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Conference Paper

#### Curve reconstruction: Connecting dots with good reason

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##### Citation

Dey, T. K., Mehlhorn, K., & Ramos, E. A. (1999). Curve reconstruction: Connecting
dots with good reason. In *Proceedings of the 15th Annual Symposium on Computational Geometry (SCG-99)*
(pp. 197-206). New York, USA: ACM.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-356C-9

##### 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 $P$.