1 \section{\Index{Transformations
} to a point
}
3 Given is an initial point $A(x,y,z)$. Now we make some
4 rotations around the axes $Ox$, $Oy$ and $Oz$ with the appropriate angles (in degrees):
5 \verb+
[RotX=valueX,RotY=valueY,RotZ=valueZ
]+, in this order,
6 then translate it with the vector $(v_x,v_y,v_z)$. The problem is to get back
7 the coordinates of the image (final point) $A'(x',y',z')$.
10 \texttt{\textbackslash psTransformPoint
[RotX=valueX,RotY=valueY,
11 RotZ=valueZ
](x y z)(vx,vy,vz)\
{A'\
}}\\
12 now allows us to save the node $A'$, the coordinates of the transformed point.
14 In the following example, $A(
2,
2,
2)$ is one of the vertices of the initial
15 cube, where the centre is placed at the origin.
18 \psSolid[object=cube,a=
4,action=draw*,linecolor=red
]%
21 Some transformations are applied to the cube:
24 \psSolid[object=cube,a=
4,action=draw*,RotX=-
30,RotY=
60,RotZ=-
60](
7.5,
11.25,
10)
%
27 To obtain the image of $A$, we use the following command:
31 \psTransformPoint[RotX=-
30,RotY=
60,RotZ=-
60](
2 2 2)(
7.5,
11.25,
10)
{A'
}
34 This allows us, for example, to name these points and then draw the vector $
\overrightarrow{AA'
}$.
36 \begin{pspicture
}(-
2,-
4)(
6,
6)
38 \psset{viewpoint=
50 20 30 rtp2xyz,Decran=
50,unit=
0.5}
39 \psSolid[object=cube,a=
4,action=draw*,linecolor=red
]%
40 \psPoint(
2,
2,
2)
{A
}\psdot(A)
41 \psSolid[object=cube,a=
4,action=draw*,RotX=-
30,RotY=
60,RotZ=-
60](
7.5,
11.25,
10)
%
42 \psTransformPoint[RotX=-
30,RotY=
60,RotZ=-
60](
2 2 2)(
7.5,
11.25,
10)
{A'
}
43 \psdot(A')
\psline[linecolor=blue,arrowsize=
0.3]{{o-v
}}(A)(A')
44 \uput[u
](A')
{$A'$
}\uput[u
](A)
{$A$
}
45 \psset{solidmemory,action=none
}
46 \psSolid[object=cube,a=
4,name=A1,
](
0,
0,
0)
47 \psSolid[object=plan,definition=solidface,args=A1
0,name=P0
]
48 \psSolid[object=plan,definition=solidface,args=A1
1,name=P1
]
49 \psSolid[object=plan,definition=solidface,args=A1
4,name=P4
]
51 \psProjection[object=texte,linecolor=red,text=A,plan=P0
]
52 \psProjection[object=texte,linecolor=red,text=B,plan=P1
]
53 \psProjection[object=texte,linecolor=red,text=E,plan=P4
]
54 \psSolid[object=cube,a=
4,RotX=-
30,RotY=
60,RotZ=-
60,name=A2,
](
7.5,
11.25,
10)
55 \psSolid[object=plan,definition=solidface,args=A2
0,name=P'
0]
56 \psSolid[object=plan,definition=solidface,args=A2
1,name=P'
1]
57 \psSolid[object=plan,definition=solidface,args=A2
2,name=P'
2]
58 \psProjection[object=texte,text=A,plan=P'
0]
59 \psProjection[object=texte,text=B,plan=P'
1]
60 \psProjection[object=texte,text=C,plan=P'
2]
61 \axesIIID(
2,
2,
2)(
10,
10,
8)