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parallelpiped.tex
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% Copyright © 2017-2018 Martin Ueding <martin-ueding.de>
% Licensed under CC-BY 4.0
\documentclass{scrartcl}
\pagestyle{empty}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, calc}
\begin{document}
\newcommand\boostfactorTwoD{0.3}
\newcommand\boostfactorThreeD{0.3}
No boost:
\begin{tikzpicture}[
rotate around x=-90,
rotate around z=-15,
scale=2,
]
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(1, 0, 0) node[below] {$x$};
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(0, 1, 0) node[above] {$y$};
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(0, 0, 1) node[left] {$z$};
\coordinate (boostx) at (1, 0, 0);
\coordinate (boosty) at (0, 1, 0);
\coordinate (boostz) at (0, 0, 1);
\foreach \a in {0,1}
\foreach \b in {0,1}
{
\draw ($\a*(boostx) + \b*(boosty)$) -- ++(boostz);
\draw ($\a*(boosty) + \b*(boostz)$) -- ++(boostx);
\draw ($\a*(boostz) + \b*(boostx)$) -- ++(boosty);
}
\end{tikzpicture}
\vspace{10ex}
Boost along the $(1, 1, 0)$ direction:
\begin{tikzpicture}[
rotate around x=-90,
rotate around z=-15,
scale=2,
]
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(1, 0, 0) node[below] {$x$};
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(0, 1, 0) node[above] {$y$};
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(0, 0, 1) node[left] {$z$};
\coordinate (boostx) at (1+\boostfactorTwoD, \boostfactorTwoD, 0);
\coordinate (boosty) at (\boostfactorTwoD, 1+\boostfactorTwoD, 0);
\coordinate (boostz) at (0, 0, 1);
\foreach \a in {0,1}
\foreach \b in {0,1}
{
\draw ($\a*(boostx) + \b*(boosty)$) -- ++(boostz);
\draw ($\a*(boosty) + \b*(boostz)$) -- ++(boostx);
\draw ($\a*(boostz) + \b*(boostx)$) -- ++(boosty);
}
\end{tikzpicture}
\vspace{10ex}
Boost along the $(1, 1, 1)$ direction:
\begin{tikzpicture}[
rotate around x=-90,
rotate around z=-15,
scale=2,
]
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(1, 0, 0) node[below] {$x$};
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(0, 1, 0) node[above] {$y$};
\draw[thick, ->, >=Latex] (0, 0, 0) -- ++(0, 0, 1) node[left] {$z$};
\coordinate (boostx) at (1+\boostfactorThreeD, \boostfactorThreeD, \boostfactorThreeD);
\coordinate (boosty) at (\boostfactorThreeD, 1+\boostfactorThreeD, \boostfactorThreeD);
\coordinate (boostz) at (\boostfactorThreeD, \boostfactorThreeD, 1+\boostfactorThreeD);
\foreach \a in {0,1}
\foreach \b in {0,1}
{
\draw ($\a*(boostx) + \b*(boosty)$) -- ++(boostz);
\draw ($\a*(boosty) + \b*(boostz)$) -- ++(boostx);
\draw ($\a*(boostz) + \b*(boostx)$) -- ++(boosty);
}
\end{tikzpicture}
\end{document}