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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.