均匀混合三角多项式B-样条曲线

Uniform Mixed Trigonometric Polynomial B-splines

提出一种新的均匀样条曲线,均匀混合三角多项式B-样条.它是建立在空间{sint,cost,tsint,tcost,1,t,…,tk-5}上,其中k是任意大于等于5的整数.这种曲线与传统的B-样条曲线有很多相似的性质,给出了它具体的性质.基于曲线的明确的表述之上,也给出了这种新曲线的细分公式.由于新样条把多项式曲线、三角曲线以及三角多项式B-样条曲线做为其特殊情况,所以它是CAD/CAM领域中一种新的有效的新模型.

A new kind of uniform spline curve, named uniform mixed trigonometric polynomial B-splines is presented; it is on the space {sint,cost,tsint,tcost,1,t,…,t^k-5} of whichk is an arbitrary integer larger than or equal to 5. It is shown that the mixed trigonometric polynomial B-spline curves have many similar properties to traditional B-splines. Based on the explicit representation of the curve, the subdivision formulae for this new kind of curve is also given. Since the new spline can include both polynomial curves and trigonometriccurves as special cases without rational form,it can be used as an efficient new model for geometric design in the fields of CAD/CAM.