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 extract...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.展开更多
Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method n...Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.展开更多
We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To...We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To obtain the pure anomaly field,the main field and the induced field of the ionospheric and magnetospheric fields were removed from measured data.We also compared the SS model anomalies and the data obtained with Kriging interpolation（KI）.The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0-1990.0 to 2000.0.The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity.The anomalous distributions in the X-,Y-,and Z-direction and F are mainly negative.The 3DTP model anomalies suggest that the intensity in the X-direction increases from-100 nT to 0 nT with longitude,whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative.The intensity in the Z-direction and F are very similar and in most areas it is about-50 nT and higher in western Tibet.The SS model anomalies overall reflect the actual distribution of the magnetic field anomalies;however,because of the uneven distribution of measurements,it yields several big anomalies.Owing to the added altitude term,the 3DTP model offers higher precision and is consistent with KI.展开更多
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 surfa...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].展开更多
Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput...Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.展开更多
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 alg...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.展开更多
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...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.展开更多
High resolution data have become an important source of data, before they can be integrating into a GIS database. It requires processing for ortho-rectification to generate image map with high accuracy and low cost. U...High resolution data have become an important source of data, before they can be integrating into a GIS database. It requires processing for ortho-rectification to generate image map with high accuracy and low cost. Using surface splines interpolation for rectification is quite different with traditional grid method in photogrammetric. To introduce surface splines is important. In fact the actual name is mechanical surface splines because it must add mechanical conditions to form the formula. The main advantages of the surface splines are that the coordinate of the known points are not located in a rectangular array and the function may be differentiated in find slopes. Surface splines are a mathematical tool to interpolate a function of two variables. It bases upon small deflection equation of an infinite plate, it originally developed for interpolation wing deflection of aircraft 1972 by Harderaed and Desmarais contributed. An example map size is beyond the custom. Only five control points for rectification （60 cm × 200 cm） if the number of control points is increasing also the map size increasing large and operating easy. The other UAV in Civilian world gives low cost. Obvious aerial imaging using surface splines in cartographic is a tool for supporting geospatial decisions.展开更多
A surface spline function is used to fit a coal seam surface in structural anal ysis in coal geology. From the surface spline function, the first and second partial derivatives can also be derived and used to structur...A surface spline function is used to fit a coal seam surface in structural anal ysis in coal geology. From the surface spline function, the first and second partial derivatives can also be derived and used to structural analysis, especially for recogni tion of the concealed structures. The detection of structures related to faulting is em phasized.展开更多
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a ...In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both endpoints for the rulings. We circumvent such difficulty by resorting to degree elevation of the developable surface. This is useful for solving not only this problem, but also other problems dealing with triangular developable patches.展开更多
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 re...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.展开更多
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 t...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.展开更多
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...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.展开更多
基金supported by Japan Society for the Promotion of Science[grant number 21 K01021].
文摘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.
基金Project (No. G1998030401) supported by the National Natural Sci-ence Foundation of China
文摘Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.
基金supported by the National Natural Science Foundation of China(No.41404053)Special Project for MeteoScientific Research in the Public Interest(No.GYHY201306073)+1 种基金Natural Science Foundation of Jiangsu Province(No.BK20140994),Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.14KJB170012)Training Program of Innovation and Entrepreneurship for Undergraduates of NUIST(No.201510300178)
文摘We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To obtain the pure anomaly field,the main field and the induced field of the ionospheric and magnetospheric fields were removed from measured data.We also compared the SS model anomalies and the data obtained with Kriging interpolation（KI）.The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0-1990.0 to 2000.0.The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity.The anomalous distributions in the X-,Y-,and Z-direction and F are mainly negative.The 3DTP model anomalies suggest that the intensity in the X-direction increases from-100 nT to 0 nT with longitude,whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative.The intensity in the Z-direction and F are very similar and in most areas it is about-50 nT and higher in western Tibet.The SS model anomalies overall reflect the actual distribution of the magnetic field anomalies;however,because of the uneven distribution of measurements,it yields several big anomalies.Owing to the added altitude term,the 3DTP model offers higher precision and is consistent with KI.
文摘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].
基金supported by the National Key Basic Research Project of China(No.2004CB318000)One Hundred Talent Project of the Chinese Academy of Sciences,the NSF of China(No.60225002,No.60533060)Doctorial Program of MOE of China and the 111 Project(No.B07033).
文摘Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.
文摘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.
基金This work was supported by the National Natural Science Foundation of China(Nos.41974073,41404053)Special Project for Meteo-Scientifi c Research in the Public Interest(No.GYHY201306073)。
文摘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.
文摘High resolution data have become an important source of data, before they can be integrating into a GIS database. It requires processing for ortho-rectification to generate image map with high accuracy and low cost. Using surface splines interpolation for rectification is quite different with traditional grid method in photogrammetric. To introduce surface splines is important. In fact the actual name is mechanical surface splines because it must add mechanical conditions to form the formula. The main advantages of the surface splines are that the coordinate of the known points are not located in a rectangular array and the function may be differentiated in find slopes. Surface splines are a mathematical tool to interpolate a function of two variables. It bases upon small deflection equation of an infinite plate, it originally developed for interpolation wing deflection of aircraft 1972 by Harderaed and Desmarais contributed. An example map size is beyond the custom. Only five control points for rectification （60 cm × 200 cm） if the number of control points is increasing also the map size increasing large and operating easy. The other UAV in Civilian world gives low cost. Obvious aerial imaging using surface splines in cartographic is a tool for supporting geospatial decisions.
文摘A surface spline function is used to fit a coal seam surface in structural anal ysis in coal geology. From the surface spline function, the first and second partial derivatives can also be derived and used to structural analysis, especially for recogni tion of the concealed structures. The detection of structures related to faulting is em phasized.
基金partially supported by the Spanish Ministerio de Economía y Competividad(No.TRA2014-56792-P)
文摘In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both endpoints for the rulings. We circumvent such difficulty by resorting to degree elevation of the developable surface. This is useful for solving not only this problem, but also other problems dealing with triangular developable patches.
文摘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.
基金the National Basic Research Program(973)of China(No.2009CB320206)the National Natural Science Foundation of China(No.60821062)
文摘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.
文摘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.
