A class of quasi Bézier curves based on hyperbolic polynomials

Abstract

This paper presents a basis for the space of hyperbolic polynomialsΓm=span{1, sht, cht, sh2t, ..., 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 construct quasi Bezier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variablet to arbitrary close interval [r,s] (r<s).