From b0d87e769be21018fcf843cbca5e3384a2fcfcc0 Mon Sep 17 00:00:00 2001 From: Michal Kleinbort Date: Wed, 30 May 2012 06:52:43 +0000 Subject: [PATCH] tex update --- .../Arrangement_on_surface_2/arr_queries.tex | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2/arr_queries.tex b/Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2/arr_queries.tex index be4fc18d154..8af9025d282 100644 --- a/Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2/arr_queries.tex +++ b/Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2/arr_queries.tex @@ -126,7 +126,9 @@ choosing points on a grid, are also available; see the Reference Manual for more details. % \item \ccc{Arr_trapezoid_ric_point_location} implements -Mulmuley's point-location algorithm~\cite{m-fppa-90} (see +%Mulmuley's point-location algorithm~\cite{m-fppa-90} (see +a point location algorithm presented by Siedel~\cite{}, which uses a +randomized incremental construction described by Mulmuley~\cite{m-fppa-90} (see also~\cite[Chapter~6]{bkos-cgaa-00}). The arrangement faces are decomposed into simpler cells of constant complexity known as {\em pseudo-trapezoids} and a search-structure @@ -166,6 +168,10 @@ scenarios where the query time can be linear. In practice however, the query times of both strategies are competitive. For a detailed experimental comparison, see \cite{cgal:hh-eplca-05} +A significant advantage of the trapezoid RIC strategy +comparing to the other methods +is the possibility to work with unbounded subdivisions. + The main drawback in the current implementation of the landmark strategy, compared to the trapezoidal RIC strategy, is that while the updating the auxiliary data structures @@ -270,7 +276,7 @@ void vertical_ray_shooting_query typename Arrangement_on_surface_2::Halfedge_const_handle e; typename Arrangement_on_surface_2::Face_const_handle f; - std::cout << "Shooting up from " << q << " : "; + std::cout << "Shooting up from " << q << " : "; if (CGAL::assign (e, obj)) \{ // We hit an edge: std::cout << "hit an edge: " << e->curve() << std::endl; @@ -285,8 +291,8 @@ void vertical_ray_shooting_query else if (CGAL::assign (f, obj)) \{ // We did not hit anything: CGAL_assertion (f->is_unbounded()); - - std::cout << "hit nothing." << std::endl; + + std::cout << "hit nothing." << std::endl; \} else \{ CGAL_assertion_msg (false, "Invalid object.");