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)