par-point_en_corr.tex

\section{Point}
 
\subsection{Definition via coordinates}
 
The object \verb+point+ defines a point. The simplest method is to use the argument \texttt{[args=$x$ $y$ $z$]} to specify its coordinates.
If we have already named a point $M(x, y, z)$ (see chapter ``\textit{Advanced usage\/}''), we can easily use the argument \texttt{[args=$M$]}.
 
\subsection{Some other definitions}
 
There are some other possibilities for defining a point. Here a list of possible definitions with the appropriate arguments:
 
\begin{itemize}
 
\item \verb+[definition=solidgetsommet]+;
\verb+args=+ $solid$ $k$.
 
The vertex with index $k$ of the solid $solid$.
 
\item \verb+[definition=solidcentreface]+;
\verb+args=+ $solid$ $k$.
 
The center of the face with index $k$ of the solid $solid$.
 
\item \verb+[definition=isobarycentre3d]+;
\verb+args=+
   {\{$[$ $A_0$ $\ldots $ $A_{n}$ $]$\}}.
 
   {The isobarycenter of the system $[(A_0, 1);
   \ldots ; (A_n, 1)]$.}
 
\item \verb+[definition=barycentre3d]+;
\verb+args=+
   {\{$[$ $A$ $a$ $B$ $b$ $]$\}}.
 
   {The barycenter of the system $[(A, a) ; (B, b)]$.}
 
\item \verb+[definition=hompoint3d]+;
\verb+args=+
   {$M$ $A$ $\alpha $}.
 
   {The image of $M$ via a homothety with center $A$ and ratio $\alpha $.}
 
\item \verb+[definition=sympoint3d]+;
\verb+args=+
   {$M$ $A$}.
 
   {The image of $M$ via the center of symmetry $A$}%I don't understand
 
\item \verb+[definition=translatepoint3d]+;
\verb+args=+
   {$M$ $u$}.
 
   {The image of $M$ under the translation via the vector $\vec u$}
 
\item \verb+[definition=scaleOpoint3d]+;
\verb+args=+
   {$x$ $y$ $z$  $k_1$ $k_2$ $k_3$}.
 
   {This gives a ``dilation'' \ of the coordinates of the point $M (x, y,
   z)$ on the axes $Ox$, $Oy$ and $Oz$ each multiplied by an appropriate factor $k_1$,
   $k_2$ and $k_3$}
 
\item \verb+[definition=rotateOpoint3d]+;
\verb+args=+
   {$M$ $\alpha_x$ $\alpha_y$ $\alpha_z$}.
 
   {The image of $M$ through consecutive rotations -- centered at $O$ -- and with respective angles
   $\alpha_x$, $\alpha_y$ and $\alpha_z$ around the axes $Ox$,
   $Oy$ and $Oz$.}
 
 
 
%% Projection orthogonale d'un point 3d sur un plan
%% Mx My Mz (=le point a projeter)
%% Ax Ay Az (=un point du plan)
%% Vx Vy Vz (un vecteur normal au plan)
\item \verb+[definition=orthoprojplane3d]+;
\verb+args=+
   {$M$ $A$ $\vec v$}.
 
   {The projection of the point $M$ to the plane $P$ which is defined
   by the point $A$ and the vector $\vec v$, perpendicular to $P$.}
 
\item \verb+[definition=milieu3d]+;
\verb+args=+
   {$A$ $B$}.
 
   {The midpoint of $[AB]$}
 
\item \verb+[definition=addv3d]+;
\verb+args=+
   {$A$ $u$}.
 
   {Gives the point $B$ so that $\overrightarrow {AB} = \vec u$}
 
\end{itemize}