Uniform hyperbolic polynomial B-spline curves

摘要

This Paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span {sinh, cosh t, t~k-3, t~k-4, …, t, 1} in which k is an arbitrary integer larger than or equal to 3. hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of curves and then prove that they have the variation dimishing Properties and the control polygons of the subdivisions converge.