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:
  • Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
  • Year:
  • 2007

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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, few valley components, and how to obtain it for higher-order Delaunay triangulations. This gives rise to a third heuristic. Tables and visualizations show how the heuristics perform for the drainage characteristics on real-world data.