Curve reconstruction: Connecting dots with good reason

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 $\Gamma$ that justifies $G$ as the reconstruction from $P$