title: Uniform hyperbolic polynomial B-spline curves
abstract: This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Omega =span{sinh t, cosh t, t/sup k-3/, t/sup k-3/, t/sup 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 of B-splines in polynomial space. We give subdivision formulae for this new kind of curve and then prove that they have variation diminishing properties and the control polygons of the subdivisions converge. Hyperbolic polynomial B-splines can handle freeform curves as well as remarkable curves such as the hyperbola and the catenary. The generation of tensor product surfaces using these new splines is straightforward. Examples of such tensor product surfaces: the saddle surface, the catenary cylinder, and a certain kind of ruled surface are given
keyphrases: uniform hyperbolic polynomial B-spline curves arbitrary integer subdivision formulae subdivisions control polygons freeform curves hyperbola catenary saddle surface catenary cylinder ruled surface tensor product surface generation