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determinant_3d.tex
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determinant_3d.tex
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\documentclass[tikz,border=10pt]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{backgrounds}
\begin{document}
\tdplotsetmaincoords{60}{110}
\begin{tikzpicture}[scale=2, tdplot_main_coords, background rectangle/.style={fill=white}, show background rectangle,]
% Draw minor grid lines (0.2 step)
\begin{scope}[canvas is xy plane at z=0]
\draw[gray!30, ultra thin, step=0.2] (0,0) grid (1.2,1.2);
\end{scope}
\begin{scope}[canvas is xz plane at y=0]
\draw[gray!30, ultra thin, step=0.2] (0,0) grid (1.2,1.2);
\end{scope}
\begin{scope}[canvas is yz plane at x=0]
\draw[gray!30, ultra thin, step=0.2] (0,0) grid (1.2,1.2);
\end{scope}
\draw[thick,->] (0,0,0) -- (1.2,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,1.2,0) node[anchor=north west]{$y$};
\draw[thick,->] (0,0,0) -- (0,0,1.2) node[anchor=south]{$z$};
\draw[blue!50, thick, fill=blue!20,opacity=0.5, fill opacity = .2] (0,0,0) -- (1,0,0) -- (1,1,0) -- (0,1,0) -- cycle;
\draw[blue!50, thick, fill=blue!20,opacity=0.5, fill opacity = .2] (0,0,0) -- (0,1,0) -- (0,1,1) -- (0,0,1) -- cycle;
\draw[blue!50, thick, fill=blue!20,opacity=0.5, fill opacity = .2] (0,0,0) -- (1,0,0) -- (1,0,1) -- (0,0,1) -- cycle;
\draw[blue!50, thick, fill=blue!20,opacity=0.5, fill opacity = .2] (1,0,0) -- (1,1,0) -- (1,1,1) -- (1,0,1) -- cycle;
\draw[blue!50, thick, fill=blue!20,opacity=0.5, fill opacity = .2] (0,1,0) -- (1,1,0) -- (1,1,1) -- (0,1,1) -- cycle;
\draw[blue!50, thick, fill=blue!20,opacity=0.5, fill opacity = .2] (0,0,1) -- (1,0,1) -- (1,1,1) -- (0,1,1) -- cycle;
\coordinate (O) at (0,0,0); // original position (0,0,0)
\coordinate (A) at (0.9330127, 0.2500000, -0.2588190); // original position (1,0,0)
\coordinate (B) at (-0.2588190, 0.9659258, 0.0000000); // original position (0,1,0)
\coordinate (C) at (0.2500000, 0.0669873, 0.9659258); // original position (0,0,1)
\coordinate (D) at (0.6741937, 1.2159258, -0.2588190); // original position (1,1,0)
\coordinate (E) at (1.1830127, 0.3169873, 0.7071068); // original position (1,0,1)
\coordinate (F) at (-0.008819045, 1.032913124, 0.965925826); // original position (0,1,1)
\coordinate (G) at (0.9241937, 1.2829131, 0.7071068); // original position (1,1,1)
\draw[->] (1,0,1) arc [start angle=-45,end angle=0,x radius=2.3,y radius=.68];
\draw[->] (1,0,0) arc [start angle=-45,end angle=0,x radius=1.2,y radius=.56];
\draw[->] (1,1,0) arc [start angle=-25,end angle=0,x radius=.9,y radius=.86];
\draw[red!50, thick, fill=red!20,opacity=0.4, fill opacity = .3] (O) -- (A) -- (D) -- (B) -- cycle;
\draw[red!50, thick, fill=red!20,opacity=0.4, fill opacity = .3] (O) -- (B) -- (F) -- (C) -- cycle;
\draw[red!50, thick, fill=red!20,opacity=0.4, fill opacity = .3] (O) -- (A) -- (E) -- (C) -- cycle;
\draw[red!50, thick, fill=red!20,opacity=0.4, fill opacity = .3] (A) -- (D) -- (G) -- (E) -- cycle;
\draw[red!50, thick, fill=red!20,opacity=0.4, fill opacity = .3] (B) -- (D) -- (G) -- (F) -- cycle;
\draw[red!50, thick, fill=red!20,opacity=0.4, fill opacity = .3] (C) -- (E) -- (G) -- (F) -- cycle;
\begin{scope}[plane origin = (C),plane x = (E), plane y = (F), canvas is plane]
\draw[red!30, ultra thin, step=0.05] (0,0) grid (1,1);
\end{scope}
\begin{scope}[plane origin = (A),plane x = (D), plane y = (E), canvas is plane]
\draw[red!30, ultra thin, step=0.05] (0,0) grid (1,1);
\end{scope}
\begin{scope}[plane origin = (O),plane x = (A), plane y = (C), canvas is plane]
\draw[red!30, ultra thin, step=0.5] (0,0) grid (1,1);
\end{scope}
\begin{scope}[plane origin = (O),plane x = (A), plane y = (C), canvas is plane]
\draw[red!30, ultra thin, step=0.5] (0,0) grid (1,1);
\end{scope}
\end{tikzpicture}
\end{document}