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par-point-en.tex
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\section{The object \texttt{point}}
\subsection{Definition via coordinates}
The object \Lkeyword{point} defines a \Index{point}. The simplest method is to use the argument \texttt{\Lkeyword{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 \texttt{\Lkeyword{definition}=\Lkeyval{solidgetsommet}};
\texttt{\Lkeyword{args}= $solid$ $k$}.
The vertex with index $k$ of the solid $solid$.
\item \texttt{\Lkeyword{definition}=\Lkeyval{solidcentreface}};
\texttt{\Lkeyword{args}=$solid$ $k$}.
The centre of the face with index $k$ of the solid $solid$.
\item \texttt{\Lkeyword{definition}=\Lkeyval{isobarycentre3d}};
\texttt{\Lkeyword{args}=\{[ $A_0$ $\ldots $ $A_{n}$ ]\}}.
{The isobarycentre of the system $[(A_0, 1);
\ldots ; (A_n, 1)]$.}
\item \texttt{\Lkeyword{definition}=\Lkeyval{barycentre3d}};
\Lkeyword{args}= \{[ $A$ $a$ $B$ $b$ ] \}.
{The barycentre of the system $[(A, a) ; (B, b)]$.}
\item \texttt{\Lkeyword{definition}=\Lkeyval{hompoint3d}};
\texttt{\Lkeyword{args}={$M$ $A$ $\alpha $}}.
{The image of $M$ via a homothety with centre $A$ and ratio $\alpha $.}
\item \texttt{\Lkeyword{definition}=\Lkeyval{sympoint3d}};
\texttt{\Lkeyword{args}= {$M$ $A$}}.
{The image of $M$ via the center of symmetry $A$}%I don't understand
\item \texttt{\Lkeyword{definition}=\Lkeyval{translatepoint3d}};
\texttt{\Lkeyword{args}= {$M$ $u$}}.
{The image of $M$ under the translation via the vector $\vec u$}
\item \texttt{\Lkeyword{definition}=\Lkeyval{scaleOpoint3d}};
\texttt{\Lkeyword{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 \texttt{\Lkeyword{definition}=\Lkeyval{rotateOpoint3d}};
\texttt{\Lkeyword{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 \Lkeyword{definition}=\Lkeyval{orthoprojplane3d};
\texttt{\Lkeyword{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 \texttt{\Lkeyword{definition}=\Lkeyval{milieu3d}};
\texttt{\Lkeyword{args}= {$A$ $B$}}.
{The midpoint of $[AB]$}
\item \texttt{\Lkeyword{definition}=\Lkeyval{addv3d}};
\texttt{\Lkeyword{args}= {$A$ $u$}}.
{Gives the point $B$ so that $\overrightarrow {AB} = \vec u$}
\end{itemize}
\endinput

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