A Novel Half-Way Shifting Bezier Curve Model

Bezier curves can cause a considerable gap to occur between the approximation curve and its control polygon, due to considering only the global information of the control points. In order to reduce this error in curve representations, localised information needs to be incorporated, with the main philosophy to narrow down the gap by shifting the Bezier curve points closer to the control polygon. To integrate this idea into the theoretical framework of the classical Bezier curve model, this paper presents a novel Half-way shifting Bezier Curve (HBC) model, which automatically incorporates localised information along with the global Bezier information. Both subjective and objective performance evaluations of the HBC model using upon a number of objects having arbitrary shape confirm its considerable improvement over the classical Bezier curve model without increasing the order of computational complexity

Enhanced Bezier curve models incorporating local information

The Bezier curve is fundamental to many challenging and practical applications, ranging from computer aided geometric design and postscript font representations through to generic object shape descriptors and surface representation. A drawback of the Bezier curve however, is that it only considers global information about the control points, so there is often a large gap between the curve and its control polygon, leading to considerable error in curve representations. To address this issue, this paper presents enhanced Bezier curve (EBC) models which seamlessly incorporate local information. The performance of the models is empirically evaluated upon a number of natural and synthetic objects having arbitrary shape and both qualitative and quantitative results confirm the superiority of both EBC models in comparison with the classical Bezier curve representation, with no increase in the order of computational complexity