a Department of CIS, The Ohio State University, Columbus, OH 43210, USA
b Max-Planck-Institut für Informatik, D-66123 Saarbrücken, Germany
Abstract:
Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a sufficiently dense sample of a closed smooth curve, the algorithms construct the correct polygonal reconstruction. Nothing is claimed about the output of the algorithms, if the input is not a dense sample of a closed smooth curve, e.g., a sample of a curve with endpoints. We present an algorithm that comes with a guarantee for any set P of input points. The algorithm constructs a polygonal reconstruction G and a smooth curve Γ that justifies G as the reconstruction from P.