Modeling of CHAMP satellite data according to the 3D surface spline model of geomagnetic fi elds

Surface observations and CHAMP measurement data are employed to develop a three-dimensional surface spline(3DSS)model of China's Mainland.The magnetic field distribution at the satellite level is then demonstrated using the model obtained.The results of this model are compared and verifi ed by deriving the corresponding two(2DTY)and threedimensional(3DTY)Taylor polynomial models.Issues such as the removal of disruptive geomagnetic fi elds,the data gap between the surface and satellite levels,and boundary eff ects are carefully considered during modeling.We then focus on evaluating the modeling eff ect of the satellite data.Ten satellite points not involved in the modeling procedure are selected,and the residuals,absolute change rates,and RMSEs of these points are calculated.Results show that the distribution of the magnetic fi eld determined by the 3DSS model is highly consistent with that obtained from the IGRF12 model.Expect for component Y,the absolute change rates of other components are less than 0.5%.Specifi cally,the RMSE of Y of 3DSS is nearly 60%lower than those of 3DTY and 2DTY;the RMSE of other components of the former are also over 90%lower than those of the latter.This fi nding implies that the 3DSS model has good performance for modeling satellite data and its results are reliable.Moreover,the modeling eff ect of 3DTY is better than that of 2DTY.

Surface Spline Interpolation Method for Thermal Reconstruction with Limited Sensor Data of Non-Uniform Placements

With the characteristic size reducing as well as the power densities exponentially increasing, elevated chip temperatures are true limiters to the performance and reliability of integrated circuits. To address these thermal issues, it is essential to use a set of on-chip thermal sensors to monitor temperatures during operation.These temperature sampling results are then used by thermal management techniques to appropriately manage chip performance. In this paper, we propose a surface spline interpolation method to reconstruct the full thermal characterization of integrated circuits with non-uniform thermal sensor placements. We construct the thermal surface function using the mathematical tool of surface spline with the matrix calculation of the non-uniform sample data. Then, we take the coordinates of the points at grid locations into the surface function to get its temperature value so that we can reconstruct the full thermal signals. To evaluate the effiectiveness of our method,we develop an experiment for reconstructing full thermal status of a 16-core processor. Experimental results show that our method outperforms the inverse distance weighting method based on dynamic Voronoi diagram and spectral analysis techniques both in the average absolute error metric and the hot spot absolute error metric with short enough runtime to meet the real-time process demand. Besides, our method still has the advantages such as its mathematical simplicity with no need of pre-process.

Research into Freedom Surface Modeling System of Double Beta Spline in Space

In this paper, we present the double Beta spline curved surface which is controlled by double parameters including the algorithm principles, the treatment of boundary conditions, the alternation of projection, the algorithms of elimination hiddle line, the process to display and the primiples to produce the shaded curved surface. Based on all the above, a freedom surface modeling system (FSMS) is designed and some examples developed on FSMS are verified and analyzed.

Contour detection with bicubic spline surfaces

Contour detection has a rich history in multiplefields such as geography,engineering,and earth science.The predominant approach is based on piecewise planar tessellation and now being challenged concerning the extraction of contour objects for non-linear elevation functions,particularly with respect to bicubic spline functions.A storage-efficient method was developed in previous research,but the detection of the complete set of contour objects is yet to be realized.Although intractable,theoretical underpinnings pertinent to curvature resulted in an approach to realize the complete detection of objects.Given a digital elevation model dataset,in this study,a bicubic spline surface function wasfirst determined.Thereafter,candidate initial points on the edges across the region of interest were identified,and the recursive disaggregation of rectangles was repeated if the non-existence of a solution could not be assured.A developed tracking method was then applied.During advancement,other initial points on the same contour curve were identified and eliminated to circumvent duplicate detection.The completeness of the outlets provides analytical tools for elevation and other geographical assessments.Demonstrative experiments included the development of a three-dimensional contour-based network and slope assessments.The latter application transforms the slope analysis type from raster-based to vector-based.Highlights.Detection of a complete set of contour objects amenable to bicubic spline surfaces..Small closure inside a single patch is detectable if size exceeds the standard..Curvature&tolerances central to step length adjustment and tangent angle determination..Redundant initial points are identified and eliminated during the tracking process..Various potential applications in addition to geographical elevations.

Observation and analysis of geomagnetic abnormity associated with the M_S=5.7 Jiu-jiang-Ruichang earthquakeb

A three-component geomagnetic survey was carried out during the period from 2002 to 2004 in China including Jiujiang-Ruichang region. Comparing the ＂2005.0 surface spline model of China geomagnetic field＂ created on the basis of the survey data with the ＂1970.0 surface spline model of China geomagnetic field＂, we can see an obvious abnormity in the geomagnetic horizontal component within a range of about 100 km around the epicenter of the Ms=5.7 Jiujiang-Ruichang earthquake occurred on November 26, 2005. After the earthquake, we carded out a repeated geomagnetic survey at 21 stations in the Jiujiang-Ruichang region and created a corresponding ＂2005.0 partially revised surface spline model of China geomagnetic field＂. By comparing the above three models, analyzing the geomagnetic horizontal component at the profile in the Jiujiang-Ruichang region and quantitatively studying the geomagnetic data of every stations around the Ms=5.7 earthquake, we have obtained the geomagnetic abnormity associated with this earthquake. Then the geomagnetic abnormity and its relation with seismic activity are discussed in this paper.

C^2-(C^3-) Continuous Interpolation Spline Curve and Surface

Free-formed or sculptured surfaces in engineering products are frequently constructed from a set of measured 3D data points. C2- (C3-) continuity approach is important in this field. This paper presents a method of rectangular interpolation of given 3D data array which is regularly arranged. The interpolation surface which is constructed by tensor product has desirable properties (second-order or third-order continuity locality) and is implemented and adjusted easily. Higher order continuity methods are also briefly discussed.

A FAST PARALLEL ALGORITHM OF BIVARIATE SPLINE SURFACES

A fast algorithm for evaluating and displaying bivariate splines in a three direction is presented based on two-level transfomation of the corresponding B-splines. The efficiency has been shown by experiments of surface modelling design[5].