極座標と球座標
直交座標と,2つの最も重要な非直交座標である極座標,球座標の間の変換を行うための関数が利用可能になった.
直交座標と極座標の間の変換を行う.
In[1]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_42.png)
ToPolarCoordinates[{x, y}]
Out[1]=
![](assets.ja/polar-and-spherical-coordinates/O_37.png)
In[2]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_43.png)
FromPolarCoordinates[{r, \[Theta]}]
Out[2]=
![](assets.ja/polar-and-spherical-coordinates/O_38.png)
直交座標と球座標の間の変換を行う.
In[3]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_44.png)
ToSphericalCoordinates[{x, y, z}]
Out[3]=
![](assets.ja/polar-and-spherical-coordinates/O_39.png)
In[4]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_45.png)
FromSphericalCoordinates[{r, \[Theta], \[CurlyPhi]}]
Out[4]=
![](assets.ja/polar-and-spherical-coordinates/O_40.png)
極座標は,自然に高次元に一般化される.
In[5]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_46.png)
ToPolarCoordinates[{w, x, y, z}]
In[6]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_47.png)
{Sqrt[w^2 + x^2 + y^2 + z^2], ArcCos[w/Sqrt[w^2 + x^2 + y^2 + z^2]],
ArcCos[x/Sqrt[x^2 + y^2 + z^2]], ArcTan[y, z]}
In[7]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_48.png)
FromPolarCoordinates[{r, \[Theta]1, \[Theta]2, \[Theta]3, \
\[CurlyPhi]}]
Out[7]=
![](assets.ja/polar-and-spherical-coordinates/O_41.png)
極座標と球座標で表された曲線をプロットする.
In[8]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_49.png)
ParametricPlot[
FromPolarCoordinates[{Exp[-t/10], t}] // Evaluate, {t, 0, 50},
PlotRange -> All]
Out[8]=
![](assets.ja/polar-and-spherical-coordinates/O_42.png)
In[9]:=
![Click for copyable input](assets.ja/polar-and-spherical-coordinates/In_50.png)
ParametricPlot3D[
FromSphericalCoordinates[{1, TriangleWave[{0, Pi}, p/(2 Pi)], p}] //
Evaluate, {p, 0, 2 Pi}]
Out[9]=
![](assets.ja/polar-and-spherical-coordinates/O_43.png)