Finding planar regions in a terrain: in practice and with a guarantree

Authors:
Stefan Funke;Theocharis Malamatos;Rahul Ray
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany
Venue:
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Year:
2004

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Abstract

We consider the problem of computing large connected regions in a triangulated terrain of size n for which the normals of the triangles deviate by at most some small fixed angle. In previous work an exact near-quadratic algorithm was presented, but only a heuristic implementation with no guarantee was practicable. We present a new approximation algorithm for the problem which runs in O(n∈2) time and---apart from giving a guarantee on the quality of the produced solution---has been implemented and shows good performance on real data sets representing fracture surfaces consisting of around half a million triangles. Further we present a simple approximation algorithm for a related problem: given a set of n points in the plane, determine the placement of the unit disc which contains most points. This algorithm runs in linear time as well.