A class of quasi Bézier curves based on hyperbolic polynomials

This paper presents a basis for the space of hyperbolic polynomials Γm=span{ 1, sht, cht, sh2t, ch2t, ..., shmt, chmt} on the interval 0,α] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we rameter variable t to arbitrary close interval r, s] (r＜s).