Abstract: This paper deals with the reconstruction of 2-dimensional geometric shapes from unorganized 1-dimensional cross-sections. We study the problem in its full generality following the approach of Boissonnat and Memari [BM07] for the analogous 3D problem. We propose a new variant of this method and provide sampling conditions to guarantee that the output of the algorithm has the same topology as the original object and is close to it (for the Hausdorff distance).