Abstract: In this paper, two new kinds of B-basis functions called algebraic hyperbolic (AH) Bézier basis and AH B-Spline basis are presented in the space Γ_k=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 Bézier 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.

Key words: Algebraic hyperbolic Bézier basis, Algebraic hyperbolic B-Spline basis, Algebraic hyperbolic Bézier curve, Algebraic hyperbolic B-Spline curve

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