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