摘要
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.
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 Bezier 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 Bezier 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 Bezier curve and increase the efficiency of CAGD systems.
出处
《浙江大学学报（工学版）》
EI
CAS
CSCD
北大核心
2004年第12期1570-1574,共5页
Journal of Zhejiang University：Engineering Science
基金
国家自然科学基金资助项目(60373033)
国家"973"重点基础研究发展规划资助项目(2002CB312101).
