A Shape-Adjustable BéZier Model and Its De Casteljau-Type Algorithm

This paper considers a generalized Bézier model with shape parameters (so called <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha \beta$</tex>-Bézier curve). The properties and the influence of the shape parameters on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha \beta$</tex> Bézier curve are investigated, and a practical De Casteljau-type algorithm for the curve evaluation is also presented. The algorithm, which is implemented by a series of linear operations on the control vertices of the curve, is simple and stable, several calculation examples show the feasibility and effectiveness of the algorithm.