Generating realistic terrains with higher-order delaunay triangulations

Authors:
Thierry de Kok;Marc van Kreveld;Maarten Löffler
Affiliations:
Institute of Information and Computing Sciences, Utrecht University, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, The Netherlands
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

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Abstract

For hydrologic applications, terrain models should have few local minima, and drainage lines should coincide with edges. We show that triangulating a set of points with elevations such that the number of local minima of the resulting terrain is minimized is NP-hard for degenerate point sets. The same result applies when there are no degeneracies for higher-order Delaunay triangulations. Two heuristics are presented to reduce the number of local minima for higher-order Delaunay triangulations, which start out with the Delaunay triangulation. We give efficient algorithms for their implementation, and test on real-world data how well they perform. We also study another desirable drainage characteristic, namely few valley components.