Abstract
For a set P of points in the plane, we introduce a class of triangulations that is an extension of the Delaunay triangulation. Instead of requiring that for each triangle the circle through its vertices contains no points of P inside, we require that at most k points are inside the circle. Since there are many different higher order Delaunay triangulations for a point set, other useful criteria for triangulations can be incorporated without sacrificing the well-shapedness too much. Applications include realistic terrain modelling, and mesh generation.
This research is partially supported by the ESPRIT IV LTR Project No. 21957 (CGAL)
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Gudmundsson, J., Hammar, M., van Kreveld, M. (2000). Higher Order Delaunay Triangulations. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_22
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DOI: https://doi.org/10.1007/3-540-45253-2_22
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