doc-en/par-point-en.tex

   1 \section{The object \texttt{point}}
   2
   3 \subsection{Definition via coordinates}
   4
   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=$M$}.
   7
   8 \subsection{Some other definitions}
   9
  10 There are some other possibilities for defining a point. Here a list of possible definitions with the appropriate arguments:
  11
  12 \begin{itemize}
  13
  14 \item \texttt{\Lkeyword{definition}=\Lkeyval{solidgetsommet}};
  15 \texttt{\Lkeyword{args}= $solid$ $k$}.
  16
  17 The vertex with index $k$ of the solid $solid$.
  18
  19 \item \texttt{\Lkeyword{definition}=\Lkeyval{solidcentreface}};
  20 \texttt{\Lkeyword{args}=$solid$ $k$}.
  21
  22 The centre of the face with index $k$ of the solid $solid$.
  23
  24 \item \texttt{\Lkeyword{definition}=\Lkeyval{isobarycentre3d}};
  25 \texttt{\Lkeyword{args}=\{[ $A_0$ $\ldots $ $A_{n}$ ]\}}.
  26
  27    {The isobarycentre of the system $[(A_0, 1);
  28    \ldots ; (A_n, 1)]$.}
  29
  30 \item \texttt{\Lkeyword{definition}=\Lkeyval{barycentre3d}};
  31 \Lkeyword{args}=  \{[ $A$ $a$ $B$ $b$ ] \}.
  32
  33    {The barycentre of the system $[(A, a) ; (B, b)]$.}
  34
  35 \item \texttt{\Lkeyword{definition}=\Lkeyval{hompoint3d}};
  36 \texttt{\Lkeyword{args}={$M$ $A$ $\alpha $}}.
  37
  38    {The image of $M$ via a homothety with centre $A$ and ratio $\alpha $.}
  39
  40 \item \texttt{\Lkeyword{definition}=\Lkeyval{sympoint3d}};
  41 \texttt{\Lkeyword{args}= {$M$ $A$}}.
  42
  43    {The image of $M$ via the center of symmetry $A$}%I don't understand
  44
  45 \item \texttt{\Lkeyword{definition}=\Lkeyval{translatepoint3d}};
  46 \texttt{\Lkeyword{args}=   {$M$ $u$}}.
  47
  48    {The image of $M$ under the translation via the vector $\vec u$}
  49
  50 \item \texttt{\Lkeyword{definition}=\Lkeyval{scaleOpoint3d}};
  51 \texttt{\Lkeyword{args}= {$x$ $y$ $z$  $k_1$ $k_2$ $k_3$}}.
  52
  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 $k_1$,
  55    $k_2$ and $k_3$}
  56
  57 \item \texttt{\Lkeyword{definition}=\Lkeyval{rotateOpoint3d}};
  58 \texttt{\Lkeyword{args}= {$M$ $\alpha_x$ $\alpha_y$ $\alpha_z$}}.
  59
  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 $Ox$,
  62    $Oy$ and $Oz$.}
  63
  64
  65
  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}= {$M$ $A$ $\vec v$}}.
  72
  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 $P$.}
  75
  76 \item \texttt{\Lkeyword{definition}=\Lkeyval{milieu3d}};
  77 \texttt{\Lkeyword{args}= {$A$ $B$}}.
  78
  79    {The midpoint of $[AB]$}
  80
  81 \item \texttt{\Lkeyword{definition}=\Lkeyval{addv3d}};
  82 \texttt{\Lkeyword{args}= {$A$ $u$}}.
  83
  84    {Gives the point $B$ so that $\overrightarrow {AB} = \vec u$}
  85
  86 \end{itemize}
  87
  88 \endinput