+\commande|\meshAddPointBW[«options»]{«list of points» or «file name»}{«point» or «number of line»}|\medskip
+
+This command allows to plot the different step of the addition of a
+point in a Delaunay triangulation, using the Bowyer and Watson
+algorithm.
+
+This macro produce the Delaunay triangulation (using the Bowyer and
+Watson algorithm) of the given \meta{list of points} and shows a step
+of the algorithm when the \meta{point} is added. The list of
+points must be given in the following way:
+\begin{center}
+ \verb+(x1,y1);(x2,y2);(x3,y3);...;(xn,yn)+
+\end{center}
+and the point is of the form \verb+(x,y)+. The \meta{file name}
+and \meta{number of line} will be explained in the option
+description.
+
+One can use the macro as fallow:
+\begin{Exemple}
+ \meshAddPointBW[step=badtriangles]{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+ \meshAddPointBW[step=cavity]{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+ \meshAddPointBW[step=newtriangles]{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+\end{Exemple}
+The default value for \Verb+step+ is \Verb+badtriangles+. The first
+line is then equivalent to
+\begin{latexcode}
+\meshAddPointBW{(1.5,1);(4,0);(4.5,2.5);(1.81,2.14);(2.5,0.5);(2.8,1.5)}{(2.2,1.8)}
+\end{latexcode}
+
+\subsubsection{The Options}
+
+There are several options (some of them are the same as for
+\Verb+\buildMeshBW+) to customize the drawing.
+\begin{optionsenum}
+\item[mode = int (default) \textme{or} ext:] this option allows to
+ use either the previously described set of point in the argument
+ number one, or
+ a file, containing, line by line (2 columns), the points. Such a
+ file looks like :
+\begin{verbatim}
+x1 y1
+x2 y2
+x3 y3
+...
+xn yn
+\end{verbatim}
+For the second argument of the macro, if we are in the
+\Verb+mode = ext+, the argument must be the \emph{line number} of the file
+corresponding to the point we want to add. The algorithm will stop the
+line before to build the initial triangulation for which it will add
+the point corresponding to the line. The other lines of the file are
+ignored.
+\item[bbox = none (default) \textme{or} show:] this option allows to draw the
+ added points to form a \emph{bounding box} and the corresponding
+ triangulation. By default, these triangles are removed at the end of
+ the algorithm.
+\item[color = \meta{value} (default: black):] The color of the
+ drawing.
+\item[colorBbox = \meta{value} (default: black):] The color of the
+ drawing for the elements (points and triangles) belonging to the
+ bounding box.
+\item[colorNew = \meta{value} (default: red):] The color of the
+ drawing of the ``new'' elements which are the point to add, the
+ polygon of the cavity, and the new triangles.
+\item[colorBack = \meta{value} (default: black!20):] The color for the
+ filling of the region concerned by the addition of the new point.
+\item[colorCircle = \meta{value} (default: green):] The color for
+ circoncircle of the triangles containing the point to add.
+\item[meshpoint = \meta{value} (default: P):] The letter(s) used to
+ label the vertices of the triangulation. It is include in the math
+ mode delimiters \Verb+$...$+. The bounding box points are labeled
+ with a star exponent, and numbered from 1 to 4.
+\item[step = badtriangles (default) \textme{or} cavity \textme{or}
+ newtriangles:] To choose the step we want to draw, corresponding to
+ the steps of the Bowyer and Watson algorithm.
+\item[newpoint = \meta{value} (default: P):] The letter(s) used to
+ label the new point of the triangulation. It is include in the math
+ mode delimiters \Verb+$...$+.
+\item[tikz (boolean, default:false):] By default, this boolean is set
+ to \Verb+false+, and MetaPost (with \Verb+luamplib+) is used to draw
+ the picture. With this option, it is \Verb+tikz+ the \textit{drawing
+ engine}.
+\item[scale = \meta{value} (default: 1cm):] The scale option defines
+ the scale at which the picture is draw (the same for the two
+ axis). It must contain the unit of length (cm,
+ pt, etc.).
+\end{optionsenum}