Abstract
We show how to delete a vertex q from a three-dimensional Delaunay triangulation DT(S) in expected O(C ⊗ (P)) time, where P is the set of vertices neighboring q in DT(S) and C ⊗ (P) is an upper bound on the expected number of tetrahedra whose circumspheres enclose q that are created during the randomized incremental construction of DT(P). Experiments show that our approach is significantly faster than existing implementations if q has high degree, and competitive if q has low degree.
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Buchin, K., Devillers, O., Mulzer, W., Schrijvers, O., Shewchuk, J. (2013). Vertex Deletion for 3D Delaunay Triangulations. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_22
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DOI: https://doi.org/10.1007/978-3-642-40450-4_22
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