1 \section[Curves of functions from R in R
\textsuperscript{3}]%
2 {Curves of functions from $
\mathbb{R
}$ in $
\mathbb{R
}^
3$
} %$
4 %% \section{Fonctions R --> R\textsuperscript{3}}
6 The line of a defined
\Index{function
} calls the object
\Lkeyval{courbe
} and the option
\Lkeyword{function
}.
7 We can realize a helix in algebraic notation with the function:
10 \defFunction[algebraic
]{helice
}(t)
{3*cos(
4*t)
}{3*sin(
4*t)
}{t
}
13 \psset{lightsrc=
10 -
20 50,viewpoint=
50 -
20 20 rtp2xyz,Decran=
50}
14 \begin{LTXexample
}[width=
6.5cm
]
16 \begin{pspicture
}(-
6,-
3)(
6,
8)
17 \psframe*
[linecolor=blue!
50](-
6,-
3)(
6,
8)
18 \psSolid[object=grille,base=-
4 4 -
4 4,linecolor=red,linewidth=
0.5\pslinewidth]%
19 \axesIIID(
0,
0,
0)(
4,
4,
7)
20 \defFunction[algebraic
]{helice
}(t)
{3*cos(
4*t)
}{3*sin(
4*t)
}{t
}
21 \psSolid[object=courbe,
24 linecolor=blue,linewidth=
0.1,
30 \begin{LTXexample
}[width=
6.5cm
]
32 \begin{pspicture
}(-
6,-
3)(
6,
8)
33 \psframe*
[linecolor=blue!
50](-
6,-
3)(
6,
8)
34 \psset{lightsrc=
10 -
20 50,viewpoint=
50 -
20 30 rtp2xyz,Decran=
50}
35 \psSolid[object=grille,base=-
4 4 -
4 4,linecolor=red,linewidth=
0.5\pslinewidth]%
36 \axesIIID(
0,
0,
0)(
4,
4,
7)
38 \defFunction{cosRad
}(t)
{ t
2 mul Cos
4 mul
}{ t
}{ 0 }
39 \psSolid[object=courbe,linewidth=
0.1,
43 \psSolid[object=grille,base=-
4 4 -
4 4,linecolor=blue,linewidth=
0.5\pslinewidth](
0,
0,
3)
44 \psPoint(
0,
0,
3)
{O1
}\psPoint(
0,
0,
7)
{Z1
}\psline(O1)(Z1)
\psline[linestyle=dashed
](O1)(O)
45 \pstVerb{/tmin -
4 def /tmax
4 def
}%
46 \defFunction{sinRad
}(t)
{ t
}{ t Sin
3 mul
}{ 3 }
47 \psSolid[object=courbe,linewidth=
0.1,
54 \begin{LTXexample
}[width=
6.5cm
]
56 \begin{pspicture
}(-
6.5,-
3)(
7,
11)
57 \psset{lightsrc=
10 -
20 50,viewpoint=
50 -
20 20 rtp2xyz,Decran=
50}
58 \psSolid[object=grille,base=-
4 4 -
4 4,
59 linecolor=lightgray,linewidth=
0.5\pslinewidth]%
60 \psSolid[object=grille,base=-
4 4 0 8,
61 linecolor=lightgray,RotX=
90,
62 linewidth=
0.5\pslinewidth](
0,
4,
0)
63 \psSolid[object=grille,base=-
4 4 -
4 4,
64 linecolor=lightgray,RotY=
90,
65 linewidth=
0.5\pslinewidth](-
4,
0,
4)
66 \defFunction[algebraic
]{helice
}(t)
%
67 {1.3*(
1-cos(
2.5*t))*cos(
6*t)
}
68 {1.3*(
1-cos(
2.5*t))*sin(
6*t)
}{t
}
69 \defFunction[algebraic
]{helice_xy
}(t)
%
70 {1.3*(
1-cos(
2.5*t))*cos(
6*t)
}
71 {1.3*(
1-cos(
2.5*t))*sin(
6*t)
}{0}
72 \defFunction[algebraic
]{helice_xz
}%
73 (t)
{1.3*(
1-cos(
2.5*t))*cos(
6*t)
}{4}{t
}
74 \defFunction[algebraic
]{helice_yz
}%
75 (t)
{-
4}{1.3*(
1-cos(
2.5*t))*sin(
6*t)
}{t
}
77 \psSolid[object=courbe,r=
0,linecolor=blue,
78 linewidth=
0.05,resolution=
360,
79 normal=
0 0 1,function=helice_xy
]
80 \psSolid[object=courbe,r=
0,
81 linecolor=green,linewidth=
0.05,
82 resolution=
360,normal=
0 0 1,
84 \psSolid[object=courbe,r=
0,
85 linewidth=
0.05,resolution=
360,
86 normal=
0 0 1,function=helice_yz
]
87 \psSolid[object=courbe,r=
0,
88 linecolor=red,linewidth=
0.1,
89 resolution=
360,function=helice
]
94 These last function lines are found in an animated form on the website:
96 \centerline{\url{http://melusine.eu.org/syracuse/pstricks/pst-solides3d/animations/
}}