3

Please consider the following configuration of vectors.

\begin{tikzpicture}
\draw[thick,->] (0,0,0) -- (3,0,0) node[anchor=north east]{$\varepsilon_1$};
\draw[thick,->] (0,0,0) -- (0,3,0) node[anchor=north west]{$\varepsilon_2$};
\draw[thick,->] (0,0,0) -- (0,0,3) node[anchor=south east]{$\tilde{\beta}_3=\varepsilon_3$};
\draw[thick,->] (0,0,0) -- (3,-3,0) node[anchor=east]{$\tilde{\beta}_1$};
\draw[thick,->] (0,0,0) -- (0,3,-3) node[anchor=north west]{$\tilde{\beta}_2$};
\draw[thick,->] (0,0,0) -- (0,-3,-3) node[anchor=east]{$\beta_2$};
\draw[thick,->] (0,0,0) -- (1,2,1) node[anchor=north west]{$\beta_1$};
\end{tikzpicture}
  • I want to add the plane spanned by \beta_1 and \beta_2 and label it with a math variable.
  • I would like to make the picture appear more three dimensional, e.g. by shaded color of the plane or by dashed lines depending on wether something is in front of or behind the plane.
  • I don't want the boundary of the plane be drawn but just the inside in color. This command does not work \filldraw[fill=blue!20] (0,-3,-3) -- (1,-1,-2) -- (1,2,1) --- (0,0,0); but it gives an error.

I am currently experimenting with tikz. It might not be possible to make this specific configuration "good looking". The question is therefore not very specific.

I thank you for your help!

This is the closest I found on the site and uses some of the tricks I want to implement, cf. the last answer by the OP itself.

How far I got...

How far I got...

Christoph Mark
  • 362
  • 4
  • 15

1 Answers1

2

Here is a proposal.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[font=\sffamily]
\draw[thick,->] (0,0,0) coordinate(O) -- (0,-3,-3) coordinate(b2) node[anchor=east]{$\beta_2$};
\draw[thick,->] (O) -- (1,2,1) coordinate(b1) node[anchor=north west]{$\beta_1$};
\fill[gray,opacity=0.3,name path=plane] (O) -- (b1) -- ++ (b2) 
node[midway,above,sloped,black,opacity=1]{plane} -- (b2) -- cycle;
\path[name path=E1] (O) -- (3,0,0);
\draw[name intersections={of=plane and E1,by={aux,i1}},dashed] (O)--(i1);
\draw[thick,->] (i1) -- (3,0,0) node[anchor=north east]{$\varepsilon_1$};
\draw[thick,->] (O) -- (0,3,0) node[anchor=north west]{$\varepsilon_2$};
\draw[thick,->] (O) -- (0,0,3) node[anchor=south east]{$\tilde{\beta}_3=\varepsilon_3$};
\path[name path=B1] (O) -- (3,-3,0);
\draw[name intersections={of=plane and B1,by={aux,i2}},dashed] (O) -- (i2);
\draw[thick,->] (i2) -- (3,-3,0)  node[anchor=east]{$\tilde{\beta}_1$};
\draw[thick,->] (O) -- (0,3,-3) node[anchor=north west]{$\tilde{\beta}_2$};
\end{tikzpicture}
\end{document}

enter image description here

Your command \filldraw[fill=blue!20] (0,-3,-3) -- (1,-1,-2) -- (1,2,1) --- (0,0,0); would not throw an error if you were to use 2 - in the last segment instead of 3.