diff --git a/Generator/doc/Generator/CGAL/random_convex_hull_in_disc_2.h b/Generator/doc/Generator/CGAL/random_convex_hull_in_disc_2.h
index 995967276f2..2a84df06100 100644
--- a/Generator/doc/Generator/CGAL/random_convex_hull_in_disc_2.h
+++ b/Generator/doc/Generator/CGAL/random_convex_hull_in_disc_2.h
@@ -4,8 +4,8 @@ namespace CGAL {
 \ingroup PkgGenerators
 
 
-\brief Computes a random convex polygon by writing its vertices (oriented
-counterclockwise) in an `OutputIterator`, as the convex hull of \f$ n \f$ random points in a disc centered in \f$0\f$ with radius `radius`.
+\brief Computes a random convex polygon as the convex hull of \f$ n \f$ random points in a disc centered in \f$0\f$ with radius `radius`. 
+The vertices are stored counterclockwise in `it`.
 The generated polygon will have an average number of vertices \f$ n^\frac{1}{3}(1+o(1))\f$. 
 
 
@@ -15,7 +15,7 @@ The generated polygon will have an average number of vertices \f$ n^\frac{1}{3}(
 
 - `Generator` has to be a Boost random generator, such as `boost::random::mt19937`.
 
-- `fast` is a Boolean value, `true` for a time-efficient behavior and `false` for a memory-efficient behavior.
+- `fast` is a Boolean , set to `true` for time efficiency and to `false` for memory efficiency.
 
 - `Traits` is a model of the concept `RandomConvexHullTraits_2`. 
 
@@ -26,14 +26,14 @@ The generated polygon will have an average number of vertices \f$ n^\frac{1}{3}(
 
 \cgalHeading{Implementation}
 
-The implementation is based on an incremental construction of a convex hull. At each step a quantity of points that won't be change the convex hull is evaluted using a binomial law. 
-Thus, all the points doesn't have to be generated, reducing the time and size complexities.
+The implementation is based on an incremental construction of a convex hull. At each step, we choose a number of points to pick uniformly at random in the disc. Then, a subset of these points, that won't change the convex hull, is evaluated using a Binomial law. 
+As these points won't be generated, the time and size complexities are reduced.
 A tradeoff between time and memory is provided with the option `fast`, true by default. Using the `fast` option, both time and size expected complexities are \f$O\left(n^\frac{1}{3}\log^\frac{2}{3}n \right)\f$.
  If this option is disabled, the expected size complexity becomes \f$O\left(n^\frac{1}{3}\right)\f$ but the expected time complexity becomes \f$O\left(n^\frac{1}{3}\log^2 n \right)\f$. 
 
 \cgalHeading{Example}
 
-The following program computes a random polygon defined as the convex hull of \f$10000\f$ points uniformly generated in a disc.
+The following program computes a random polygon defined as the convex hull of \f$10000\f$ points uniformly generated in the disc of radius \f$1\f$ centered in \f$0\f$.
 
 \cgalExample{Generator/random_convex_hull_2.cpp}