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Bézier curves with shape parameter 被引量:5
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作者 王文涛 汪国昭 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第6期497-501,共5页
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
关键词 Bézier curve Bézier basis with shape parameter Bernstein basis
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A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves
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作者 Nihat Arslan Kali Gurkahraman 《Computers, Materials & Continua》 SCIE EI 2023年第4期331-350,共20页
Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an... Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves. 展开更多
关键词 Contour tracing algorithm bézier curve B-spline curve object shape reconstruction
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A synthetic aperture radar sea surface distribution estimation by n-order Bézier curve and its application in ship detection 被引量:3
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作者 LANG Haitao ZHANG Jie +2 位作者 WANG Yiduo ZHANG Xi MENG Junmin 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2016年第9期117-125,共9页
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
关键词 Bézier curve nonparametric method ship detection sea surface distribution synthetic aperture radar
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Rational offset approximation of rational Bézier curves 被引量:2
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作者 CHENG Min WANG Guo-jin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第9期1561-1565,共5页
The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve ... The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational approximation algorithm of offset curve, which preserves the direction of normal, is presented. 展开更多
关键词 Rational Bézier curve Parametric speed OFFSET Rational approximation
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Improvement of the termination criterion for subdivision of the rational Bézier curves 被引量:2
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作者 章仁江 王国瑾 《Journal of Zhejiang University Science》 EI CSCD 2003年第1期47-52,共6页
By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of t... By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed. 展开更多
关键词 Rational Bézier curves SUBDIVISION Termination criterion.
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Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization 被引量:2
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作者 Xuli Han Jing Yang 《Journal of Applied Mathematics and Physics》 2016年第1期8-15,共8页
In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to ... In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure of the distance between original high order Bézier curve and degree-reduced curve. The other part represents the second derivative of degree-reduced curve. We tackle two kinds of conditions which are position vector constraint and tangent vector constraint respectively. The explicit representations of unknown points are presented. Some examples are illustrated to show the influence of the differential terms to approximation and smoothness effect. 展开更多
关键词 Bézier curve Degree Reduction Endpoint Constraint Differential Constraint L2-Norm
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Unifying representation of Bézier curve and two kinds of generalized ball curves 被引量:4
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作者 ZHU Xiaolin WANG Zhihua 《Computer Aided Drafting,Design and Manufacturing》 2012年第2期32-38,共7页
This paper presents a new basis, the WSB basis, which unifies the Bemstein basis, Wang-Ball basis and Said-Ball basis, and therefore the Bézier curve, Wang-Ball curve and Said-Ball curve are the special cases of ... This paper presents a new basis, the WSB basis, which unifies the Bemstein basis, Wang-Ball basis and Said-Ball basis, and therefore the Bézier curve, Wang-Ball curve and Said-Ball curve are the special cases of the WSB curve based on the WSB basis In addition, the relative degree elevation formula, recursive algorithm and conversion formula between the WSB basis and the Bern- stein basis are given. 展开更多
关键词 BASIS WSB curve Wang-Ball curve Bézier curve degree elevation formula recursive algorithm
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Sine Transformation and the Reparametrization of Bézier Curves 被引量:1
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作者 LIANG Xi-kun TAO Li-min 《Computer Aided Drafting,Design and Manufacturing》 2007年第2期23-27,共5页
A solution to the reparametrization of Bézier curves by sine transformation of Bemstein basis is presented. The new effective reparametrization method is given through the following procedures: educing Sine Bems... A solution to the reparametrization of Bézier curves by sine transformation of Bemstein basis is presented. The new effective reparametrization method is given through the following procedures: educing Sine Bemstein-Bézier Class-SBBC function, defining SBBC curve and discussing the relation between SBBC and Bézier curve. 展开更多
关键词 sine transformation SBBC functions SBBC curves Bézier curve repararnetrization
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PH-spline approximation for Bézier curve and rendering offset
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作者 郑志浩 汪国昭 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2004年第3期94-100,共7页
In this paper, a G1, C1, C2 PH-spline is employed as an approximation for a given Bzier curve within error bound and further renders offset which can be regarded as an approximate offset to the Bzier curve. The errors... In this paper, a G1, C1, C2 PH-spline is employed as an approximation for a given Bzier curve within error bound and further renders offset which can be regarded as an approximate offset to the Bzier curve. The errors between PH-spline and the Bzier curve, the offset to PH-spline and the offset to the given Bzier curve are also estimated. A new algorithm for constructing offset to the Bzier curve is proposed. 展开更多
关键词 PH-spline Bézier curve OFFSET Approximation Error
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A class of quasi Bézier curves based on hyperbolic polynomials
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作者 沈莞蔷 汪国昭 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第B08期116-123,共8页
This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis fo... This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variable t to arbitrary close interval [r, s] (r〈s). 展开更多
关键词 Bemstein basis Bézier curve Hyperbolic polynomials Extended Tchebyshev system B-base
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Shape modification of Bézier curves by constrained optimization
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作者 吴庆标 夏飞海 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第B08期124-127,共4页
The Bézier curve is one of the most commonly used parametric curves in CAGD and Computer Graphics and has many good properties for shape design. Developing more convenient techniques for designing and modifying B... The Bézier curve is one of the most commonly used parametric curves in CAGD and Computer Graphics and has many good properties for shape design. Developing more convenient techniques for designing and modifying Bézier curve is an im- portant problem, and is also an important research issue in CAD/CAM and NC technology fields. This work investigates the optimal shape modification of Bézier curves by geometric constraints. This paper presents a new method by constrained optimi- zation based on changing the control points of the curves. By this method, the authors modify control points of the original Bézier curves to satisfy the given constraints and modify the shape of the curves optimally. Practical examples are also given. 展开更多
关键词 Shape modification Bézier curve Constrained optimization
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A New Fractional Rational Bézier Curve
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作者 吴蓓蓓 顾传青 《Journal of Shanghai University(English Edition)》 CAS 2005年第3期216-218,共3页
Based on rational Bézier curves given by Ron Goldman, a new fractional rational Bézier curve was first defined in terms of fractional Bernstein bases. Moreover, some basic properties were dicussed and a theo... Based on rational Bézier curves given by Ron Goldman, a new fractional rational Bézier curve was first defined in terms of fractional Bernstein bases. Moreover, some basic properties were dicussed and a theorem connected to Poisson curves was obtained. Some examples in this paper were given by the visual results. 展开更多
关键词 fractional Bernstein bases fractional rational Bézier curves Poisson curves.
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An optimization method for rational Bézier curve design
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作者 HAN Xuli SHUAI Jun HAN Jing 《Computer Aided Drafting,Design and Manufacturing》 2012年第4期41-45,共5页
Adjusting weights as a shape control tool in rational B6zier curve design is not easy because the weights have a global in- fluence. The curve could not approximate control polygon satisfactorily by an interactive man... Adjusting weights as a shape control tool in rational B6zier curve design is not easy because the weights have a global in- fluence. The curve could not approximate control polygon satisfactorily by an interactive manner. In order to produce a curve close enough to control polygon at every control vertex, an optimization model is established to minimize the distance between rational B6zier curve and its control points. This optimization problem is converted to a quadratic programming problem by separating and recombining the objective function. The new combined multi-objective optimization problem is reasonable and easy to solve. With an optimal parameter, the computing process is discussed. Comparative examples show that the designed curve is closer to control polygon and preserves the shape of the control polygon well. 展开更多
关键词 curve design OPTIMIZATION rational B6zier curve shape modification quadratic programming
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COMPUTING AREAS BOUNDED BYRATIONAL BEZIER CURVES 被引量:4
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作者 Guojin Wang Thomas W. Sederberg 《Computer Aided Drafting,Design and Manufacturing》 1994年第2期18-27,共2页
An approach is presented for computing integral values, such as areas and volumes of revo-lution . of regions bounded by rational plane B zier curves. The method approximates rational curveswith polynomial curves, an... An approach is presented for computing integral values, such as areas and volumes of revo-lution . of regions bounded by rational plane B zier curves. The method approximates rational curveswith polynomial curves, and then computes the integral values on those polynomial curves. Errorbounds are provided. For high precision, this new algorithm performs much more quickly than con-ventional numerical methods. 展开更多
关键词 B zier curves area : volume of revolution polynomial approximation: error bounds
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TP-Bézier曲线的光滑拼接
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作者 张丹丹 吴欢欢 《佳木斯大学学报(自然科学版)》 CAS 2016年第5期812-814,共3页
讨论了一种扩展的Bézier曲线-TP-Bézier曲线的拼接问题,分析了三次TP-Bézier曲线间的、和、光滑拼接的充要条件,并给出了几何造型的实例。
关键词 tp-bézier曲线 基函数 形状参数 曲线拼接
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Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation 被引量:5
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作者 Karsten Bock Jorg Stiller 《Applied Mathematics》 2014年第21期3318-3327,共10页
We investigate different techniques for fitting Bézier curves to surfaces in context of high-order curvilinear mesh generation. Starting from distance-based least-squares fitting we develop an incremental algorit... We investigate different techniques for fitting Bézier curves to surfaces in context of high-order curvilinear mesh generation. Starting from distance-based least-squares fitting we develop an incremental algorithm, which incorporates approximations of stretch and bending energy. In the process, the algorithm reduces the energy weight in favor of accuracy, leading to an optimized set of sampling points. This energy-minimizing fitting strategy is applied to analytically defined as well as triangulated surfaces. The results confirm that the proposed method straightens and shortens the curves efficiently. Moreover the method preserves the accuracy and convergence behavior of distance-based fitting. Preliminary application to surface mesh generation shows a remarkable improvement of patch quality in high curvature regions. 展开更多
关键词 curvilinear Mesh Generation High-Order Methods Bézier curves curve Fitting Energy Minimization
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Curve intersection based on cubic hybrid clipping
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作者 Yaqiong Wu Xin Li 《Visual Computing for Industry,Biomedicine,and Art》 EI 2022年第1期201-213,共13页
This study presents a novel approach to computing all intersections between two Bézier curves using cubic hybridclipping. Each intersection is represented by two strip intervals that contain an intersection. In e... This study presents a novel approach to computing all intersections between two Bézier curves using cubic hybridclipping. Each intersection is represented by two strip intervals that contain an intersection. In each step, one curve isbounded by two fat lines, and the other is bounded by two cubic Bézier curves, clipping away the domain that doesnot contain the intersections. By selecting the moving control points of the cubic hybrid curves, better cubic polynomial bounds are obtained to make the proposed method more efficient. It was proved that the two strip intervalshave second- and fourth-order convergence rates for transversal intersections. Experimental results show that thenew algorithm is the most efficient among all existing curve/curve intersection approaches. 展开更多
关键词 Bézier curve curve intersection Hybrid clipping
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Free-Form Laminated Doubly-Curved Shells and Panels of Revolution Resting on Winkler-Pasternak Elastic Foundations: A 2-D GDQ Solution for Static and Free Vibration Analysis
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作者 Francesco Tornabene Alessandro Ceruti 《World Journal of Mechanics》 2013年第1期1-25,共25页
This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations using the Generalized Differential Quadrature (GDQ) method... This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations using the Generalized Differential Quadrature (GDQ) method. The analyses are worked out considering the First-order Shear Deformation Theory (FSDT) for the above mentioned moderately thick structural elements. The effect of the shell curvatures is included from the beginning of the theory formulation in the kinematic model. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Simple Rational Bézier curves are used to define the meridian curve of the revolution structures. The discretization of the system by means of the GDQ technique leads to a standard linear problem for the static analysis and to a standard linear eigenvalue problem for the dynamic analysis. Comparisons between the present formulation and the Reissner-Mindlin theory are presented. Furthermore, GDQ results are compared with those obtained by using commercial programs. Very good agreement is observed. Finally, new results are presented in order to investtigate the effects of the Winkler modulus, the Pasternak modulus and the inertia of the elastic foundation on the behavior of laminated shells of revolution. 展开更多
关键词 Doubly-curved SHELLS of REVOLUTION Rational Bézier curves LAMINATED Composite SHELLS Winkler-Pasternak Foundation First-Order Shear Deformation Theory Generalized Differential Quadrature Method
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正则有理Bezier曲线的等距曲线算法 被引量:3
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作者 方逵 赵军 《国防科技大学学报》 EI CAS CSCD 北大核心 1996年第1期110-113,共4页
通过利用改进的有理德卡斯特里奥算法求得正则有理n次Bezier曲线各点处的切矢,由此得到各点的单位法矢量,应用于求原始曲线的等距曲线,从而巧妙地解决了原始正则有理n次Bezier曲线上各点的单位法矢量难求的困难。该方... 通过利用改进的有理德卡斯特里奥算法求得正则有理n次Bezier曲线各点处的切矢,由此得到各点的单位法矢量,应用于求原始曲线的等距曲线,从而巧妙地解决了原始正则有理n次Bezier曲线上各点的单位法矢量难求的困难。该方法几何意义明显,算法简洁,实践效果比较好,最后本文给出了两个实例。 展开更多
关键词 CAGD 等距曲线 算法 有理曲线 BEzier曲线
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三次T-Bézier曲线的光顺延拓 被引量:2
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作者 喻德生 江卯 曾接贤 《计算机工程与设计》 CSCD 北大核心 2013年第4期1318-1323,共6页
将曲线的最小物理变形能量作为目标函数,提出了一种三次T-Bézier曲线曲面的光顺延拓算法。利用G2连续性作为约束条件,则延拓的曲线具有两个自由度,并取其中的一个自由度为零;基于延拓曲线的最小物理变形能量确定第二个自由度及延... 将曲线的最小物理变形能量作为目标函数,提出了一种三次T-Bézier曲线曲面的光顺延拓算法。利用G2连续性作为约束条件,则延拓的曲线具有两个自由度,并取其中的一个自由度为零;基于延拓曲线的最小物理变形能量确定第二个自由度及延拓曲线的控制点,进而确定延拓曲线,重新参数化所延拓的曲线可以与原曲线在拼接点处C3连续拼接;此外,将该方法应用于双三次T-Bézier曲面的延拓。实例表明,该方法构造的曲线曲面具有较好的光顺性。 展开更多
关键词 物理变形能量 三次T-Bézier曲线 光顺延拓 G2连续 C3连续
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