diff --git a/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex b/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex index f71e93c6b09..8e70b6f29d5 100644 --- a/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex +++ b/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex @@ -162,8 +162,7 @@ sufficient for practical cases. \section{Delaunay Triangulation} The class \ccc{Delaunay_triangulation_3} represents a three-dimensional -Delaunay triangulation. This implementation is fully dynamic: it -supports both insertions of points and vertex removal. +Delaunay triangulation. Delaunay triangulations have the specific \textit{empty sphere property}, that is, the circumscribing sphere of each cell of such a triangulation @@ -172,6 +171,8 @@ These triangulations are uniquely defined except in degenerate cases where five points are cospherical. Note however that the \cgal\ implementation computes a unique triangulation even in these cases. +This implementation is fully dynamic: it supports both insertions of points +and vertex removal. The user is advised to use the class \ccc{Triangulation_hierarchy_3} in order to benefit from an increased efficiency for large data sets. diff --git a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex index f71e93c6b09..8e70b6f29d5 100644 --- a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex +++ b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex @@ -162,8 +162,7 @@ sufficient for practical cases. \section{Delaunay Triangulation} The class \ccc{Delaunay_triangulation_3} represents a three-dimensional -Delaunay triangulation. This implementation is fully dynamic: it -supports both insertions of points and vertex removal. +Delaunay triangulation. Delaunay triangulations have the specific \textit{empty sphere property}, that is, the circumscribing sphere of each cell of such a triangulation @@ -172,6 +171,8 @@ These triangulations are uniquely defined except in degenerate cases where five points are cospherical. Note however that the \cgal\ implementation computes a unique triangulation even in these cases. +This implementation is fully dynamic: it supports both insertions of points +and vertex removal. The user is advised to use the class \ccc{Triangulation_hierarchy_3} in order to benefit from an increased efficiency for large data sets.