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$
}