UAH B样条与均匀B样条关系研究

Relationship between UAH B-splines and uniform B-splines

推出了当参数α→0+,α→+∞时k阶均匀双曲多项式B样条(Uniform Algebraic Hyperbolic B-splines:UAH B-splines)的极限形式.对4阶UAH B样条重新参数化,在给定误差范围内,UAH B样条可由4阶均匀B样条精确逼近.最后,用UAH B样条精确表示了双曲正弦曲线与指数曲线,并揭示了UAH B样条曲面与均匀B样条曲面间的关系.

The limiting form for the k-order uniform algebraic hyperbolic B-splines （UAH B-splines） is derived at parameter α→0^＋ and α→＋∞. A new re-parametrized form of the 4-order UAH B-splines is worked out. Any UAH B- splines can be approximated by the 4-order uniform B-splines at a high accuracy within an error range. As an application, a hyperbolic sine curve and an exponential curve are expressed accurately by the UAH B-splines. Finally, the relationship between UAH B-spline surface and uniform B-spline surface is studied.