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 广义ball基
 generalized ball basis
 Dual Basis Functions for Generalized Ball Basis and Its Application 广义Ball基函数的对偶基及其应用 短句来源 Generalized Ball curves of arbitrary degree were gained by extending that of odd degree, and its many properties and applications, such as degree raising formula, transformation between gerenalized Ball curves and Bézier curves, limiting theorem, dual basis, Marsden equavilent under generalized Ball basis, elvaution algorithm by lowing degree and unit properity etc. , were discussed. 本文讨论了任意次数的广义Ball曲线的性质和它们的应用，如：一般的升阶公式，Bézier曲线与广义Ball曲线之间的转换，极限定理，对偶基，广义Ball基函数下的Maraden恒等式，降阶赋值算法，单位分解性质等． 短句来源
 generalized ball bases
 Dual basis of generalized Ball bases and its applications 一类广义Ball基函数的对偶基及其应用 短句来源 Total Positivity of Said-Bézier Type Generalized Ball Bases Said-Bézier型广义Ball基的全正性 短句来源 The emphasis of the next two chapters are laid upon the two new families of the generalized Ball bases which are introduced by Wu HongYi, i.e., Said-Bezier type generalized Ball (SBGB)bases and Wang-Said type generalized Ball (WSGB)bases, the curves constructed on these bases include the Bezier curve, the Said-Ball curve, the Wall-Ball curve and some intermediate curves. 接下来的两章主要介绍了邬弘毅所提出的两族广义Ball基：SBGB型基函数和WSGB型基函数，用这两族基函数构成的广义Ball曲线，不仅包含了Bézier曲线，Sai-Ball曲线和Wall-Ball曲线，还包含若干介于这些著名曲线之间的中间曲线。 短句来源 Total Positivity of Generalized Ball Bases & Conversion between Triangular and Rectangular SBGB Patches 广义Ball基的全正性及三角域与矩形域上曲面片的转化 短句来源 2. By introducing a family of generalized Ball bases and generalized Ball surfaces with position parameter H and using the relation between the bases of adjacent surfaces, this dissertation presents a new algorithm for conversion of Said-Ball surfaces and Bezier surfaces on triangular domain, which is easy for programming. 而本文通过引入一族三角域上带位置参数H的广义Ball基和广义Ball曲面,利用相邻两曲面的基函数之间的关系,给出三角域上Said-Ball曲面与Bézier曲面之间互相转换的递归算法。 该算法计算量小,编程简单,更有助于广义Ball曲面的推广应用。 短句来源 更多
 generalized ball basis
 Dual Basis Functions for Generalized Ball Basis and Its Application 广义Ball基函数的对偶基及其应用 短句来源 Generalized Ball curves of arbitrary degree were gained by extending that of odd degree, and its many properties and applications, such as degree raising formula, transformation between gerenalized Ball curves and Bézier curves, limiting theorem, dual basis, Marsden equavilent under generalized Ball basis, elvaution algorithm by lowing degree and unit properity etc. , were discussed. 本文讨论了任意次数的广义Ball曲线的性质和它们的应用，如：一般的升阶公式，Bézier曲线与广义Ball曲线之间的转换，极限定理，对偶基，广义Ball基函数下的Maraden恒等式，降阶赋值算法，单位分解性质等． 短句来源
 generalized ball basis
 Dual Basis Functions for Generalized Ball Basis and Its Application 广义Ball基函数的对偶基及其应用 短句来源 Generalized Ball curves of arbitrary degree were gained by extending that of odd degree, and its many properties and applications, such as degree raising formula, transformation between gerenalized Ball curves and Bézier curves, limiting theorem, dual basis, Marsden equavilent under generalized Ball basis, elvaution algorithm by lowing degree and unit properity etc. , were discussed. 本文讨论了任意次数的广义Ball曲线的性质和它们的应用，如：一般的升阶公式，Bézier曲线与广义Ball曲线之间的转换，极限定理，对偶基，广义Ball基函数下的Maraden恒等式，降阶赋值算法，单位分解性质等． 短句来源

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 Generalized Ball curves of arbitrary degree were gained by extending that of odd degree, and its many properties and applications, such as degree raising formula, transformation between gerenalized Ball curves and Bézier curves, limiting theorem, dual basis, Marsden equavilent under generalized Ball basis, elvaution algorithm by lowing degree and unit properity etc., were discussed. 本文讨论了任意次数的广义Ｂａｌｌ曲线的性质和它们的应用，如：一般的升阶公式，Ｂéｚｉｅｒ曲线与广义Ｂａｌｌ曲线之间的转换，极限定理，对偶基，广义Ｂａｌｌ基函数下的Ｍａｒａｄｅｎ恒等式，降阶赋值算法，单位分解性质等． By introducing a family of generalized Ball bases and generalized Ball surfaces with position parameter H and using the relation between the bases of adjacent surfaces,this paper presents a new algorithm for the conversion of Said-Ball and B zier surfaces on a triangular domain. The algorithm is easy for programming. 通过引入一族三角域上带位置参数H的广义Ball基和广义Ball曲面 ,并利用相邻两曲面的基函数之间的关系 ,给出三角域上Said Ball曲面与B啨ｚｉｅｒ曲面之间的一种新的递归转换算法 .该算法计算量小 ,编程简单 In order to make maximal use of generalized Ball bases in computer aided geometric design (CAGD) systems, a type of generalized Ball bases defined as β basis was investigated,which could generate the parametric curve located between the Bézier curve and the Said-Ball curve. The dual basis of β basis was provided with the combinational calculation method. Utilizing the dual basis, Marsden identity under β basis was obtained, based on which conversion formulae between Bernstem basis and β basis were given. The... In order to make maximal use of generalized Ball bases in computer aided geometric design (CAGD) systems, a type of generalized Ball bases defined as β basis was investigated,which could generate the parametric curve located between the Bézier curve and the Said-Ball curve. The dual basis of β basis was provided with the combinational calculation method. Utilizing the dual basis, Marsden identity under β basis was obtained, based on which conversion formulae between Bernstem basis and β basis were given. The Bézier curve could be converted into the parametric curve with the conversion formulae. The operating results of example matrices show that β basis can accelerate the computational speed of the Bézier curve and increase the efficiency of CAGD systems. 为进一步发挥广义Ball基在计算机辅助几何设计(CAGD)中的优越性.对能生成几何位置介于B啨zier曲线与Said Ball曲线之间的参数曲线的一类广义Ball基即β基作了深入研究.通过组合运算找到β基的对偶基,利用这种对偶基推导幂基函数在β基函数下的Marsden恒等式.在此基础上推出Bernstein基到β基的转换公式,进而实现B啨zier曲线到β基所表示的参数曲线的转换.矩阵实例运算表明,借助β基可以加快B啨zier曲线的求值速度,提高计算机辅助几何设计系统的效率. << 更多相关文摘
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