From ecc438200adcdbfc3f6f2084c32bef0eb8e487b8 Mon Sep 17 00:00:00 2001 From: Andreas Fabri Date: Mon, 3 Sep 2012 08:06:41 +0000 Subject: [PATCH] move figure to the right section --- Partition_2/doc/Partition_2/Partition_2.txt | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/Partition_2/doc/Partition_2/Partition_2.txt b/Partition_2/doc/Partition_2/Partition_2.txt index a4bb1678035..2cf6f84dc16 100644 --- a/Partition_2/doc/Partition_2/Partition_2.txt +++ b/Partition_2/doc/Partition_2/Partition_2.txt @@ -38,9 +38,7 @@ is a polygon whose vertices \f$ v_1, \ldots, v_n\f$ can be divided into two chai intersects either chain at most once. For producing a \f$ y\f$-monotone partition of a given polygon, the sweep-line algorithm presented in \cite bkos-cgaa-97 is implemented by the function -`::y_monotone_partition_2` -. -This algorithm runs in \f$ O(n \log n)\f$ time and requires \f$ O(n)\f$ space. +`::y_monotone_partition_2`. This algorithm runs in \f$ O(n \log n)\f$ time and requires \f$ O(n)\f$ space. This algorithm does not guarantee a bound on the number of polygons produced with respect to the optimal number. @@ -50,7 +48,6 @@ which determines if a sequence of points in 2D defines a \f$ y\f$-monotone polygon or not. For examples of the use of these functions, see the corresponding reference pages. -\image html approximate_optimal_vs_optimal.png "Examples of an approximate optimal convex partition (left) and an optimal convex partition (right)." \section secpartition_2_convex Convex Partitioning @@ -64,6 +61,8 @@ no more than four times the optimal number of convex pieces but they differ in their runtime complexities. Though the triangulation-based approximation algorithm often results in fewer convex pieces, this is not always the case. +\image html approximate_optimal_vs_optimal.png "Examples of an approximate optimal convex partition (left) and an optimal convex partition (right)." + An optimal convex partition can be produced using the function `::optimal_convex_partition_2`. This function provides an