From 6fadf5d1d08044616c7a0365e486596dd1de5fc2 Mon Sep 17 00:00:00 2001 From: Olivier Devillers Date: Tue, 15 Jun 2010 14:00:05 +0000 Subject: [PATCH] new removal in Delaunay implementation section --- Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex | 3 +++ 1 file changed, 3 insertions(+) diff --git a/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex b/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex index 4a2799fe7cd..4b5ee67ce4b 100644 --- a/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex +++ b/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex @@ -637,6 +637,9 @@ satisfied. Removal of a vertex of degree $d$ takes time $O(d^2)$. The degree $d$ is $O(1)$ for a random vertex in the triangulation. +When the degree of the removed vertex is small ($\leq7$) a special +procedure is used that allows to increase global removal time by a factor of 2 +for random points~\cite{d-vrtdd-09}. The displacement of a vertex $v$ at a point $p$ to a new location $p'$, first checks whether the triangulation embedding remains planar or not after moving $v$ to $p'$. If yes, it moves $v$ to $p'$ and simply performs a sequence of flips