二次带形状参数双曲B样条曲线

Quadratic hyperbolic B-spline curves with a shape parameter

在空间Ω_5=span{1,sinh t,cosh t,sinh 2t,cosh 2t}上给出了二次带形状参数双曲B样条的基函数.由这组基组成的二次双曲B样条曲线是C^1连续的,同时具有很多与二次B样条曲线类似的性质和几何结构,并且可以精确表示双曲线.在控制多边形固定的情况下,可以通过调节形状参数的大小来进一步调整曲线的形状.

The basis functions of quadratic hyperbolic B-spline with a shape parameter are presented,which are generated by the spaceΩ_5=span{1,sinh t,cosh t,sinh 2t,cosh 2t}.Based on these functions,the constructed quadratic hyperbolic B-spline curves are C^1 continuous and share mostly similar properties and geometry structure of classical B-spline curves.And the hyperbola can be explicitly expressed.With the control polygon fixed,the shape of the B-spline curve can be further changed by adjusting the parameter valu...