The approximation of implicit planar curves by line segments is a very classical problem.Many algorithms use interval analysis to approximate this curve, and to handle the topology of thefinal reconstruction. In this article, we use discrete geometry tools to build an original geometricaland topological representation of the implicit curve. The polygonal approximation contains fewsegments, and the Reebgraph permits to sum up efficiently the shape and the topology of the curve.Furthermore, we propose two algorithms to process local cells refinement and local cells groupingschemes.We illustrate these schemes with a global system thatefficiently handles manual or automatic fast updates on the global reconstruction, by consideringtopological or geometrical constraints.We also compare the speed and the quality of our approach with two classical methods.