point set processing: more on user ref

Point_set_processing_3/doc_tex/Point_set_processing_3/normals.tex

@@ -1,15 +1,13 @@
 \section{Normal Estimation}
 
-Two functions are provided to estimate the normal direction of the inferred surface at each point from the input point set. In both cases, the result is an unoriented normal vector for each input point.
+Two functions are provided to estimate the normal direction of the inferred surface at each point af an input point set. In both cases the result is an unoriented normal vector for each input point.
 
-Function \ccc{CGAL::jet_estimate_normals()} estimates the normal direction at each point from the set by fitting a jet surface over its $k$ nearest neighbors. The default jet is a quadric surface.\\
-This algorithm is well suited to point sets scattered over curved surfaces.
+Function \ccc{CGAL::jet_estimate_normals()} estimates the normal direction at each point from the input set by fitting a jet surface over its $k$ nearest neighbors. The default jet is a quadric surface. This algorithm is well suited to point sets scattered over curved surfaces.
 
-Function \ccc{CGAL::pca_estimate_normals()} estimates the normal direction at each point from the set by linear least squares fitting of a plane over its $k$ nearest neighbors.\\
-This algorithm is well suited to point sets scattered over plane surfaces. It is much faster than \ccc{CGAL::jet_estimate_normals()}.
+Function \ccc{CGAL::pca_estimate_normals()} estimates the normal direction at each point from the set by linear least squares fitting of a plane over its $k$ nearest neighbors. This algorithm is simpler and faster than \ccc{CGAL::jet_estimate_normals()}.
 
-\ccRefIdfierPage{CGAL::pca_estimate_normals}  \\
 \ccRefIdfierPage{CGAL::jet_estimate_normals}  \\
+\ccRefIdfierPage{CGAL::pca_estimate_normals}  \\
 
 % % Insert image pca_estimate_normals.jpg/eps
 % \begin{center}
@@ -27,14 +25,9 @@ This algorithm is well suited to point sets scattered over plane surfaces. It is
 %     \end{figure}
 % \end{center}
 
-Example:
-
-\ccIncludeExampleCode{Point_set_processing_3/pca_estimate_normals_example.cpp}
-
-
 \section{Normal Orientation}
 
-Function \ccc{CGAL::mst_orient_normals()} orients the normals of a set of points with (unoriented) normals using the method described by Hoppe et al. in {\em Surface reconstruction from unorganized points} \cite{cgal:hddms-srup-92}. More specifically, this method constructs a Riemannian graph over the input points and propagates a seed normal orientation within a minimum spanning tree computed over the graph with the Boost graph library. The result is an oriented normal vector for each input point/normal.
+Function \ccc{CGAL::mst_orient_normals()} orients the normals of a set of points with unoriented normals using the method described by Hoppe et al. in \emph{Surface reconstruction from unorganized points} \cite{cgal:hddms-srup-92}. More specifically, this method constructs a Riemannian graph over the input points (the graph of the $K$ nearest neighbor points) and propagates a seed normal orientation within a minimum spanning tree computed over the graph with the Boost graph library. The result is an oriented normal vector for each input point with normal.
 
 \ccRefIdfierPage{CGAL::mst_orient_normals}  \\
 
@@ -50,10 +43,13 @@ Function \ccc{CGAL::mst_orient_normals()} orients the normals of a set of points
     \end{ccHtmlOnly}
     % Title
     \begin{figure}[h]
-        \caption{Normal orientation of a cube's normals. Notice the left and bottom normals orientation.}
+        \caption{Normal orientation of a sampled cube surface.
+                 Left: unoriented normals.
+                 Right: oriented normals.}
     \end{figure}
 \end{center}
 
-Example: see \ccc{pca_estimate_normals_example.cpp} example above.
+The following example reads a point set from a file, estimates the normals through PCA over the 7 nearest neighbors and orient the normals:
+\ccIncludeExampleCode{Point_set_processing_3/normals_example.cpp}
 
 

Point_set_processing_3/doc_tex/Point_set_processing_3/smoothing.tex

@@ -18,6 +18,5 @@ Function \ccRefIdfierPage{CGAL::jet_smooth_point_set} smoothes the input point s
 %     \end{figure}
 % \end{center}
 
-Example:
-
+The following example generates a set of 9 points close to the $xy$ plane and smoothes them using the 8 nearest neighbors:
 \ccIncludeExampleCode{Point_set_processing_3/jet_smoothing_example.cpp}

Point_set_processing_3/examples/Point_set_processing_3/jet_smoothing_example.cpp

@@ -10,15 +10,15 @@ int main(void)
 {
     // generate point set
     std::deque<Point> points;
-    points.push_back(Point( 0.0, 0.0, 0.01));
-    points.push_back(Point(-0.1,-0.1, 0.02));
-    points.push_back(Point(-0.1,-0.2, 0.01));
-    points.push_back(Point(-0.1, 0.1, 0.02));
-    points.push_back(Point( 0.1,-0.1, 0.00));
-    points.push_back(Point( 0.1, 0.2, 0.01));
-    points.push_back(Point( 0.2, 0.0, 0.02));
-    points.push_back(Point( 0.2, 0.1, 0.00));
-    points.push_back(Point( 0.0,-0.1, 0.01));
+    points.push_back(Point( 0.0, 0.0, 0.001));
+    points.push_back(Point(-0.1,-0.1, 0.002));
+    points.push_back(Point(-0.1,-0.2, 0.001));
+    points.push_back(Point(-0.1, 0.1, 0.002));
+    points.push_back(Point( 0.1,-0.1, 0.000));
+    points.push_back(Point( 0.1, 0.2, 0.001));
+    points.push_back(Point( 0.2, 0.0, 0.002));
+    points.push_back(Point( 0.2, 0.1, 0.000));
+    points.push_back(Point( 0.0,-0.1, 0.001));
 
     // smoothing
     const unsigned int nb_neighbors = 8;