1 \section{The object \texttt{point}}
3 \subsection{Definition via coordinates}
5 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.
6 If we have already named a point $M(x, y, z)$ (see chapter ``\textit{Advanced usage\/}''), we can easily use the argument \texttt{args=$M$}.
8 \subsection{Some other definitions}
10 There are some other possibilities for defining a point. Here a list of possible definitions with the appropriate arguments:
14 \item \texttt{\Lkeyword{definition}=\Lkeyval{solidgetsommet}};
15 \texttt{\Lkeyword{args}= $solid$ $k$}.
17 The vertex with index $k$ of the solid $solid$.
19 \item \texttt{\Lkeyword{definition}=\Lkeyval{solidcentreface}};
20 \texttt{\Lkeyword{args}=$solid$ $k$}.
22 The centre of the face with index $k$ of the solid $solid$.
24 \item \texttt{\Lkeyword{definition}=\Lkeyval{isobarycentre3d}};
25 \texttt{\Lkeyword{args}=\{[ $A_0$ $\ldots $ $A_{n}$ ]\}}.
27 {The isobarycentre of the system $[(A_0, 1);
30 \item \texttt{\Lkeyword{definition}=\Lkeyval{barycentre3d}};
31 \Lkeyword{args}= \{[ $A$ $a$ $B$ $b$ ] \}.
33 {The barycentre of the system $[(A, a) ; (B, b)]$.}
35 \item \texttt{\Lkeyword{definition}=\Lkeyval{hompoint3d}};
36 \texttt{\Lkeyword{args}={$M$ $A$ $\alpha $}}.
38 {The image of $M$ via a homothety with centre $A$ and ratio $\alpha $.}
40 \item \texttt{\Lkeyword{definition}=\Lkeyval{sympoint3d}};
41 \texttt{\Lkeyword{args}= {$M$ $A$}}.
43 {The image of $M$ via the center of symmetry $A$}%I don't understand
45 \item \texttt{\Lkeyword{definition}=\Lkeyval{translatepoint3d}};
46 \texttt{\Lkeyword{args}= {$M$ $u$}}.
48 {The image of $M$ under the translation via the vector $\vec u$}
50 \item \texttt{\Lkeyword{definition}=\Lkeyval{scaleOpoint3d}};
51 \texttt{\Lkeyword{args}= {$x$ $y$ $z$ $k_1$ $k_2$ $k_3$}}.
53 {This gives a ``dilation'' \ of the coordinates of the point $M (x, y,
54 z)$ on the axes $Ox$, $Oy$ and $Oz$ each multiplied by an appropriate factor $k_1$,
57 \item \texttt{\Lkeyword{definition}=\Lkeyval{rotateOpoint3d}};
58 \texttt{\Lkeyword{args}= {$M$ $\alpha_x$ $\alpha_y$ $\alpha_z$}}.
60 {The image of $M$ through consecutive rotations---centered at $O$---and with respective angles
61 $\alpha_x$, $\alpha_y$ and $\alpha_z$ around the axes $Ox$,
66 %% Projection orthogonale d'un point 3d sur un plan
67 %% Mx My Mz (=le point a projeter)
68 %% Ax Ay Az (=un point du plan)
69 %% Vx Vy Vz (un vecteur normal au plan)
70 \item \Lkeyword{definition}=\Lkeyval{orthoprojplane3d};
71 \texttt{\Lkeyword{args}= {$M$ $A$ $\vec v$}}.
73 {The projection of the point $M$ to the plane $P$ which is defined
74 by the point $A$ and the vector $\vec v$, perpendicular to $P$.}
76 \item \texttt{\Lkeyword{definition}=\Lkeyval{milieu3d}};
77 \texttt{\Lkeyword{args}= {$A$ $B$}}.
79 {The midpoint of $[AB]$}
81 \item \texttt{\Lkeyword{definition}=\Lkeyval{addv3d}};
82 \texttt{\Lkeyword{args}= {$A$ $u$}}.
84 {Gives the point $B$ so that $\overrightarrow {AB} = \vec u$}