individually and execute one particular operation as numerical data reduction or analysis,and graphical visualization.This MySAS package can implement the input and output routines via scanning certain properties,thus recalling completely sets of repetition input and selecting the input files.On starting from the two-dimensional files,the MySAS package can correct the anisotropic or isotropic data for physical interpretation and select the relevant pixels.Over 50 model functions are fitted by the POWELL code using x^2 as the figure of merit function.
文摘A method of 3D model reconstruction based on scattered point data in reverse engineering is presented here. The topological relationship of scattered points was established firstly, then the data set was triangulated to reconstruct the mesh surface model. The curvatures of cloud data were calculated based on the mesh surface, and the point data were segmented by edge-based method; Every patch of data was fitted by quadric surface of freeform surface, and the type of quadric surface was decided by parameters automatically, at last the whole CAD model was created. An example of mouse model was employed to confirm the effect of the algorithm.
文摘An assistant surface was constructed on the base of boundary that being auto-matically extracted from the scattered data.The parameters of every data point corre-sponding to the assistant surface and their applied fields were calculated respectively.Inevery applied region,a surface patch was constructed by a special Hermite interpolation.The final surface can be obtained by a piecewise bicubic Hermite interpolation in the ag-gregate of applied regions of metrical data.This method avoids the triangulation problem.Numerical results indicate that it is efficient and accurate.
基金The project supported by the National Science Foundation of China(No.10075049 and No.10275068)
文摘This article describes the data processing and acquisition system for the HT-7 mul-tipulse Thomson scattering diagnostic. An eight-pulse laser is used in the Thomson scattering system to obtain electron temperature profiles at eight different times throughout an entire plasma discharge. The major components of the diagnostic system consist of a multipulse Nd-glass laser, a photodetector's subsystem, a calibration set and a CAMAC data processing and acquisition system. The data processing software along with LeCroy 2250L will perform the data acquisition. In order to simplify the operation and extend the capability of its compatibility with other math softwares, the processing software has been improved by the authors. The new software based on the VC++ easily utilizes some math softwares to calculate the electron temperature. The new software is simpler and more operational than the old one.
文摘Fourier transform is a basis of the analysis. This paper presents a kind ofmethod of minimum sampling data determined profile of the inverted object ininverse scattering.
