Curve approximation is a challenging issue to precisely depict exquisite shapes of natural phenomena, in which the piecewise Bézier curve is one of the most widely utilized tools due to its beneficial properties. It is essential to determine the quantity and location of control points through the process of generating the mathematical representation of desired objects. This paper presents a new algorithm called adaptive extension fitting scheme (AEFS) to determine a piecewise Bézier curve that best fits a given sequence of data points as well as locate the coordinates of the connecting points between the pieces adaptively. Taking full advantage of the scalability of the Bézier curve segment, AEFS is effective in sequential knot searching within an impressively small computational consumption. The capability of the proposed stepwise extension strategy is deduced from rigorous theoretical proof, resulting in proper connecting points together with well-fitted Bézier curves. The proposed algorithm is evaluated by some popular benchmarks for curve fitting, and compared with several state-of-the-art approaches. Experimental results indicate that AEFS outperforms other models involved in terms of execution time, fitting accuracy, number of segments, and the authenticity of shape contours.

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