diff --git a/Point_set_processing_3/doc/Point_set_processing_3/Point_set_processing_3.txt b/Point_set_processing_3/doc/Point_set_processing_3/Point_set_processing_3.txt
index 528f2f9f7aa..239cadab87a 100644
--- a/Point_set_processing_3/doc/Point_set_processing_3/Point_set_processing_3.txt
+++ b/Point_set_processing_3/doc/Point_set_processing_3/Point_set_processing_3.txt
@@ -162,6 +162,12 @@ points has the appearance of a curve in 2D or a surface in 3D
 - `estimate_global_k_neighbor_scale()`
 - `estimate_global_range_scale()`
 
+Functions such as `jet_estimate_normals()` or
+`remove_outliers()` require a K neighbor scale while others such as
+`grid_simplify_point_set()` require a range
+scale. `vcm_estimate_normals()` is an example of a function that
+accepts both.
+
 In some specific cases, the scale of a point set might not be
 homogeneous (for example if the point set contains variable
 noise). \cgal also provides 2 functions that automatically estimate
@@ -170,19 +176,27 @@ the scales of a point set at a set of user-defined locations:
 - `estimate_local_k_neighbor_scales()`
 - `estimate_local_range_scales()`
 
-Notice that the 4 functions presented here work both with 2D points
-and 3D points and that they shouldn't be used if the point sets do not
-sample a curve in 2D or a surface in 3D.
+The 4 functions presented here work both with 2D points and 3D points
+and they shouldn't be used if the point sets do not sample a curve in
+2D or a surface in 3D.
 
-\subsection Point_set_processing_3Example_scale_estimation Example
+\subsection Point_set_processing_3Examples_scale_estimation Examples
 
-The following example reads a point set in the `xyz` format and
-estimates the global scale (both in K neighbor sense and in a range
-sense). If no `xyz` point set can be read, it tries to read a 2D point
-set and perform the same scales estimation.
+The following example reads a 3D point set in the `xyz` format and:
+
+- Estimates the K neighbor global scale
+- Uses it to smooth the point set
+- Estimates the range global scale
+- Uses it to simplify the point set
 
 \cgalExample{Point_set_processing_3/scale_estimation_example.cpp}
 
+This second example generates a 2D point set sampling a circle with
+variable noise. It then estimates the scale at 3 different locations
+of the domain.
+
+\cgalExample{Point_set_processing_3/scale_estimation_2d_example.cpp}
+
 
 
 \section Point_set_processing_3OutlierRemoval Outlier Removal
diff --git a/Point_set_processing_3/doc/Point_set_processing_3/examples.txt b/Point_set_processing_3/doc/Point_set_processing_3/examples.txt
index bfc21ed1d29..bd9a495d190 100644
--- a/Point_set_processing_3/doc/Point_set_processing_3/examples.txt
+++ b/Point_set_processing_3/doc/Point_set_processing_3/examples.txt
@@ -3,6 +3,7 @@
 \example Point_set_processing_3/read_ply_points_with_colors_example.cpp
 \example Point_set_processing_3/average_spacing_example.cpp
 \example Point_set_processing_3/scale_estimation_example.cpp
+\example Point_set_processing_3/scale_estimation_2d_example.cpp
 \example Point_set_processing_3/remove_outliers_example.cpp
 \example Point_set_processing_3/grid_simplification_example.cpp
 \example Point_set_processing_3/grid_simplify_indices.cpp