双曲混合多项式形式的Ball曲线

Hyperbolic polynomials Ball curves.

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.

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.