Abstract
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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k-2</sup> }, 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.
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