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
Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curv...Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.展开更多
A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two par...A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.展开更多
Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline...Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline curves and surfaces are concentrated on open ones. In this paper, we focus on the multiresolution representations and editing of closed B-spline curves and surfaces using wavelets. A repetition approach is adopted for the multiresolution analysis of closed B-spline curves and surfaces. Since the closed curve or surface itself is periodic, it can overcome the drawback brought by the repetition method, i.e. introducing the discontinuities at the boundaries. Based on the models at different multiresolution levels, the multiresolution editing methods of closed curves and surfaces are introduced. Users can edit the overall shape of a closed one while preserving its details, or change its details without affecting its overall shape.展开更多
This paper presents a parallel implementation of computing uniform bicubic B spline surfaces on Transputer networks. The work is essential for building Transputer based CAD and graphics systems.
To dates,most ship detection approaches for single-pol synthetic aperture radar（SAR） imagery try to ensure a constant false-alarm rate（CFAR）.A high performance ship detector relies on two key components：an accura...To dates,most ship detection approaches for single-pol synthetic aperture radar（SAR） imagery try to ensure a constant false-alarm rate（CFAR）.A high performance ship detector relies on two key components：an accurate estimation to a sea surface distribution and a fine designed CFAR algorithm.First,a novel nonparametric sea surface distribution estimation method is developed based on n-order Bézier curve.To estimate the sea surface distribution using n-order Bézier curve,an explicit analytical solution is derived based on a least square optimization,and the optimal selection also is presented to two essential parameters,the order n of Bézier curve and the number m of sample points.Next,to validate the ship detection performance of the estimated sea surface distribution,the estimated sea surface distribution by n-order Bézier curve is combined with a cell averaging CFAR（CA-CFAR）.To eliminate the possible interfering ship targets in background window,an improved automatic censoring method is applied.Comprehensive experiments prove that in terms of sea surface estimation performance,the proposed method is as good as a traditional nonparametric Parzen window kernel method,and in most cases,outperforms two widely used parametric methods,K and G0 models.In terms of computation speed,a major advantage of the proposed estimation method is the time consuming only depended on the number m of sample points while independent of imagery size,which makes it can achieve a significant speed improvement to the Parzen window kernel method,and in some cases,it is even faster than two parametric methods.In terms of ship detection performance,the experiments show that the ship detector which constructed by the proposed sea surface distribution model and the given CA-CFAR algorithm has wide adaptability to different SAR sensors,resolutions and sea surface homogeneities and obtains a leading performance on the test dataset.展开更多
In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline th...In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.展开更多
According to inverse heat transfer theory, the evolutions of synthetic surface heat transfer coefficient（SSHTC） of the quenching surface of 7B50 alloy during water-spray quenching were simulated by the Pro CAST soft...According to inverse heat transfer theory, the evolutions of synthetic surface heat transfer coefficient（SSHTC） of the quenching surface of 7B50 alloy during water-spray quenching were simulated by the Pro CAST software based on accurate cooling curves measured by the modified Jominy specimen and temperature-dependent thermo-physical properties of 7 B50 alloy calculated using the JMat Pro software. Results show that the average cooling rate at 6 mm from the quenching surface and 420-230 ℃（quench sensitive temperature range） is 45.78℃/s. The peak-value of the SSHTC is 69 kW/（m^2·K） obtained at spray quenching for 0.4 s and the corresponding temperature of the quenching surface is 160 ℃. In the initial stage of spray quenching, the phenomenon called ＂temperature plateau＂ appears on the cooling curve of the quenching surface. The temperature range of this plateau is 160-170℃ with the duration about 3 s. During the temperature plateau, heat transfer mechanism of the quenching surface transforms from nucleate boiling regime to single-phase convective regime.展开更多
We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces that interpolate the curve network of a ship huliform.First,the curves in the network are classified into two types;bo...We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces that interpolate the curve network of a ship huliform.First,the curves in the network are classified into two types;boundary curves and ＂reference curves＂,The boundary curves correspond to a set of rectangular（or triangular）topological type that can be representes with tensot-product （or degenerate）B-spline surface patches.Next,in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing ＂virtual＂isoparametric curves.Finally,a discrete G^1 continuous B-spline surface is gencrated by a surface fitting algorithm.Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.展开更多
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 (60873111, 60933007)
文摘Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.
基金This project is supported by National Natural Science Foundation of China(No.50575098).
文摘A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.
文摘Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline curves and surfaces are concentrated on open ones. In this paper, we focus on the multiresolution representations and editing of closed B-spline curves and surfaces using wavelets. A repetition approach is adopted for the multiresolution analysis of closed B-spline curves and surfaces. Since the closed curve or surface itself is periodic, it can overcome the drawback brought by the repetition method, i.e. introducing the discontinuities at the boundaries. Based on the models at different multiresolution levels, the multiresolution editing methods of closed curves and surfaces are introduced. Users can edit the overall shape of a closed one while preserving its details, or change its details without affecting its overall shape.
文摘This paper presents a parallel implementation of computing uniform bicubic B spline surfaces on Transputer networks. The work is essential for building Transputer based CAD and graphics systems.
基金The National Natural Science Foundation of China under contract No.61471024the National Marine Technology Program for Public Welfare under contract No.201505002-1the Beijing Higher Education Young Elite Teacher Project under contract No.YETP0514
文摘To dates,most ship detection approaches for single-pol synthetic aperture radar（SAR） imagery try to ensure a constant false-alarm rate（CFAR）.A high performance ship detector relies on two key components：an accurate estimation to a sea surface distribution and a fine designed CFAR algorithm.First,a novel nonparametric sea surface distribution estimation method is developed based on n-order Bézier curve.To estimate the sea surface distribution using n-order Bézier curve,an explicit analytical solution is derived based on a least square optimization,and the optimal selection also is presented to two essential parameters,the order n of Bézier curve and the number m of sample points.Next,to validate the ship detection performance of the estimated sea surface distribution,the estimated sea surface distribution by n-order Bézier curve is combined with a cell averaging CFAR（CA-CFAR）.To eliminate the possible interfering ship targets in background window,an improved automatic censoring method is applied.Comprehensive experiments prove that in terms of sea surface estimation performance,the proposed method is as good as a traditional nonparametric Parzen window kernel method,and in most cases,outperforms two widely used parametric methods,K and G0 models.In terms of computation speed,a major advantage of the proposed estimation method is the time consuming only depended on the number m of sample points while independent of imagery size,which makes it can achieve a significant speed improvement to the Parzen window kernel method,and in some cases,it is even faster than two parametric methods.In terms of ship detection performance,the experiments show that the ship detector which constructed by the proposed sea surface distribution model and the given CA-CFAR algorithm has wide adaptability to different SAR sensors,resolutions and sea surface homogeneities and obtains a leading performance on the test dataset.
基金Supported by the National Natural Science Foundation of China(61572430,61303144)the Natural Science Foundation of Zhejiang Province(LY15F020002,LY16F020020)the Ningbo Natural Science Foundation(2016A610223)
文摘In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.
基金Project(2016YFB0300801)supported by the National Key Research and Development Program of ChinaProject(51371045)supported by the National Natural Science Foundation of China
文摘According to inverse heat transfer theory, the evolutions of synthetic surface heat transfer coefficient（SSHTC） of the quenching surface of 7B50 alloy during water-spray quenching were simulated by the Pro CAST software based on accurate cooling curves measured by the modified Jominy specimen and temperature-dependent thermo-physical properties of 7 B50 alloy calculated using the JMat Pro software. Results show that the average cooling rate at 6 mm from the quenching surface and 420-230 ℃（quench sensitive temperature range） is 45.78℃/s. The peak-value of the SSHTC is 69 kW/（m^2·K） obtained at spray quenching for 0.4 s and the corresponding temperature of the quenching surface is 160 ℃. In the initial stage of spray quenching, the phenomenon called ＂temperature plateau＂ appears on the cooling curve of the quenching surface. The temperature range of this plateau is 160-170℃ with the duration about 3 s. During the temperature plateau, heat transfer mechanism of the quenching surface transforms from nucleate boiling regime to single-phase convective regime.
文摘We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces that interpolate the curve network of a ship huliform.First,the curves in the network are classified into two types;boundary curves and ＂reference curves＂,The boundary curves correspond to a set of rectangular（or triangular）topological type that can be representes with tensot-product （or degenerate）B-spline surface patches.Next,in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing ＂virtual＂isoparametric curves.Finally,a discrete G^1 continuous B-spline surface is gencrated by a surface fitting algorithm.Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.
