document: Uniform hyperbolic polynomial B-spline curves This paper presents a new kind of uniform splines , called hyperbolic polynomial B-splines , generated over the space Omega = span -LCB- sinh t , cosh t , t/sup k-3 / , t/sup k-3 / , t/sup k-4 / , ... , t 1 -RCB- 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
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