## Combinatorial Curve Reconstruction and the Efficient Exact Implementation of Geometric Algorithms (2001)

by
Stefan Funke

### BibTeX

@MISC{Funke01combinatorialcurve,

author = {Stefan Funke},

title = {Combinatorial Curve Reconstruction and the Efficient Exact Implementation of Geometric Algorithms},

year = {2001}

}

### OpenURL

### Abstract

This thesis has two main parts. The first part deals with the problem of curve reconstruction. Given a finite sample set S from an unknown collection of curves #, the task is to compute the graph G(S,#) which has vertex set S and an edge between exactly those pairs of vertices that are adjacent on some curve in #. We present a purely combinatorial algorithm that solves the curve reconstruction problem in polynomial time. It is the first algorithm which provably handles collections of curves with corners and endpoints. In the second