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In this paper, a new methodology for curve approximation is presented. The method is suitable for both self-intersected and non self-intersected curves, it combines elements from graph theory and from elementary geometry and it is fully automated. More specifically, graph theory tools are utilized in order: 1) to remove the details that are irrelevant to the general shape of the curve under study and 2) to decompose the curve into non self-intersecting smaller curves. Then, each such smaller curve is processed via geometrical tools in order to approximate it efficiently with linear segments. Experimental results show that the proposed method compares well with several other methods of the same purpose.