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 ball基
 ball basis
 Extension of the Ball Basis Ball基的推广 短句来源 By means of dual basis for Said Ball basis of even degree, we obtained Marsden identity and realized the conversion from Bézier curve to Said Ball curve These results are useful for the application of Said Ball curve and its popularization in Computer Aided Geometric Design 利用任意偶数次Said Ball基的对偶基 ,给出Said Ball基函数下的Marsden恒等式 ,并实现B啨zier曲线到Said Ball曲线的转换 这些结果对Said Ball曲线在CAGD中的应用及推广是极为有益的 短句来源 A new kind of Ball basis and curves in space K_n=span{1,t,t~2,\:,t~(n-1),sh t, ch t} are discussed. 详细讨论了双曲混合多项式空间Kn=span{1,t,t2,…,tn-2,sht,cht}中的Ball基和Ball曲线. 短句来源
 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 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 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. 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 . 短句来源 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. 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. 短句来源
 ball basis
 Extension of the Ball Basis Ball基的推广 短句来源 By means of dual basis for Said Ball basis of even degree, we obtained Marsden identity and realized the conversion from Bézier curve to Said Ball curve These results are useful for the application of Said Ball curve and its popularization in Computer Aided Geometric Design 利用任意偶数次Said Ball基的对偶基 ,给出Said Ball基函数下的Marsden恒等式 ,并实现B啨zier曲线到Said Ball曲线的转换 这些结果对Said Ball曲线在CAGD中的应用及推广是极为有益的 短句来源 A new kind of Ball basis and curves in space K_n=span{1,t,t~2,\:,t~(n-1),sh t, ch t} are discussed. 详细讨论了双曲混合多项式空间Kn=span{1,t,t2,…,tn-2,sht,cht}中的Ball基和Ball曲线. 短句来源

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 ball basis
 The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said-Ball and the Wang-Ball basis, respectively. We prove that the Wang-Ball basis is strictly monotonicity preserving for all m. However, it is not geometrically convexity preserving and is not totally positive for m>amp;gt;3, in contrast with the Said-Ball basis. We prove that the Said-Ball basis is better conditioned than the Wang-Ball basis and we include a stable conversion between both generalized Ball bases. The Wang-Ball basis has an evaluation algorithm with linear complexity.
 ball bases
 Dual functionals of said-bézier type generalized ball bases over triangle domain and their application We prove that the Said-Ball basis is better conditioned than the Wang-Ball basis and we include a stable conversion between both generalized Ball bases.
 ball base
 This will funnel water away from the root ball base and reduce the danger of roots becoming waterlogged.
 ball basis
 The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said-Ball and the Wang-Ball basis, respectively. We prove that the Wang-Ball basis is strictly monotonicity preserving for all m. However, it is not geometrically convexity preserving and is not totally positive for m>amp;gt;3, in contrast with the Said-Ball basis. We prove that the Said-Ball basis is better conditioned than the Wang-Ball basis and we include a stable conversion between both generalized Ball bases. The Wang-Ball basis has an evaluation algorithm with linear complexity.
其他
 By means of dual basis for Said Ball basis of even degree, we obtained Marsden identity and realized the conversion from Bézier curve to Said Ball curve These results are useful for the application of Said Ball curve and its popularization in Computer Aided Geometric Design 利用任意偶数次Said Ball基的对偶基 ,给出Said Ball基函数下的Marsden恒等式 ,并实现B啨ｚｉｅｒ曲线到Said Ball曲线的转换 这些结果对Said Ball曲线在CAGD中的应用及推广是极为有益的 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 Ball curves were investigated extensively in polynomial spaces and applied in CAD systems. A new kind of Ball basis and curves in space K_n=span{1,t,t~2,\:,t~(n-1),sh t, ch t} are discussed. The basis of space K_n, called H-Ball basis, is constructed based on H-Bézier basis, and then H-Ball curves are defined with this new basis. H-Ball curves inherit wonderful geometric properties of Bézier curves, and furthermore, they could be degree-elevated and degree-reduced rapidly. Shape of curves could be adjusted... Ball curves were investigated extensively in polynomial spaces and applied in CAD systems. A new kind of Ball basis and curves in space K_n=span{1,t,t~2,\:,t~(n-1),sh t, ch t} are discussed. The basis of space K_n, called H-Ball basis, is constructed based on H-Bézier basis, and then H-Ball curves are defined with this new basis. H-Ball curves inherit wonderful geometric properties of Bézier curves, and furthermore, they could be degree-elevated and degree-reduced rapidly. Shape of curves could be adjusted by changing vertices of control polygon, and forced to approximate to control polygon by changing a shape factor α. H-Ball curves could be applied for curves design and shape modeling in CAD systems and related fields. Ball曲线在多项式空间中得到了广泛的研究,而且在CAD系统中也有着广泛应用.详细讨论了双曲混合多项式空间Kn=span{1,t,t2,…,tn-2,sht,cht}中的Ball基和Ball曲线.在H-Bézier基的基础上构造的一组新的基称为空间Kn的H-Ball基,用这组H-Ball基定义的曲线称为H-Ball曲线.H-Ball曲线继承了Bézier曲线的很好的几何性质,而且在曲线升阶和降阶上比Bézier曲线更加快速方便.另外H-Ball曲线不仅可以通过调整控制多边形来控制曲线形状,还可以通过调整形状因子来调节曲线对控制多边形的逼近程度.H-Ball曲线在CAD系统和相关领域的曲线设计和建模中得到了重要的应用. << 更多相关文摘
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