:: is better than () as it then looks as it did with the old tools

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Andreas Fabri 2012-08-20 10:39:50 +00:00
parent bcb04bb768
commit d12b1916ca
1 changed files with 14 additions and 14 deletions

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@ -50,30 +50,30 @@ class need not be specified and defaults to types and operations defined
in the kernel in which the input point type is defined.
Given a sequence of \f$ n\f$ input points with \f$ h\f$ extreme points,
the function `convex_hull_2()` uses either the output-sensitive \f$ O(n h)\f$ algorithm of Bykat \cite b-chfsp-78
the function `::convex_hull_2` uses either the output-sensitive \f$ O(n h)\f$ algorithm of Bykat \cite b-chfsp-78
(a non-recursive version of the quickhull \cite bdh-qach-96 algorithm) or the algorithm of Akl and Toussaint, which requires \f$ O(n \log n)\f$ time
in the worst case. The algorithm chosen depends on the kind of
iterator used to specify the input points. These two algorithms are
also available via the functions `ch_bykat()` and `ch_akl_toussaint()`,
also available via the functions `::ch_bykat` and `::ch_akl_toussaint`,
respectively. Also available are
the \f$ O(n \log n)\f$ Graham-Andrew scan algorithm \cite a-aeach-79, \cite m-mdscg-84
(`ch_graham_andrew()`),
(`::ch_graham_andrew`),
the \f$ O(n h)\f$ Jarvis march algorithm \cite j-ichfs-73
(`ch_jarvis()`),
(`::ch_jarvis`),
and Eddy's \f$ O(n h)\f$ algorithm \cite e-nchap-77
(`ch_eddy()`), which corresponds to the
(`::ch_eddy`), which corresponds to the
two-dimensional version of the quickhull algorithm.
The linear-time algorithm of Melkman for producing the convex hull of
simple polygonal chains (or polygons) is available through the function
`ch_melkman()`.
`::ch_melkman`.
# Example using Graham-Andrew's Algorithm #
In the following example a convex hull is constructed from point data read
from standard input using `Graham_Andrew` algorithm. The resulting convex
polygon is shown at the standard output console. The same results could be
achieved by substituting the function `ch_graham_andrew()` by other
function like `ch_bykat()`.
achieved by substituting the function `::ch_graham_andrew` by other
function like `::ch_bykat`.
\cgalexample{Convex_hull_2/ch_from_cin_to_cout.cpp}
@ -83,7 +83,7 @@ In addition to the functions for producing convex hulls, there are a
number of functions for computing sets and sequences of points related
to the convex hull.
The functions `lower_hull_points_2()` and `upper_hull_points_2()`
The functions `::lower_hull_points_2` and `::upper_hull_points_2`
provide the computation of the counterclockwise
sequence of extreme points on the lower hull and upper hull,
respectively. The algorithm used in these functions is
@ -92,13 +92,13 @@ which has worst-case running time of \f$ O(n \log n)\f$.
There are also functions available for computing certain subsequences
of the sequence of extreme points on the convex hull. The function
`ch_jarvis_march()` generates the counterclockwise ordered subsequence of
`::ch_jarvis_march` generates the counterclockwise ordered subsequence of
extreme points between a given pair of points and
`ch_graham_andrew_scan()` computes the sorted sequence of extreme points that are
`::ch_graham_andrew_scan` computes the sorted sequence of extreme points that are
not left of the line defined by the first and last input points.
Finally, a set of functions (`ch_nswe_point()`, `ch_ns_point()`,
`ch_we_point()`, `ch_n_point()`, `ch_s_point()`, `ch_w_point()`, `ch_e_point()`)
Finally, a set of functions (`::ch_nswe_point`, `::ch_ns_point`,
`::ch_we_point`, `::ch_n_point`, `::ch_s_point`, `::ch_w_point`, `::ch_e_point`)
is provided for computing extreme points of a
2D point set in the coordinate directions.
@ -121,7 +121,7 @@ points projected into each of the three coordinate planes.
# Convexity Checking #
The functions `is_ccw_strongly_convex_2()` and `is_cw_strongly_convex_2()`
The functions `::is_ccw_strongly_convex_2` and `::is_cw_strongly_convex_2`
check whether a given sequence of 2D points forms a (counter)clockwise strongly
convex polygon. These are used in postcondition
testing of the two-dimensional convex hull functions.