ω-Bezier

A new kind of Bézier-like basis with a frequency parameter, called ω-Bezier basis, is presented. It unifies and extends the Bézier basis, C-Bézier basis and H-Bézier basis defined over polynomial space, trigonometric polynomial space and hyperbolic polynomial space respectively. The ω-Bezier basis is defined in the space spanned by {cosωt, sinωt, 1, t,..., t^k-2}, where ω = α, αϵR, κ is an arbitrary nonnegative integer. The ω-Bezier basis persists all desirable properties of the existing Bézier-like bases. Furthermore, it also has some special properties advantageous for modeling free form curves and surfaces, for example shape adjustability relative to the frequency parameter.