From a40c2d14b4c9d6e26dd1730347ce4f5ef2e6722f Mon Sep 17 00:00:00 2001 From: Peter Hachenberger Date: Wed, 22 Apr 2009 13:57:55 +0000 Subject: [PATCH] mathematical delimiter was at the wrong position --- .../doc_tex/Convex_decomposition_3/main.tex | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/Convex_decomposition_3/doc_tex/Convex_decomposition_3/main.tex b/Convex_decomposition_3/doc_tex/Convex_decomposition_3/main.tex index b3f948e7ddb..ce508d2064c 100644 --- a/Convex_decomposition_3/doc_tex/Convex_decomposition_3/main.tex +++ b/Convex_decomposition_3/doc_tex/Convex_decomposition_3/main.tex @@ -26,7 +26,8 @@ decomposing both polyhedra into convex pieces, compute pair-wise Minkowski sums of the convex pieces, and unite the pair-wise sums. While it is desirable to have a decomposition into a minimum number of -pieces, this problem is know to be NP-hard~\cite{c-cpplb-84}. Our +pieces, this problem is known to be NP-hard~\cite{c-cpplb-84}. Our + implementation decomposes a Nef polyhedron $N$ into $O(r^2)$ convex pieces, where $r$ is the number of edges, which have two adjacent facets that span an angle of more than 180 degrees with respect to the @@ -92,7 +93,7 @@ denoted as boundary items---are needed to separate the two volumes, but are also useful for representing topological properties. In case of the (closed) unit cube the boundary items are part of the polyhedron and therefore selected, but in case of the open unit cube -$[0,1)$^3 they are unselected. Each item has its own selection mark, +$[0,1)^3$ they are unselected. Each item has its own selection mark, which allows the correct representation of Nef polyhedra, which are closed under Boolean and topological operations. Details can be found in the chapter on 3D Boolean operations on Nef polyhedra for more