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A new algorithm for designing developable Bézier surfaces 被引量:3
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作者 ZHANG Xing-wang WANG Guo-jin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期2050-2056,共7页
A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient condition... A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper. 展开更多
关键词 Bézier surfaces Developable surfaces Bemstein basis Linear independence Characteristic equations
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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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Reconstruction from contour lines based on bi-cubic Bézier spline surface 被引量:1
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作者 LI Zhong MA Li-zhuang +1 位作者 TAN Wu-zheng ZHAO Ming-xi 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第7期1241-1246,共6页
A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points on every contour, then we interpolate them by using cubic Bézier spline curve. For corre... A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points on every contour, then we interpolate them by using cubic Bézier spline curve. For corresponding points of different con- tours, we interpolate them by the cubic Bézier spline curve too, so the whole surface can be reconstructed by the bi-cubic Bézier spline surface. The reconstructed surface is smooth because every Bézier surface is patched with G2 continuity, the reconstruction speed is fast because we can use the forward elimination and backward substitution method to solve the system of tridiagonal equations. We give some reconstruction examples at the end of this paper. Experiments showed that our method is applicable and effective. 展开更多
关键词 CONTOUR surface reconstruction Bi-cubic Bézier surface G^2 continuity
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Computation of lower derivatives of rational triangular Bézier surfaces and their bounds estimation 被引量:1
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作者 张磊 王国瑾 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第B08期108-115,共8页
By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents so... By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents some explicit formulas of the first and second derivatives of rational triangular Bézier surface with respect to each variable (including the mixed derivative) and derives some estimations of bound both on the direction and magnitude of the corresponding derivatives. All the results above have value not only in surface theory but also in practice. 展开更多
关键词 Computer Aided Geometric Design DERIVATIVE Rational triangular Bézier surface BOUND
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Visible region extraction from a sequence of rational Bézier surfaces
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作者 RUAN Xiao-yu ZHANG Hui YONG Jun-hai 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第7期1233-1240,共8页
A method for computing the visible regions of free-form surfaces is proposed in this paper. Our work is focused on accurately calculating the visible regions of the sequenced rational Bézier surfaces forming a so... A method for computing the visible regions of free-form surfaces is proposed in this paper. Our work is focused on accurately calculating the visible regions of the sequenced rational Bézier surfaces forming a solid model and having coincident edges but no inner-intersection among them. The proposed method calculates the silhouettes of the surfaces without tessellating them into triangle meshes commonly used in previous methods so that arbitrary precision can be obtained. The computed sil- houettes of visible surfaces are projected onto a plane orthogonal to the parallel light. Then their spatial relationship is applied to calculate the boundaries of mutual-occlusion regions. As the connectivity of the surfaces on the solid model is taken into account, a surface clustering technique is also employed and the mutual-occlusion calculation is accelerated. Experimental results showed that our method is efficient and robust, and can also handle complex shapes with arbitrary precision. 展开更多
关键词 Rational Bézier surface VISIBILITY Self-occlusion Mutual-occlusion
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Convexity and Positivity of Bivariate Quadratic Bézier Surfaces over a Rectangle
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作者 DING You dong School of Computer Engineering and Science, Shanghai University, Shanghai 200072, China 《Journal of Shanghai University(English Edition)》 CAS 2001年第1期20-28,共9页
With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+... With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given. 展开更多
关键词 Bézier surface CONVEXITY POSITIVITY DISCRIMINANT
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Real-time accurate Free-Form Deformation in terms of triangular Bézier surfaces
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作者 CUI Yuan-min FENG Jie-qing 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第4期455-467,共13页
We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previ... We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessel- lation shader algorithms. 展开更多
关键词 accurate Free-Form Deformation GPU acceleration CUDA triangular B@zier surface.
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A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle
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作者 Sai Hao Xianghuai Dong 《American Journal of Computational Mathematics》 2020年第2期252-265,共14页
Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a suff... Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bézier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bézier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface. 展开更多
关键词 Convexity Condition Bézier surface De Casteljau Arithmetic Interpolation-Type surface
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Mixed tensor product negative Bernstein-Bézier surfaces
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作者 LIU Yanhong ZHANG Yuhua +1 位作者 CHEN Shuni ZENG Xiaoming 《Computer Aided Drafting,Design and Manufacturing》 2012年第4期55-58,共4页
A kind of mixed tensor product negative Bemstein-B6zier basis function is presented in this paper. Some important prop- erties of this kind of basis function are discussed and mixed tensor product negative Bemstein-B6... A kind of mixed tensor product negative Bemstein-B6zier basis function is presented in this paper. Some important prop- erties of this kind of basis function are discussed and mixed tensor product negative Bemstein-B6zier is defined based on it. The ba- sic properties of the such surface are discussed. Via de Casteljan algorithm, the evaluation algorithm and subdivision algorithm for mixed tensor product negative Bernstein-B6zier surfaces are derived as extensions of the algorithms of B6zier curves and negative Bernstein curves. 展开更多
关键词 tensor product negative Bemstein-B6zier basis function negative Bemstein-B6zier surface SUBDIVISION
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CE-Bézier可展曲面的设计与形状调整 被引量:3
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作者 秦新强 李凯 +1 位作者 胡钢 岳丽 《西安交通大学学报》 EI CAS CSCD 北大核心 2010年第3期47-51,共5页
为了解决工程中可展曲面位置与形状难以调整和控制的问题,基于3D射影空间中点和平面间的对偶性这一重要思想,提出了2种直接、简单有效的可展曲面设计新方法.首先,构造了一组含有2个形状参数α、γ的三次多项式调配函数,并定义了一种带2... 为了解决工程中可展曲面位置与形状难以调整和控制的问题,基于3D射影空间中点和平面间的对偶性这一重要思想,提出了2种直接、简单有效的可展曲面设计新方法.首先,构造了一组含有2个形状参数α、γ的三次多项式调配函数,并定义了一种带2个形状控制参数的CE-Bézier曲线族,然后利用这种带参数的CE-Bézier调配函数生成了具有CE-Bézier基的控制平面,并由该控制平面来进行可展曲面的设计,同时给出了在CE-Bézier基函数下可展曲面的参数表示形式.由新方法生成的可展曲面不仅具有灵活的局部形状可调性和更强的描述能力,而且保留了Bézier曲面的特性,特别是当α、γ都取值为1时,所生成的可展曲面即为Bézier可展曲面.2种可展曲面设计方法的应用实例表明,该设计方法不仅简单、有效,而且易于控制曲面形状,从而为可展曲面的设计提供了一种新途径. 展开更多
关键词 可展曲面 对偶性 形状控制参数 ce-bézier曲线
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CE-Bézier曲线曲面光滑拼接的研究 被引量:3
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作者 刘飞 秦新强 +2 位作者 胡钢 党发宁 杨雅迪 《微电子学与计算机》 CSCD 北大核心 2009年第5期223-226,230,共5页
CE-Bézier曲线是三次Bézier曲线的一种新扩展,它不仅具有与三次Bézier曲线类似的性质,而且具有优良的形状可调性和更好的逼近性.文中在对其端点性质和形状参数分析的基础上,给出了第一类CE-Bézier曲线间G1、G2拼接... CE-Bézier曲线是三次Bézier曲线的一种新扩展,它不仅具有与三次Bézier曲线类似的性质,而且具有优良的形状可调性和更好的逼近性.文中在对其端点性质和形状参数分析的基础上,给出了第一类CE-Bézier曲线间G1、G2拼接的充要条件;同时分析了两张CE-Bézier曲面片间G1拼接的几何条件,并给出了几何造型的实例.实例表明,CE-Bézier曲线曲面的拼接技术可广泛地应用于工程曲线曲面的造型中. 展开更多
关键词 ce-bézier 形状参数 拼接条件
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CE-Bézier曲面光滑拼接的研究与实现 被引量:1
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作者 胡钢 吉晓民 +1 位作者 沈晓芹 宋伟杰 《图学学报》 CSCD 北大核心 2012年第5期62-67,共6页
针对CE-Bézier曲面造型中复杂曲面难以用单一曲面来表示的问题,通过分析CE-Bézier曲线的唯一性,提出了一种新的CE-Bézier曲面的光滑拼接技术。首先,在分析第1类CE-Bézier曲线基函数及其端点性质的基础上,对第1类CE-... 针对CE-Bézier曲面造型中复杂曲面难以用单一曲面来表示的问题,通过分析CE-Bézier曲线的唯一性,提出了一种新的CE-Bézier曲面的光滑拼接技术。首先,在分析第1类CE-Bézier曲线基函数及其端点性质的基础上,对第1类CE-Bézier曲线的唯一性进行了研究,得出了对于同一条第1类CE-Bézier曲线可以有很多组不相同的控制顶点和形状参数与之对应的结论;其次,利用该结论进一步给出了两相邻第1类CE-Bézier曲面片间G1光滑拼接的一般几何条件,并通过合理地选取形状参数,进一步简化了该曲面的G1拼接条件;最后,给出了第1类CE-Bézier曲面光滑拼接的几何造型实例。实例结果表明,该方法简单、直观、易实现,有效地增强了CE-Bézier方法表达复杂曲线曲面的能力,可广泛地应用于工程复杂曲面的造型系统中。 展开更多
关键词 ce-bézier曲线 ce-bézier曲面 形状参数 光滑拼接 唯一性分析
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基于CE-Bézier曲面的拖拉机造型设计 被引量:1
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作者 郭磊 张春红 胡钢 《华南农业大学学报》 CAS CSCD 北大核心 2016年第4期112-116,共5页
【目的】用多张含有形状参数的CE-Bézier曲面光滑拼接进行拖拉机造型曲面的表示,解决拖拉机造型设计中复杂曲面无法用单一曲面进行描述的问题。【方法】构建多张CE-Bézier曲面,对这些曲面进行光滑拼接,并在调整各曲面公共边... 【目的】用多张含有形状参数的CE-Bézier曲面光滑拼接进行拖拉机造型曲面的表示,解决拖拉机造型设计中复杂曲面无法用单一曲面进行描述的问题。【方法】构建多张CE-Bézier曲面,对这些曲面进行光滑拼接,并在调整各曲面公共边界的位置及其形状参数的情况下,形成不同的拖拉机造型方案。【结果】快速得到多个拖拉机机身造型方案。【结论】该方法高效、易于操作,具有良好的应用前景。 展开更多
关键词 ce-bézier曲面 拖拉机 造型设计 CAD
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CE-Bézier与H-Bézier曲线的光滑拼接及应用
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作者 秦新强 黄自友 +1 位作者 胡钢 王伟伟 《计算机工程与应用》 CSCD 2012年第13期171-175,共5页
CE-Bézier曲线作为一种重要的带多形状参数的三次扩展Bézier曲线,不仅具有与三次Bézier曲线类似的性质,而且具有优良的形状可调性和更好的逼近性。为了进一步发展CE-Bézier曲线的相关理论,针对CE-Bézier曲线... CE-Bézier曲线作为一种重要的带多形状参数的三次扩展Bézier曲线,不仅具有与三次Bézier曲线类似的性质,而且具有优良的形状可调性和更好的逼近性。为了进一步发展CE-Bézier曲线的相关理论,针对CE-Bézier曲线无法精确表示指数曲线、悬链线等超越曲线的缺点,利用CE-Bézier曲线与H-Bézier曲线间的拼接技术,来处理CE-Bézier曲线造型中指数曲线、悬链线等超越曲线的表示问题。最后,给出了具体的数值实验;造型实例表明,该方法在计算机辅助几何设计中具有一定的应用价值。 展开更多
关键词 ce-bézier曲线 H-Bézier曲线 形状参数 拼接条件
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一种快速生成CE-Bézier旋转曲面的新方法
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作者 童小红 秦新强 胡钢 《西安理工大学学报》 CAS 北大核心 2013年第1期76-80,共5页
为了解决工程旋转曲面形状难以调节和控制的问题,提出了一种带两个形状参数的新型旋转曲面—CE-Bézier旋转曲面。基于超限向量值有理插值函数,结合含有两个形状参数的三次多项式基函数进行旋转曲面的设计,该方法生成的CE-Béz... 为了解决工程旋转曲面形状难以调节和控制的问题,提出了一种带两个形状参数的新型旋转曲面—CE-Bézier旋转曲面。基于超限向量值有理插值函数,结合含有两个形状参数的三次多项式基函数进行旋转曲面的设计,该方法生成的CE-Bézier旋转曲面不仅具有灵活的局部形状可调性,而且保留了Bézier曲面的特性。本研究给出了具体的数值实例,结果表明本研究的设计方法不仅简便、有效,而且易于控制旋转曲面的形状,从而可以广泛地应用于各种CAD/CAM曲线曲面造型系统中。 展开更多
关键词 ce-bézier曲线 旋转曲面 形状参数 超限向量值有理插值函数
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CE-Bézier曲线与二次均匀B样条曲线的拼接 被引量:2
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作者 洪玲 邢燕 《大学数学》 2015年第1期26-30,共5页
将B样条曲线转换为Bézier曲线,基于Bézier曲线间的光滑拼接的理论,研究了带多形状参数的Bézier曲线(CE-Bézier曲线)与均匀B样条曲线的拼接问题,得出均匀B样条曲线与CE-Bézier曲线的G0,G1,G2光滑拼接条件.在达... 将B样条曲线转换为Bézier曲线,基于Bézier曲线间的光滑拼接的理论,研究了带多形状参数的Bézier曲线(CE-Bézier曲线)与均匀B样条曲线的拼接问题,得出均匀B样条曲线与CE-Bézier曲线的G0,G1,G2光滑拼接条件.在达到拼接条件的前提下,通过改变CE-Bézier曲线的形状参数的数值大小,可以灵活调整拼接曲线的形状. 展开更多
关键词 ce-bézier曲线 均匀B样条 Bézier构造方法 G2连续拼接
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DEGREE ELEVATION AND KNOT INSERTION FOR GENERALIZED BEZIER SURFACES AND THEIR´APPLICATION TO ISOGEOMETRIC ANALYSIS
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作者 Mengyun Wang Ye Ji Chungang Zhu 《Journal of Computational Mathematics》 SCIE CSCD 2024年第5期1197-1225,共29页
Generalized B´ezier surfaces are a multi-sided generalization of classical tensor product B´ezier surfaces with a simple control structure and inherit most of the appealing properties from B´ezier surfa... Generalized B´ezier surfaces are a multi-sided generalization of classical tensor product B´ezier surfaces with a simple control structure and inherit most of the appealing properties from B´ezier surfaces.However,the original degree elevation changes the geometry of generalized B´ezier surfaces such that it is undesirable in many applications,e.g.isogeometric analysis.In this paper,we propose an improved degree elevation algorithm for generalized B´ezier surfaces preserving not only geometric consistency but also parametric consistency.Based on the knot insertion of B-splines,a novel knot insertion algorithm for generalized B´ezier surfaces is also proposed.Then the proposed algorithms are employed to increase degrees of freedom for multi-sided computational domains parameterized by generalized B´ezier surfaces in isogeometric analysis,corresponding to the traditional p-,h-,and k-refinements.Numerical examples demonstrate the effectiveness and superiority of our method. 展开更多
关键词 Generalized Bézier surface Degree elevation Knot insertion Isogeometric analysis REFINEMENT
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The Effects of Shape Parameters for Surface Joining with High Order Geometric Continuity
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作者 Lu Xiaolin Ma Lizhuang He Zhijun 2 《Computer Aided Drafting,Design and Manufacturing》 1998年第1期20-28,共9页
The necessary and sufficient conditions and an algorithm to reach continuity between adjacent Bézier patches are presented. The effects of shape parameters for surface connection of G4 geometric continuity are in... The necessary and sufficient conditions and an algorithm to reach continuity between adjacent Bézier patches are presented. The effects of shape parameters for surface connection of G4 geometric continuity are investigated in detail. The algorithm can be generalized directly to the case of surface joining with higher order geometric continuity. It has important applications in surface modeling and surface joining. 展开更多
关键词 Bézier surface surface modeling geometric continuity
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带多形状参数的三次Bézier曲线曲面的光滑拼接 被引量:4
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作者 胡钢 张念娟 +1 位作者 秦新强 曲桢 《西安理工大学学报》 CAS 北大核心 2009年第4期482-486,共5页
研究了一种带多形状参数的三次扩展Bézier(CE-Bézier)曲线曲面的拼接技术。在对CE-Bézier曲线基函数及端点性质分析的基础上,给出了第二类CE-Bézier曲线间G1、G2和C1、C2拼接的充要条件;同时,分析了两张CE-Béz... 研究了一种带多形状参数的三次扩展Bézier(CE-Bézier)曲线曲面的拼接技术。在对CE-Bézier曲线基函数及端点性质分析的基础上,给出了第二类CE-Bézier曲线间G1、G2和C1、C2拼接的充要条件;同时,分析了两张CE-Bézier曲面片间G1、C1光滑拼接的几何条件,通过合理选取形状参数,进一步简化了曲面的拼接条件,并给出了几何造型的实例。实例结果表明,CE-Bézier曲线曲面的光滑拼接技术可广泛地应用于工程复杂曲线、曲面的造型系统中。 展开更多
关键词 ce-bézier曲线 ce-bézier曲面 形状参数 拼接条件
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区间Bézier曲面的降阶 被引量:11
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作者 孙红兵 陈效群 《中国科学技术大学学报》 CAS CSCD 北大核心 2002年第2期147-154,共8页
论文讨论了用低阶的区间Bzier曲面来界定高阶的区间Bzier曲面的问题 ,提出了两种不同的解决方法———线性规划及最佳一致逼近 ,最后提供的实例结果表明线性规划方法能得到一个界 。
关键词 区间Bezier曲面 降价 线性规划 最佳一致逼近 CAD 区间多项式曲面 实体结构
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