Abstract: A robust algorithm is proposed for discretely sampling continuous planar curves and
reconstructing the curves from the sampled point sets. The algorithm covers two processes, sampling
and reconstruction. In the sampling part, the points are evenly obtained from a given planar closed
curve, and then the distances are calculated between each point and the medial-axis of the planar area
surrounded by the closed curve. Subsequently, the sampling intervals are decided by the distances and
finds the sampling points. In the reconstruction part, a Delaunay triangulation is first built for the
sampled points, and then edges are selected from the triangulation to build the initialize graph. Finally,
the reconstructed curve is obtained by modifying the graph to a new version. Experiments show that
the point sets sampled by our algorithm are locally adapted to the local geometric characteristics of
the curves, and the reconstructed curves can approximate the original curves well.

Key words: curve reconstruction, discretely sampling, scattered points, 2D graphics