File:Bsp-wuerfel.png

Beispielskizze zur Einführung in die Rotation mit Quaternionen: Würfel im euklidischen Raum.

Gezeichnet in LaTeX mit TikZ/PGF:

\begin{tikzpicture}[x={(-3.85mm, -3.85mm)}, y={(10mm, 0mm)}, z={(0mm, 10mm)}]
\coordinate[label=above left:$\vec{P}_1$] (P1) at (1,-1,-1);
\coordinate[label=above left:$\vec{P}_2$] (P2) at (1,-1,1);
\coordinate[label=right:$\vec{P}_3$] (P3) at (1,1,1);
\coordinate[label=right:$\vec{P}_4$] (P4) at (1,1,-1);
\coordinate[label=above left:$\vec{P}_5$] (P5) at (-1,-1,-1);
\coordinate[label=above left:$\vec{P}_6$] (P6) at (-1,-1,1);
\coordinate[label=right:$\vec{P}_7$] (P7) at (-1,1,1);
\coordinate[label=right:$\vec{P}_8$] (P8) at (-1,1,-1);

\draw[->] (0,0,0) -- (5,0,0);
\draw[->] (0,0,0) -- (0,2.5,0);
\draw[->] (0,0,0) -- (0,0,2.5);
\draw[thick] (P1) -- (P2) -- (P3) -- (P4);
\draw[thick, red] (P4) -- (P1) node[pos=0.5, below]{$\vec{P}_{41}$};
\draw[dashed] (P5) -- (P6);
\draw[thick] (P6) -- (P7);
\draw[thick] (P7) -- (P8);
\draw[dashed] (P8) -- (P5);
\draw[dashed] (P1) -- (P5);
\draw[thick] (P2) -- (P6);
\draw[thick] (P3) -- (P7);
\draw[thick] (P4) -- (P8);

\foreach \point in {P1,P2,P3,P4,P5,P6,P7,P8}
\draw[fill=red,opacity=1] (\point) circle (2pt);

\node at (5.6,0,0) {$x$};
\node at (0,2.7,0) {$y$};
\node at (0,0,2.7) {$z$};
\end{tikzpicture}