Two kinds of B-basis of the algebraic hyperbolic space

Abstract

In this paper, two new kinds of B-basis functions called algebraic hyperbolic (AH) Bezier basis and AH B-Spline basis are presented in the space Γk=span{1,t,…,t k−3 ,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bezier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms: AH B-Spline surface and AH T-Spline surface.