Non-uniform hyperbolic blending B-spline curves

This paper presents a new kind of non-uniform splines, called non-uniform hyperbolic blending B-splines defined on a given knot sequence T, generated over the space Ω_k[T]=span{sinht, cosht, tsinht, tcosht, 1, t, ...,t^k-5} in which k is an arbitary integer larger than or equal to 5. Non-uniform hyperbolic blending B-splines share most of the properties as those of the traditional B-splines. We give the curves defined by this kind of splines, the subdivision formulae for these new curves and then prove that they have the variation diminishing properties and the control polygons of the subdivisions converge. At the same time, we show B-basis property of splines.