【作者】 汪志华；

【导师】 朱晓临；

【作者基本信息】 合肥工业大学 ， 计算数学， 2009， 硕士

【摘要】 在计算机辅助几何设计中,定义在千变万化的拓扑结构上的自由型曲线曲面,存在着千变万化的形式,而广义Ball曲线则是其中一种在曲线求值及升降阶的计算速度方面明显优于Bézier曲线。本文对广义Ball曲线曲面的相关问题进行了较深入的研究。首先,通过引入多个形状参数,给出了Wang-Said型曲线的多形状参数的扩展。改变形状参数的值,可以局部或整体调控曲线的形状,同时给出了Said-Ball曲线的多形状参数的扩展。通过引入一个形状参数,生成了Wang-Ball曲线与三角域上Wang-Ball曲面的扩展。其次,给出了Wang-Ball曲线与Bézier曲线的统一表示,构造了介于二者之间的新型曲线族,并称之为Wang-Bézier曲线。同时给出了它的升阶公式、递推算法以及与Bézier曲线相互转化的公式。最后,给出Wang-Ball曲线、Said-Ball曲线与Bézier曲线三者的统一表示以及相关的升阶公式、递推算法。更多还原

【Abstract】 Free curves/surfaces defined in different topological structure have different expressions in CAGD, and generalized Ball curves are more efficient than Bézier curves in calculation, the degree elevation and reduction。This dissertation focuses on the research about the generalized Ball curves/surfaces。Firstly, the extension of Wang-Said type generalized curves is provided by introducing some shape parameters。By changing the values of those shape parameters, the shape of these new curves can be adjusted locally or entirely, and Said-Ball curve with multiple shape parameters is provided。The extension of Wang-Ball surface is made to get a kind of new surface over triangular domain by introducing a shape parameter。Secondly, this paper presents a family of new curves which unify the representations of Bézier curve and Wang-Ball curve。The corresponding degree elevation scheme, recursive algorithm and explicit conversion formulae between this new family of curves and Bézier curve are given。Finally, a family of new basis is offered to unify the Berntein basis, Wang-Ball and Said-Ball basis。In addition, the corresponding degree elevation scheme and recursive algorithm are presented。更多还原