From b554f4d4cbee5a54c933eee0413cd2da9cdb3e5d Mon Sep 17 00:00:00 2001
From: Susan Hert <hert@mpi-sb.mpg.de>
Date: Thu, 21 Jun 2001 10:11:08 +0000
Subject: [PATCH] rearranged function signatures and requirements

---
 .../ConvexHull_ref/convex_hull_3.tex          | 50 ++++++++++++-------
 1 file changed, 31 insertions(+), 19 deletions(-)

diff --git a/Packages/Convex_hull_3/doc_tex/basic/ConvexHull/ConvexHull_ref/convex_hull_3.tex b/Packages/Convex_hull_3/doc_tex/basic/ConvexHull/ConvexHull_ref/convex_hull_3.tex
index 0b656f97afa..c4aeb4b2516 100644
--- a/Packages/Convex_hull_3/doc_tex/basic/ConvexHull/ConvexHull_ref/convex_hull_3.tex
+++ b/Packages/Convex_hull_3/doc_tex/basic/ConvexHull/ConvexHull_ref/convex_hull_3.tex
@@ -6,8 +6,8 @@
 \ccDefinition
 
 The function \ccRefName\ computes the convex hull of a given set of 
-three-dimensional points using the quickhull algorithm of Barnard
-\textit{et al.} \cite{bdh-qach-96}.  Two versions of this function 
+three-dimensional points 
+Two versions of this function 
 are available.  The first can be used when it is known that the result
 will be a polyhedron and the second when a degenerate hull
 may also be possible.
@@ -22,23 +22,12 @@ void convex_hull_3(InputIterator first, InputIterator last,
 }
 {
 computes the convex hull of the set of points in the range
-[\ccc{first}, \ccc{last}).  The result is stored in \ccc{polyhedron}.
+[\ccc{first}, \ccc{last}).  The result is stored in \ccc{polyhedron}
+and the plane equations of each face are computed.
 \ccPrecond: There are at least four points in the range 
 [\ccc{first}, \ccc{last}) not all of which are collinear.
 }
 
-\ccHeading{Requirements}
-\begin{enumerate}
-   \item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_3}.
-   \item \ccc{Traits} is a model of the concept ConvexHullTraits\_3
-         \ccIndexMainItem[c]{ConvexHullTraits_3}.
-         For the purposes of checking the postcondition that the convex hull
-         is valid, \ccc{Traits} should also be a model of the concept
-         IsStronglyConvexTraits\_3.
-        %\ccIndexMainItem[c]{IsStronglyConvexTraits_3}
-  \item \ccc{Polyhedron_3} must be a model of ConvexHullPolyhedron\_3.
-\end{enumerate}
-
 \ccFunction{
 template <class InputIterator, class Polyhedron_3, class Traits>
 void convex_hull_3(InputIterator first, InputIterator last,
@@ -48,13 +37,32 @@ void convex_hull_3(InputIterator first, InputIterator last,
 {
 computes the convex hull of the set of points in the range
 [\ccc{first}, \ccc{last}).  The result, which may be a point, a segment,
-a triangle, or a polyhedron, is stored in \ccc{ch_object}.
+a triangle, or a polyhedron, is stored in \ccc{ch_object}.  When
+the result is a polyhedron, the plane equations of each face are computed.
 }
 
 \ccHeading{Requirements}
-In addition to the first two requirements listed above, \ccc{Traits} must
-define a type \ccc{Polyhedron_3} that is a model of ConvexHullPolyhedron\_3
-for this version of the function. 
+Both functions require the following:
+\begin{enumerate}
+   \item \ccc{InputIterator::value_type} is equivalent to \ccc{Traits::Point_3}.
+   \item \ccc{Traits} is a model of the concept ConvexHullTraits\_3
+         \ccIndexMainItem[c]{ConvexHullTraits_3}.
+         For the purposes of checking the postcondition that the convex hull
+         is valid, \ccc{Traits} should also be a model of the concept
+         IsStronglyConvexTraits\_3.
+        %\ccIndexMainItem[c]{IsStronglyConvexTraits_3}
+\end{enumerate}
+
+Both functions have an additional requirement for the polyhedron that is
+to be constructed. For the first version this is that:
+\begin{itemize}
+  \item \ccc{Polyhedron_3} is a model of ConvexHullPolyhedron\_3,
+\end{itemize}
+and for the second, it is required that
+\begin{itemize}
+ \item \ccc{Traits} defines a type \ccc{Polyhedron_3} that is a model of 
+       ConvexHullPolyhedron\_3.
+\end{itemize}
 
 The default traits class for both versions of \ccc{convex_hull_3} is 
 \ccc{Convex_hull_traits_3<R>},%
@@ -66,6 +74,10 @@ with the representation determined by \ccc{InputIterator::value_type}.
 \ccRefIdfierPage{CGAL::ch_eddy}  \\
 \ccRefIdfierPage{CGAL::convex_hull_points_2} 
 
+\ccImplementation
+The algorithm implemented by these functions is the quickhull algorithm of 
+Barnard \textit{et al.} \cite{bdh-qach-96}.  
+
 \ccExample
 
 The following program computes the convex hull of a set of 250 random