An interpolating reproducing kernel particle method for two-dimensional scatter points

An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.

Numerical simulation of scattering wave imaging in a goaf

Goafs are threats to safe mining.Their imaging effects or those of other complex geological bodies are often poor in conventional reflected wave images.Hence,accurate detection of goafs has become an important problem,to be solved with a sense of urgency.Based on scattering theory,we used an equivalent offset method to extract Common Scattering Point gathers,in order to analyze different scattering wave characteristics between Common Scattering Point and Common Mid Point gathers and to compare stack and migration imaging effects.Our research results show that the scattering wave imaging method is more efficient than the conventional imaging method and is therefore a more effective imaging method for detecting goafs and other complex geological bodies.It has important implications for safe mining procedures and infrastructures.

C^1 C^2INTERPOLATION OF SCATTERED DATA POINTS

In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.

Microwave Doppler spectra of sea return at small incidence angles:specular point scattering contribution

It is well known that the sea return echo contains contributions from at least two scattering mechanisms. In addition to the resonant Bragg scattering, the specular point scattering plays an important role as the incidence angle becomes smaller （≥ 20°）. Here, in combination with the Kirchhoff integral equation of scattering field and the stationary phase approximation, analytical expressions for Doppler shift and spectral bandwidth of specular point scattering, which are insensitive to the polarization state, are derived theoretically. For comparison, the simulated results related to the two-scale method （TSM） and the method of moment （MOM） are also presented. It is found that the Doppler shift and the spectral bandwidth given by TSM are insufficient at small incidence angles. However, a comparison between the analytical results and the numerical simulations by MOM in the backscatter configuration shows that our proposed formulas are valid for the specular point scattering case. In this work, the dependences of the predicted results on incidence angle, radar frequency, and wind speed are also discussed. The obtained conclusions seem promising for a better understanding of the Doppler spectra of the specular point scattering fields from time-varying sea surfaces.

Application of the equivalent offset migration method in acoustic log reflection imaging

Borehole acoustic reflection logging can provide high resolution images of nearborehole geological structure. However, the conventional seismic migration and imaging methods are not effective because the reflected waves are interfered with the dominant borehole-guided modes and there are only eight receiving channels per shot available for stacking. In this paper, we apply an equivalent offset migration method based on wave scattering theory to process the acoustic reflection imaging log data from both numerical modeling and recorded field data. The result shows that, compared with the routine post-stack depth migration method, the equivalent offset migration method results in higher stack fold and is more effective for near-borehole structural imaging with low SNR acoustic reflection log data.

COMPLEX SURFACE RECONSTRUCTION BASED ON OBJECT-ORIENTED DEVELOPING TOOL VBA

Taking AutoCAD2000 as platform, an algorithm for the reconstruction ofsurface from scattered data points based on VBA is presented. With this core technology customerscan be free from traditional AutoCAD as an electronic board and begin to create actual presentationof real-world objects. VBA is not only a very powerful tool of development, but with very simplesyntax. Associating with those solids, objects and commands of AutoCAD 2000, VBA notably simplifiesprevious complex algorithms, graphical presentations and processing, etc. Meanwhile, it can avoidappearance of complex data structure and data format in reverse design with other modeling software.Applying VBA to reverse engineering can greatly improve modeling efficiency and facilitate surfacereconstruction.

Inverse Construction Methods of Heterogeneous NURBS Object Based on Additive Manufacturing

According to the requirement of heterogeneous object modeling in additive manufacturing(AM),the Non-Uniform Rational B-Spline(NURBS)method has been applied to the digital representation of heterogeneous object in this paper.By putting forward the NURBS material data structure and establishing heterogeneous NURBS object model,the accurate mathematical unified representation of analytical and free heterogeneous objects have been realized.With the inverse modeling of heterogeneous NURBS objects,the geometry and material distribution can be better designed to meet the actual needs.Radical Basis Function(RBF)method based on global surface reconstruction and the tensor product surface interpolation method are combined to RBF-NURBS inverse construction method.The geometric and/or material information of regular mesh points is obtained by RBF interpolation of scattered data,and the heterogeneous NURBS surface or object model is obtained by tensor product interpolation.The examples have shown that the heterogeneous objects fitting to scattered data points can be generated effectively by the inverse construction methods in this paper and 3D CAD models for additive manufacturing can be provided.

Mesh Generation from Dense 3D Scattered Data Using Neural Network

An improved self-organizing feature map (SOFM) neural network is presented to generate rectangular and hexagonal lattic with normal vector attached to each vertex. After the neural network was trained, the whole scattered data were divided into sub-regions where classified core were represented by the weight vectors of neurons at the output layer of neural network. The weight vectors of the neurons were used to approximate the dense 3-D scattered points, so the dense scattered points could be reduced to a reasonable scale, while the topological feature of the whole scattered points were remained.

Thin-film approximate point scattered function and its application to neutron radiography

A simpler and improved utility approximate point scattered function for thin-film converters currently used in neutron photographic devices is proposed as a correction method to produce clearer,more realistic images.The validity of the model was demonstrated through a simulation experiment.Based on the results,an error analysis was carried out,certain corrections were made to the original model,and the final model achieved a very low relative error in the simulation experiment.The model can also be optimized for quantitative neutron photographic analysis using iterative algorithms to obtain realistic neutron photographic images more quickly.At the end of the article,the model is extended to consider the case of energy spectrum hardening by introducing a temperature correction parameter.

Hermite interpolation of scattered data based on the assistant surface

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.

Geometrically modeling 2D scattered points: a review of the potential for methodologically improving mobile laser scanning in data processing

As a state-of-the-art mapping technology,mobile laser scanning(MLS)is increasingly applied to fields such as digital presentations of city environments.However,its application has recently met a bottleneck in data processing.It has been found that conventional methods for geometrically modeling 3D scattered points are inadequate when dealing with large volumes of MLS data.In fact,this is a challenge that has already been noted in the MLS-relevant fields,e.g.remote sensing,robot perception,and pattern recognition.A variety of algorithms under the schematic frame of analysis,modeling and synthesis(AMS)have been developed in these fields.The AMS paradigm is to first extract the implicit geometric primitives within each scan profile by geometrically modeling its 2D scattered points(GM2P).The resultant 2D geometric primitives are then integrated to restore the real 3D geometrical models.In this process,GM2P is a kernel procedure whereby a review of the GM2P algorithms is assumed to be of significance for developing new efficient algorithms for geometrically modeling 3D scattered points.This idea is supported by MLS sampling often being executed via parallel scan profiles.Indeed,the results of the literature review indicate an avenue for methodologically improving MLS in data processing.

THEORETICAL ANALYSES ON DISCRETE FORMULAE OF DIRECTIONAL DIFFERENTIALS IN THE FINITE POINT METHOD

For the five-point discrete formulae of directional derivatives in the finite point method,overcoming the challenge resulted from scattered point sets and making full use of the explicit expressions and accuracy of the formulae,this paper obtains a number of theoretical results:(1)a concise expression with definite meaning of the complicated directional difference coefficient matrix is presented,which characterizes the correlation between coefficients and the connection between coefficients and scattered geometric characteristics;(2)various expressions of the discriminant function for the solvability of numerical differentials along with the estimation of its lower bound are given,which are the bases for selecting neighboring points and making analysis;(3)the estimations of combinatorial elements and of each element in the directional difference coefficient matrix are put out,which exclude the existence of singularity.Finally,the theoretical analysis results are verified by numerical calculations.The results of this paper have strong regularity,which lay the foundation for further research on the finite point method for solving partial differential equations.