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tex update

This commit is contained in:
Michal Kleinbort 2012-05-30 06:52:43 +00:00
parent 4ab8ddd93d
commit b0d87e769b
1 changed files with 10 additions and 4 deletions
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14
Arrangement_on_surface_2/doc_tex/Arrangement_on_surface_2/arr_queries.tex
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@ -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<Arrangement>} 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.");