Handbook of discrete and computational geometry
On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Higher order Delaunay triangulations
Computational Geometry: Theory and Applications
Optimal higher order Delaunay triangulations of polygons
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
A faster circle-sweep Delaunay triangulation algorithm
Advances in Engineering Software
Generating realistic terrains with higher-order delaunay triangulations
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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We extend the notion of higher-order Delaunay triangulations to constrained higher-order Delaunay triangulations and provide various results. We can determine the order k of a given triangulation in O(min(nklognlogk,n^3^/^2log^O^(^1^)n)) time. We show that the completion of a set of useful order-k Delaunay edges may have order 2k-2, which is worst-case optimal. We give an algorithm for the lowest-order completion for a set of useful order-k Delaunay edges when k=