fixes on the doc

Principal_component_analysis/doc_tex/Principal_component_analysis/intro.tex

@@ -1,7 +1,8 @@
 This \cgal\ package provides functions to compute global informations
-on the shape of a set of 2D or 3D objects such as points. It provides the computation of bounding boxes, centroids of point sets, barycenters of weighted point sets, as well as linear least squares fitting. Linear least squares fitting approximates a set of objects by a linear
-sub-space such as a line or a plane.
-Formally, given a set of points in $R^d$, linear least squares fitting amounts
+on the shape of a set of 2D or 3D objects such as points. It provides the computation of bounding boxes, centroids of point sets, barycenters of weighted point sets, as well as linear least squares fitting.
+
+Linear least squares fitting approximates a set of objects by a linear
+sub-space such as a line or a plane. Formally, given a set of points in $R^d$, linear least squares fitting amounts
 to find the linear sub-space of $R^d$ which minimizes the sum of squared
 distances from the points to their projection onto this linear sub-space. This
 problem is equivalent to search for the linear sub-space which maximizes the
@@ -10,7 +11,8 @@ of the covariance matrix. Eigenvectors corresponding to large eigenvalues are
 the directions in which the data has strong component, or equivalently large
 variance. If eigenvalues are the same there is no preferable sub-space.
 This package implements the linear least squares fitting for
-several objects of a CGAL 2D or 3D kernel: the best fit 2D line for 2D
+several objects of a \cgal\ 2D or 3D kernel: the best fit 2D line for 2D
 point sets, and the best fit 3D line or plane for point and
-triangle sets. The object sets are specified by iterator ranges.
+triangle sets. The object sets are specified by iterator ranges of
+containers.
 

Principal_component_analysis/doc_tex/Principal_component_analysis/main.tex

@@ -10,7 +10,7 @@
 \section{Examples}
 \label{subsec:pca_examples}
 
-\subsection{Bounding box of a point set}
+\subsection{Bounding Box of a Point Set}
 
 In the following example we use \stl\ containers of 2D and 3D points, and
 compute their bounding box. The kernel from which the input points
@@ -18,7 +18,7 @@ come is automatically deduced by the function.
 
 \ccIncludeExampleCode{Principal_component_analysis/bounding_box.C}
 
-\subsection{Centroid of a point set}
+\subsection{Centroid of a Point Set}
 
 In the following example we use \stl\ containers of 2D and 3D points, and
 compute their centroid. The kernel from which the input points
@@ -26,7 +26,7 @@ come is automatically deduced by the function.
 
 \ccIncludeExampleCode{Principal_component_analysis/centroid.C}
 
-\subsection{Barycenter of a set of weighted points}
+\subsection{Barycenter of a Set of Weighted Points}
 
 In the following example we use \stl\ containers of 2D and 3D weighted points,
 and compute their barycenter. The kernel from which the input points come is
@@ -34,7 +34,7 @@ automatically deduced by the function.
 
 \ccIncludeExampleCode{Principal_component_analysis/barycenter.C}
 
-\subsection{Best fitting line of a 2D point set}
+\subsection{Best Fitting Line of a 2D Point Set}
 
 In the following example we use an \stl\ container of 2D points, and
 compute the best fitting line. The kernel from which the input points

Principal_component_analysis/doc_tex/Principal_component_analysis_ref/centroid.tex

@@ -54,14 +54,6 @@ The dimension is also deduced automatically.
 \ccPrecond{first != beyond.} }
 
 
-%\ccExample
-%
-%In the following example we use \stl\ containers of 2D and 3D points, and
-%compute their centroids. The kernel from which the input points
-%come is automatically deduced by the function.
-%
-%\ccIncludeExampleCode{Linear_least_squares_fitting/centroid.C}
-
 \ccSeeAlso
 \ccRefIdfierPage{CGAL::barycenter}
 

Principal_component_analysis/doc_tex/Principal_component_analysis_ref/intro.tex

@@ -12,8 +12,11 @@
 
 \ccChapterAuthor{Pierre Alliez and Sylvain Pion}
 
-\subsection*{Definition}
+This \cgal\ package provides functions to compute global informations
+on the shape of a set of 2D or 3D objects such as points. It provides the computation of bounding boxes, centroids of point sets, barycenters of weighted point sets, as well as linear least squares fitting. It assumes the set of kernel primitive elements to be stored into an iterator range of a container.
 
+
+\subsection*{Definition}
 Given a point set in $R^d$, linear least squares fitting amounts to
 find the linear sub-space of $R^d$ which minimizes the sum of squared
 distances from the points to their projection onto this linear
@@ -23,17 +26,7 @@ being obtained by eigen decomposition of the covariance
 matrix. Eigenvectors corresponding to large eigenvalues are the
 directions in which the data has strong component, or equivalently
 large variance. If eigenvalues are the same there is no preferable
-sub-space.\\
-
-This \cgal\ package implements the linear least squares fitting for
-several objects of a CGAL 2D or 3D kernel: the best fit 2D line for 2D
-point sets, and the best fit 3D line/plane for point and
-triangle sets. It assumes the set of kernel primitive elements to be stored into an
-iterator range of a container. Bounding box, centroid and barycenter
-computations are provided as well. 
-
-%\ccHeading{Concepts}
-%\ccRefConceptPage{FittingTraits}\\
+sub-space.
 
 \ccHeading{Functions}