In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the max...In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the maximum distance of any pair of nodes in the support domain.The proposed method is verified and shows good performance.The results are stable and accurate with any number of nodes and an arbitrary nodal distribution.Notably,the support domain should be large enough to obtain accurate results.This method is then applied for transient analysis of curved shell structures made from functionally graded materials with complex geometries.Through several numerical examples,the accuracy of the proposed approach is demonstrated and discussed.Additionally,the influence of various factors on the dynamic behavior of the structures,including the power-law index,different materials,loading conditions,and geometrical parameters of the structures,was investigated.展开更多
We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the ...We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.展开更多
By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Bal...By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.展开更多
In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape paramet...In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and the Bézier curves. Moreover the shape parameter can adjust the curves’ shape with the same control polygon. As the increase of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier surface with shape parameter is also constructed and it has most properties of Bézier surface.展开更多
To recognize circular objects rapidly in satellite remote sensing imagery, an approach using their geometry properties is presented. The original image is segmented to be a binary one by one dimension maximum entropy ...To recognize circular objects rapidly in satellite remote sensing imagery, an approach using their geometry properties is presented. The original image is segmented to be a binary one by one dimension maximum entropy threshold algorithm and the binary image is labeled with an algorithm based on recursion technique. Then, shape parameters of all labeled regions are calculated and those regions with shape parameters satisfying certain conditions are recognized as circular objects. The algorithm is described in detail, and comparison experiments with the randomized Hough transformation （RHT） are also provided. The experimental results on synthetic images and real images show that the proposed method has the merits of fast recognition rate, high recognition efficiency and the ability of anti-noise and anti-jamming. In addition, the method performs well when some circular objects are little deformed and partly misshapen.展开更多
In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate con...In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.展开更多
The shape parameter of the Gamma size distribution plays a key role in the evolution of the cloud droplet spectrum in the bulk parameterization schemes. However, due to the inaccurate specification of the shape parame...The shape parameter of the Gamma size distribution plays a key role in the evolution of the cloud droplet spectrum in the bulk parameterization schemes. However, due to the inaccurate specification of the shape parameter in the commonly used bulk double-moment schemes, the cloud droplet spectra cannot reasonably be described during the condensation process. Therefore, a newly-developed triple-parameter condensation scheme with the shape parameter diagnosed through the number concentration, cloud water content, and reflectivity factor of cloud droplets can be applied to improve the evolution of the cloud droplet spectrum. The simulation with the new parameterization scheme was compared to those with a high-resolution Lagrangian bin scheme, the double-moment schemes in a parcel model, and the observation in a 1.5D Eulerian model that consists of two cylinders. The new scheme with the shape parameter varying with time and space can accurately simulate the evolution of the cloud droplet spectrum. Furthermore, the volume-mean radius and cloud water content simulated with the new scheme match the Lagrangian analytical solutions well, and the errors are steady, within approximately 0.2%.展开更多
Wind power is an increasingly important alternative for obtaining energy supplies, both in large interconnected power systems and in smaller hybrid systems and even in backup systems. The temporal and spatial variabil...Wind power is an increasingly important alternative for obtaining energy supplies, both in large interconnected power systems and in smaller hybrid systems and even in backup systems. The temporal and spatial variability of the winds represent an obstacle to be overcome so that wind energy can be increasingly used. The capacity factor of wind farms shows how this variability impacts the operation of the plants and its value is of the order of 30% to 35%. The variability of the wind speed is influenced if the point of interest is on land or on sea, the shape of the surface, the proximity of water bodies, among other factors. The availability of wind is best described by the Weibull probability distribution, which has as one of its defining parameters one which is termed as shape parameter. This parameter is much higher as higher is the variability of the wind speed. This paper studies the subtle influence of Weibull shape parameter on the optimal combination of components in a wind diesel hybrid system, by means of computer simulations with the well known software Homer. The results indicate a relatively small influence (as expected) in the studied system, which appears particularly when the cost of diesel is higher and the availability of wind is lower.展开更多
In CAD/CAM, mesh rather than smooth surface is only needed sometimes. A mesh-generating method from permanence principle of Coons patch is developed. A new mesh point is defined through local small subpatch and all me...In CAD/CAM, mesh rather than smooth surface is only needed sometimes. A mesh-generating method from permanence principle of Coons patch is developed. A new mesh point is defined through local small subpatch and all mesh points are computed by a linear system with special symmetric block tridiagonal coefficient matrix. By simplification, the determinant of coefficient matrix is determined by determinants of submatrices. Condition of existence of solution is given. Whether coefficient matrix is singular can be judged by a simple polynomial function with the eigenvalue of submatrix as variable. Numerical examples demonstrate the effects of shape parameters.展开更多
We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence.These curves not only have the many valued properties of the usual non-uniform B-spline curves,but also are shape adjustab...We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence.These curves not only have the many valued properties of the usual non-uniform B-spline curves,but also are shape adjustable under fixed control polygons.Our method is based on the degree elevation of B-spline curves,where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline.We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms,which are indispensable from the user's perspective.展开更多
Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curv...Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape pa- rameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced．展开更多
This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control poin...This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.展开更多
A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape paramet...A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.展开更多
A new local control spline based on shape parameters with G^2 continuity,called BLC-spline,is pro- posed.Not only is BLC-spline very smooth,but also the spline curve's characteristic polygon has only three control...A new local control spline based on shape parameters with G^2 continuity,called BLC-spline,is pro- posed.Not only is BLC-spline very smooth,but also the spline curve's characteristic polygon has only three control vertices,and the characteristic polyhedron has only nine control vertices.The behavior of lo- cal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β_0,β_1 and β_2 of BLC-spline,which are independent of the con- trol vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construct a space arc spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.展开更多
Through the single row drilling experiment,this paper studied the regularity of the tooth shape parameter's influence to the disc teeth's rock-breaking effect,which provided some basis for the composite teeth ...Through the single row drilling experiment,this paper studied the regularity of the tooth shape parameter's influence to the disc teeth's rock-breaking effect,which provided some basis for the composite teeth type roller bit's combined experimental study and the structure design of the tooth type.This experimental research is only for the circular arc disc teeth which is arranged on the composite teeth type roller bit's main tooth.The experiments were designed using the method of orthogonal design and the results were analyzed by the fuzzy optimization method.The results show that the disc tooth's drilling effect is the best when the tip diameter is 2 mm,taper angle is 30and the groove number is 8,and the disc tooth's drilling effect is the second best when the tip diameter is 3 mm,taper angle is 30and the groove number is 7.The above two combined ways of drilling effect's difference is very small(the difference of the degree of the membership is 0.003).展开更多
In the context of increasing dimensionality of design variables and the complexity of constraints, the efficacy of Surrogate-Based Optimization(SBO) is limited. The traditional linear and nonlinear dimensionality redu...In the context of increasing dimensionality of design variables and the complexity of constraints, the efficacy of Surrogate-Based Optimization(SBO) is limited. The traditional linear and nonlinear dimensionality reduction algorithms are mainly to decompose the mathematical matrix composed of design variables or objective functions in various forms, the smoothness of the design space cannot be guaranteed in the process, and additional constraint functions need to be added in the optimization, which increases the calculation cost. This study presents a new parameterization method to improve both problems of SBO. The new parameterization is addressed by decoupling affine transformations(dilation, rotation, shearing, and translation) within the Grassmannian submanifold, which enables a separate representation of the physical information of the airfoil in a highdimensional space. Building upon this, Principal Geodesic Analysis(PGA) is employed to achieve geometric control, compress the design space, reduce the number of design variables, reduce the dimensions of design variables and enhance predictive performance during the surrogate optimization process. For comparison, a dimensionality reduction space is defined using 95% of the energy,and RAE 2822 for transonic conditions are used as demonstrations. This method significantly enhances the optimization efficiency of the surrogate model while effectively enabling geometric constraints. In three-dimensional problems, it enables simultaneous design of planar shapes for various components of the aircraft and high-order perturbation deformations. Optimization was applied to the ONERA M6 wing, achieving a lift-drag ratio of 18.09, representing a 27.25% improvement compared to the baseline configuration. In comparison to conventional surrogate model optimization methods, which only achieved a 17.97% improvement, this approach demonstrates its superiority.展开更多
The age at which a woman enters natural menopause has also been associated to death from any cause.Menopause is a natural component of aging that happens between the ages of 45 and 55,with the average menopausal age b...The age at which a woman enters natural menopause has also been associated to death from any cause.Menopause is a natural component of aging that happens between the ages of 45 and 55,with the average menopausal age being 51.Previous research has revealed the age at which women reach menopause,but there is no evidence to support the link between menopause and longevity.We made a study in assessing the limits of maximum lifespan at menopausal age in our previous article.In this paper,we aim to predict the maximum lifespan of women at mean menopausal age.展开更多
The instantaneous morphological transition of triangular Al_(2)O_(3) particles with various sizes in the molten Ca-treated steel was observed using a confocal scanning laser microscope at the steelmaking temperature.T...The instantaneous morphological transition of triangular Al_(2)O_(3) particles with various sizes in the molten Ca-treated steel was observed using a confocal scanning laser microscope at the steelmaking temperature.The composition of inclusions at different times was analyzed using scanning electron microscopy-energy dispersive spectroscopy.The shape evolution of particles was characterized by the shape parameter of overall regularity.It was found that the overall regularity of particles gradually increased with time during the calcium treatment.The geometry of particles tended to be more rounded and regular as the overall regularity increased during the modification process.An empirical formula was proposed to predict the composition of inclusion particles based on their overall regularity during the calcium treatment.When the CaO/Al_(2)O_(3) mass ratio in the particle increased to 0.451,the particle was considered an ideal spherical calcium aluminate inclusion with the overall regularity of 1.Smaller particle sizes promoted the transformation of Al_(2)O_(3) inclusions to spherical calcium aluminates during the calcium treatment.展开更多
Surface roughness and shape play an important role on the behavior of particles in various processes such as flotation. In this re- search, the influence of different grinding methods on the surface roughness and shap...Surface roughness and shape play an important role on the behavior of particles in various processes such as flotation. In this re- search, the influence of different grinding methods on the surface roughness and shape characteristics of quartz particles as well as the effect of these parameters on the flotation of the particles was investigated. The surface roughness of the particles was determined by measuring their specific surface area via the gas adsorption method. The shape characteristics of the particles were measured and calculated by images obtained by scanning electron microscopy via an image analysis system. The flotation kinetics was determined using a laboratory flotation cell. The results showed that the particles of rod mill products have higher roughness and elongation ratio and lower roundness than the parti- cles of ball mill products. The flotation kinetics constant of the particles increased with their surface roughness increasing. Particles with higher elongation and lower roundness indicated higher floatability. In addition, the influence of the surface roughness on the flotation kinet- ics was greater than that of shape parameters.展开更多
基金Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study
文摘In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the maximum distance of any pair of nodes in the support domain.The proposed method is verified and shows good performance.The results are stable and accurate with any number of nodes and an arbitrary nodal distribution.Notably,the support domain should be large enough to obtain accurate results.This method is then applied for transient analysis of curved shell structures made from functionally graded materials with complex geometries.Through several numerical examples,the accuracy of the proposed approach is demonstrated and discussed.Additionally,the influence of various factors on the dynamic behavior of the structures,including the power-law index,different materials,loading conditions,and geometrical parameters of the structures,was investigated.
基金supported by the National Natural Science Foundation ofChina (No. 60673031)the National Basic Research Program(973) of China (No. 2004CB719400)
文摘We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.
基金Supported by the National Natural Science Foundation of China(60970097 and 11271376)Postdoctoral Science Foundation of China(2015M571931)Graduate Students Scientific Research Innovation Project of Hunan Province(CX2012B111)
文摘By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.
基金Project supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973)of China (No. G2002CB12101)
文摘In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and the Bézier curves. Moreover the shape parameter can adjust the curves’ shape with the same control polygon. As the increase of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier surface with shape parameter is also constructed and it has most properties of Bézier surface.
文摘To recognize circular objects rapidly in satellite remote sensing imagery, an approach using their geometry properties is presented. The original image is segmented to be a binary one by one dimension maximum entropy threshold algorithm and the binary image is labeled with an algorithm based on recursion technique. Then, shape parameters of all labeled regions are calculated and those regions with shape parameters satisfying certain conditions are recognized as circular objects. The algorithm is described in detail, and comparison experiments with the randomized Hough transformation （RHT） are also provided. The experimental results on synthetic images and real images show that the proposed method has the merits of fast recognition rate, high recognition efficiency and the ability of anti-noise and anti-jamming. In addition, the method performs well when some circular objects are little deformed and partly misshapen.
基金Project supported by the National Basic Research Program (973) of China (No. 2004CB719400)the National Natural Science Founda-tion of China (Nos. 60673031 and 60333010) the National Natural Science Foundation for Innovative Research Groups of China (No. 60021201)
文摘In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41275147 and 41875173)the STS Program of Inner Mongolia Meteorological Service, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences and Institute of Atmospheric Physics, Chinese Academy of Sciences (Grant No. 2021CG0047)
文摘The shape parameter of the Gamma size distribution plays a key role in the evolution of the cloud droplet spectrum in the bulk parameterization schemes. However, due to the inaccurate specification of the shape parameter in the commonly used bulk double-moment schemes, the cloud droplet spectra cannot reasonably be described during the condensation process. Therefore, a newly-developed triple-parameter condensation scheme with the shape parameter diagnosed through the number concentration, cloud water content, and reflectivity factor of cloud droplets can be applied to improve the evolution of the cloud droplet spectrum. The simulation with the new parameterization scheme was compared to those with a high-resolution Lagrangian bin scheme, the double-moment schemes in a parcel model, and the observation in a 1.5D Eulerian model that consists of two cylinders. The new scheme with the shape parameter varying with time and space can accurately simulate the evolution of the cloud droplet spectrum. Furthermore, the volume-mean radius and cloud water content simulated with the new scheme match the Lagrangian analytical solutions well, and the errors are steady, within approximately 0.2%.
文摘Wind power is an increasingly important alternative for obtaining energy supplies, both in large interconnected power systems and in smaller hybrid systems and even in backup systems. The temporal and spatial variability of the winds represent an obstacle to be overcome so that wind energy can be increasingly used. The capacity factor of wind farms shows how this variability impacts the operation of the plants and its value is of the order of 30% to 35%. The variability of the wind speed is influenced if the point of interest is on land or on sea, the shape of the surface, the proximity of water bodies, among other factors. The availability of wind is best described by the Weibull probability distribution, which has as one of its defining parameters one which is termed as shape parameter. This parameter is much higher as higher is the variability of the wind speed. This paper studies the subtle influence of Weibull shape parameter on the optimal combination of components in a wind diesel hybrid system, by means of computer simulations with the well known software Homer. The results indicate a relatively small influence (as expected) in the studied system, which appears particularly when the cost of diesel is higher and the availability of wind is lower.
基金Supported by National Natural Science Foundation of China(No.60970097,No.11271376)
文摘In CAD/CAM, mesh rather than smooth surface is only needed sometimes. A mesh-generating method from permanence principle of Coons patch is developed. A new mesh point is defined through local small subpatch and all mesh points are computed by a linear system with special symmetric block tridiagonal coefficient matrix. By simplification, the determinant of coefficient matrix is determined by determinants of submatrices. Condition of existence of solution is given. Whether coefficient matrix is singular can be judged by a simple polynomial function with the eigenvalue of submatrix as variable. Numerical examples demonstrate the effects of shape parameters.
基金Project supported by the National Natural Science Foundation of China (Nos. 60970079,60933008,61100105,and 61100107)the Natural Science Foundation of Fujian Province of China (No.2011J05007)the National Defense Basic Scientific Research Program of China (No. B1420110155)
文摘We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence.These curves not only have the many valued properties of the usual non-uniform B-spline curves,but also are shape adjustable under fixed control polygons.Our method is based on the degree elevation of B-spline curves,where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline.We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms,which are indispensable from the user's perspective.
基金We, wish to express our gratitude to the referees for their valuable re- marks for improvements. The research is supported by the National Natural Science Foun-dation of China （No. 60970097, No. 11271376）, Postdoctoral Science Foundation of China （2015M571931）, and Graduate Students Scientific Research Innovation Project of Hunan Province （No. CX2012Blll）.
文摘Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape pa- rameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced．
文摘This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.
基金Supported by the National Natural Science Foundation of China(No.10871208,No.60970097)Graduate Students Scientific Research Innovation Project of Hunan Province(No.CX2012B111)+1 种基金the Postdoctoral Science Foundation of China(No.2015M571931)the Fundamental Research Funds for the Central Universities(No.2017MS121)
文摘A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.
文摘A new local control spline based on shape parameters with G^2 continuity,called BLC-spline,is pro- posed.Not only is BLC-spline very smooth,but also the spline curve's characteristic polygon has only three control vertices,and the characteristic polyhedron has only nine control vertices.The behavior of lo- cal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β_0,β_1 and β_2 of BLC-spline,which are independent of the con- trol vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construct a space arc spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.
基金The authors are grateful to Applied basic research project of Sichuan Province(No.2015JY0057)Natural science project of Sichuan Provincial Education Department(No.15ZA0046)for their financial support to carry out this research.The insightful and constructive comments of the anonymous reviewers are also gratefully acknowledged.
文摘Through the single row drilling experiment,this paper studied the regularity of the tooth shape parameter's influence to the disc teeth's rock-breaking effect,which provided some basis for the composite teeth type roller bit's combined experimental study and the structure design of the tooth type.This experimental research is only for the circular arc disc teeth which is arranged on the composite teeth type roller bit's main tooth.The experiments were designed using the method of orthogonal design and the results were analyzed by the fuzzy optimization method.The results show that the disc tooth's drilling effect is the best when the tip diameter is 2 mm,taper angle is 30and the groove number is 8,and the disc tooth's drilling effect is the second best when the tip diameter is 3 mm,taper angle is 30and the groove number is 7.The above two combined ways of drilling effect's difference is very small(the difference of the degree of the membership is 0.003).
基金supported by the National Natural Science Foundation of China (No.92371201).
文摘In the context of increasing dimensionality of design variables and the complexity of constraints, the efficacy of Surrogate-Based Optimization(SBO) is limited. The traditional linear and nonlinear dimensionality reduction algorithms are mainly to decompose the mathematical matrix composed of design variables or objective functions in various forms, the smoothness of the design space cannot be guaranteed in the process, and additional constraint functions need to be added in the optimization, which increases the calculation cost. This study presents a new parameterization method to improve both problems of SBO. The new parameterization is addressed by decoupling affine transformations(dilation, rotation, shearing, and translation) within the Grassmannian submanifold, which enables a separate representation of the physical information of the airfoil in a highdimensional space. Building upon this, Principal Geodesic Analysis(PGA) is employed to achieve geometric control, compress the design space, reduce the number of design variables, reduce the dimensions of design variables and enhance predictive performance during the surrogate optimization process. For comparison, a dimensionality reduction space is defined using 95% of the energy,and RAE 2822 for transonic conditions are used as demonstrations. This method significantly enhances the optimization efficiency of the surrogate model while effectively enabling geometric constraints. In three-dimensional problems, it enables simultaneous design of planar shapes for various components of the aircraft and high-order perturbation deformations. Optimization was applied to the ONERA M6 wing, achieving a lift-drag ratio of 18.09, representing a 27.25% improvement compared to the baseline configuration. In comparison to conventional surrogate model optimization methods, which only achieved a 17.97% improvement, this approach demonstrates its superiority.
文摘The age at which a woman enters natural menopause has also been associated to death from any cause.Menopause is a natural component of aging that happens between the ages of 45 and 55,with the average menopausal age being 51.Previous research has revealed the age at which women reach menopause,but there is no evidence to support the link between menopause and longevity.We made a study in assessing the limits of maximum lifespan at menopausal age in our previous article.In this paper,we aim to predict the maximum lifespan of women at mean menopausal age.
基金financially supported by the National Key R&D Program,China(No.2023YFB3709900)the National Nature Science Foundation of China(No.U22A20171)+1 种基金China Baowu Low Carbon Metallurgy Innovation Foudation(No.BWLCF202315)Hebei Steel Group’s Key Science and Technology Program,China(No.HG2022103)。
文摘The instantaneous morphological transition of triangular Al_(2)O_(3) particles with various sizes in the molten Ca-treated steel was observed using a confocal scanning laser microscope at the steelmaking temperature.The composition of inclusions at different times was analyzed using scanning electron microscopy-energy dispersive spectroscopy.The shape evolution of particles was characterized by the shape parameter of overall regularity.It was found that the overall regularity of particles gradually increased with time during the calcium treatment.The geometry of particles tended to be more rounded and regular as the overall regularity increased during the modification process.An empirical formula was proposed to predict the composition of inclusion particles based on their overall regularity during the calcium treatment.When the CaO/Al_(2)O_(3) mass ratio in the particle increased to 0.451,the particle was considered an ideal spherical calcium aluminate inclusion with the overall regularity of 1.Smaller particle sizes promoted the transformation of Al_(2)O_(3) inclusions to spherical calcium aluminates during the calcium treatment.
文摘Surface roughness and shape play an important role on the behavior of particles in various processes such as flotation. In this re- search, the influence of different grinding methods on the surface roughness and shape characteristics of quartz particles as well as the effect of these parameters on the flotation of the particles was investigated. The surface roughness of the particles was determined by measuring their specific surface area via the gas adsorption method. The shape characteristics of the particles were measured and calculated by images obtained by scanning electron microscopy via an image analysis system. The flotation kinetics was determined using a laboratory flotation cell. The results showed that the particles of rod mill products have higher roughness and elongation ratio and lower roundness than the parti- cles of ball mill products. The flotation kinetics constant of the particles increased with their surface roughness increasing. Particles with higher elongation and lower roundness indicated higher floatability. In addition, the influence of the surface roughness on the flotation kinet- ics was greater than that of shape parameters.
