Generating Realistic Terrains with Higher-Order Delaunay Triangulations

  • Thierry de Kok
  • Marc van Kreveld
  • Maarten Löffler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)


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.


Local Minimum Steep Descent Voronoi Diagram Delaunay Triangulation Triangulate Irregular Network 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Thierry de Kok
    • 1
  • Marc van Kreveld
    • 1
  • Maarten Löffler
    • 1
  1. 1.Institute of Information and Computing SciencesUtrecht UniversityThe Netherlands

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