3 \subsection{Direct definition}
5 The object \Lkeyword{point} defines a \Index{point}. The values $(x,y)$ of
6 its coordinates can be passed directly to the macro
7 \Lcs{psProjection} or indirectly via the option \Lkeyword{args}.
9 Thus the two commands \verb+\psProjection[object=point](1,2)+ and
10 \verb+\psProjection[object=point,arg=1 2]+ are equivalent and lead
11 to the projection of the point with coordinates $(1,2)$ onto the
16 The option \texttt{\Lkeyword{text}=my text} allows us to project a string of
17 characters onto the chosen plane next to a chosen point. The
18 positioning is made with the argument \texttt{\Lkeyword{pos}=value} where
19 \texttt{value} is one of the following $\{$ul, cl, bl, dl, ub, cb, bb,
20 db, uc, cc, bc, dc, ur, cr, br, dr$\}$.
22 The details of the parameter \Lkeyword{pos} will be discussed in a
25 \begin{LTXexample}[width=7.5cm]
26 \begin{pspicture}(-3,-3)(4,3.5)%
27 \psframe*[linecolor=blue!50](-3,-3)(4,3.5)
28 \psset{viewpoint=50 30 15,Decran=60}
30 %% definition du plan de projection
38 %% definition du point A
39 \psProjection[object=point,
43 \psProjection[object=point,
47 \axesIIID(4,2,2)(5,4,3)
53 \subsection{Naming and memorising a point}
55 If the option \texttt{\Lkeyword{name}=myName} is given, the coordinates
56 $(x,y)$ of the chosen point are saved under the name \texttt{myName} and so
59 \subsection{Some other definitions}
61 There are other methods to define a point in 2D. The options
62 \Lkeyword{definition} and \Lkeyword{args} support the following
67 \item \texttt{\Lkeyword{definition}=\Lkeyval{milieu}};
68 \texttt{\Lkeyword{args}=$A$ $B$}.
70 The midpoint of the line segment $[AB]$
72 \item \texttt{\Lkeyword{definition}=\Lkeyval{parallelopoint}};
73 \texttt{\Lkeyword{args}=$A$ $B$ $C$}.
75 The point $D$ for which $(ABCD)$ is a
78 \item \texttt{\Lkeyword{definition}=\Lkeyval{translatepoint}};
79 \texttt{\Lkeyword{args}=$M$ $u$}.
81 The image of the point $M$ shifted by the vector
85 \item \texttt{\Lkeyword{definition}=\Lkeyval{rotatepoint}};
86 \texttt{\Lkeyword{args}=$M$ $I$ $r$}.
88 The image of the point $M$ under a
89 rotation about the point $I$ through an angle $r$ (in degrees)
91 \item \texttt{\Lkeyword{definition}=\Lkeyval{hompoint}};
92 \texttt{\Lkeyword{args}=$M$ $A$ $k$}.
94 The point $M'$ satisfying
95 $\overrightarrow {AM'} = k \overrightarrow {AM}$
97 \item \texttt{\Lkeyword{definition}=\Lkeyval{orthoproj}};
98 \texttt{\Lkeyword{args}=+$M$ $d$}.
100 The orthogonal projection of the point
101 $M$ onto the line $d$.
103 \item \texttt{\Lkeyword{definition}=\Lkeyval{projx}};
104 \texttt{\Lkeyword{args}=$M$}.
106 The projection of the point $M$ onto the $Ox$
109 \item \texttt{\Lkeyword{definition}=\Lkeyval{projy}};
110 \texttt{\Lkeyword{args}=$M$}.
112 The projection of the point $M$ onto the $Oy$
115 \item \texttt{\Lkeyword{definition}=\Lkeyval{sympoint}};
116 \texttt{\Lkeyword{args}=$M$ $I$}.
118 The point of symmetry of $M$ with respect
121 \item \texttt{\Lkeyword{definition}=\Lkeyval{axesympoint}};
122 \texttt{\Lkeyword{args}=$M$ $d$}.
124 The axially symmetrical point of $M$ with
125 respect to the line $d$.
127 \item \texttt{\Lkeyword{definition}=\Lkeyval{cpoint}};
128 \texttt{\Lkeyword{args}=$\alpha $ $C$}.
130 The point corresponding to the
131 angle $\alpha $ on the circle $C$
133 \item \texttt{[definition=xdpoint]};
136 The $Ox$ intercept $x$ of the line $d$.
138 \item \texttt{\Lkeyword{definition}=\Lkeyval{ydpoint}};
139 \texttt{\Lkeyword{args}=$y$ $d$}.
141 The $Oy$ intercept $y$ of the line $d$.
143 \item \texttt{\Lkeyword{definition}=\Lkeyval{interdroite}};
144 \texttt{\Lkeyword{args}=$d_1$ $d_2$}.
146 The intersection point of the lines
149 \item \texttt{\Lkeyword{definition}=\Lkeyval{interdroitecercle}};
150 \texttt{\Lkeyword{args}=$d$ $I$ $r$}.
152 The intersection points of the line
153 $d$ with a circle of centre $I$ and radius $r$.
157 In the example below, we define and name three points $A$, $B$ and
158 $C$, and then calculate the point $D$ for which $(ABCD)$ is a
159 parallelogram together with the centre of this parallelogram.
161 \begin{LTXexample}[width=7.5cm]
162 \begin{pspicture}(-3,-3)(4,3.5)%
163 \psframe*[linecolor=blue!50](-3,-3)(4,3.5)
164 \psset{viewpoint=50 30 15,Decran=60}
166 %% definition du plan de projection
167 \psSolid[object=plan,
174 %% definition du point A
175 \psProjection[object=point,
176 text=A,pos=ur,name=A](-1,.7)
177 %% definition du point B
178 \psProjection[object=point,
179 text=B,pos=ur,name=B](2,1)
180 %% definition du point C
181 \psProjection[object=point,
182 text=C,pos=ur,name=C](1,-1.5)
183 %% definition du point D
184 \psProjection[object=point,
185 definition=parallelopoint,
187 text=D,pos=ur,name=D]
188 %% definition du point G
189 \psProjection[object=point,
193 \axesIIID(4,2,2)(5,4,3)