[Tex/LaTex] Draw two rectangles, one on top of the other, with an angle between them

diagramstikz-pgf

I'd like to make two rectangles on top of each other with an angle between them, and I'd like them both to have 4 or 5 vertical lines running down them, and a highlighted point where two of them intersect. I'm just beginning with tikz/pgf, so I'm not sure how to do any of this (the image was made in inkscape, not tikz).

Here is an image of what I'm trying to achieve:

enter image description here

but without the vertical lines. If anyone has something similar to this, or some advice for steps along the way, it is much appreciated.

Best Answer

1. Basic Drawing:

You can use a scope and apply a transformation to the outer rectangle:

enter image description here

Code:

    \documentclass[border=2pt]{standalone}
    \usepackage{tikz}
    \newcommand{\Width}{3}
    \newcommand{\Height}{5}

    \begin{document}
    \begin{tikzpicture}
    \draw [fill=green] (0,0) rectangle (\Width,\Height);
    \begin{scope}[rotate=20, xshift=1cm, yshift=-0.75cm]
        \draw [fill=blue] (0,0) rectangle (\Width,\Height);
    \end{scope}
    \end{tikzpicture}
    \end{document}

2. Vertical Lines:

Ok, so that gets you the two rectangles, easy enough. But about the vertical lines?

Since I am not sure how many lines you want, and knowing that specs often change, we had better define a constant \NumberOfVericalLines. Then it is just a matter of stepping thru them and drawing them:

    \pgfmathsetmacro{\DeltaX}{\Width/\NumberOfVericalLines}%
        \foreach \x in {0,...,\NumberOfVericalLines} {
            \pgfmathsetmacro{\NewX}{\DeltaX*\x}
            \draw (\NewX,0) -- (\NewX,\Height);
    }

This yields:

enter image description here

But wait, where are the other lines? Looks like they are behind the blue rectangle, so adding fill opacity=0.5 shows the lines that were in the background:

enter image description here

Code:

    \documentclass[border=2pt]{standalone}
    \usepackage{tikz}
    \usetikzlibrary{calc}

    \newcommand{\Width}{3}
    \newcommand{\Height}{5}
    \newcommand{\NumberOfVericalLines}{4}

    \begin{document}
    \begin{tikzpicture}
    \draw [fill=green] (0,0) rectangle (\Width,\Height);
    \pgfmathsetmacro{\DeltaX}{\Width/\NumberOfVericalLines}%
    \foreach \x in {0,...,\NumberOfVericalLines} {
        \pgfmathsetmacro{\NewX}{\DeltaX*\x}
        \draw (\NewX,0) -- (\NewX,\Height);
    }
    \begin{scope}[rotate=20, xshift=1cm, yshift=-0.75cm, fill opacity=0.5]
        \draw [fill=blue] (0,0) rectangle (\Width,\Height);
    \end{scope}
    \end{tikzpicture}

3. Macro for Rectangle:

Since we also want similar lines for the other rectangle, we probably should define a macro so we are not repeating the code:

    \newcommand*{\Rectangle}[4][]{%
        % #1 = draw/fill options
        % #2 = witdh
        % #3 = height
        % #4 = number of vertical lines
        \draw [#1] (0,0) rectangle (#2,#3);
        \pgfmathsetmacro{\DeltaX}{#2/#4}%
        \foreach \x in {0,...,#4} {
            \pgfmathsetmacro{\NewX}{\DeltaX*\x}
            \draw (\NewX,0) -- (\NewX,#3);
        }
    }

Now, using just:

    \begin{tikzpicture}
    \Rectangle[fill=green]{\Width}{\Height}{\NumberOfVericalLines}
    \begin{scope}[rotate=20, xshift=1cm, yshift=-0.75cm, fill opacity=0.5]
        \Rectangle[fill=blue]{\Width}{\Height}{\NumberOfVericalLines}
    \end{scope}

we obtain all the vertical lines:

enter image description here

4. Intersections:

Ok, now for the hard part, the intersections.

For this we need to incorporate \usetikzlibrary{intersections}, and name each of the vertical lines. Of course that means that we need to change the macro to accept one more parameter which is the prefix to name the vertical lines.

    \newcounter{Counter}
    \newcommand*{\Rectangle}[5][]{%
        % #1 = draw/fill options
        % #2 = prefix for path name
        % #3 = width
        % #4 = height
        % #5 = number of vertical lines
        \draw [#1] (0,0) rectangle (#3,#4);
        \pgfmathsetmacro{\DeltaX}{#3/#5}%
        \foreach [count=\xi] \x in {0,...,#5} {
            \pgfmathsetmacro{\NewX}{\DeltaX*\x}
            \setcounter{Counter}{\xi}%
            \expandafter\xdef\csname PathName#2\Alph{Counter}\endcsname{#2-\x}

            \draw [name path global=\csname PathName#2\Alph{Counter}\endcsname]
                (\NewX,0) -- (\NewX,#4);
        }
    }

This defines \PathNameTopA...\PathNameTopE, and \PathNameBottomA...\PathNameBottomE for the names of each of the vertical lines, then we just need to call \ShowIntersection for each of the intersections which we want to show.

Below I have displayed all of them, where the first letter in the label is a reference to the line of the intersection from the blue rectangle, and the second letter refers to the green rectangle:

enter image description here

Refernces:

Final Code:

\documentclass[border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\newcommand{\Width}{3}
\newcommand{\Height}{5}
\newcommand{\NumberOfVerticalLines}{4}

\newcounter{Counter}
\newcommand*{\Rectangle}[5][]{%
    % #1 = draw/fill options
    % #2 = prefix for path name
    % #3 = width
    % #4 = height
    % #5 = number of vertical lines
    \draw [#1] (0,0) rectangle (#3,#4);
    \pgfmathsetmacro{\DeltaX}{#3/#5}%
    \foreach [count=\xi] \x in {0,...,#5} {
        \pgfmathsetmacro{\NewX}{\DeltaX*\x}
        \setcounter{Counter}{\xi}%
        \expandafter\xdef\csname PathName#2\Alph{Counter}\endcsname{#2-\x}

        \draw [name path global=\csname PathName#2\Alph{Counter}\endcsname]
                (\NewX,0) -- (\NewX,#4);
    }
}

% https://tex.stackexchange.com/questions/24781/pgfplot-dimension-too-large-tex-capacity-exceeded-after-reduction-in-domain-and
% https://tex.stackexchange.com/questions/21408/intersections-in-pgfplots
\newcommand*{\ShowIntersection}[3]{
\fill 
    [name intersections={of=#1 and #2, name=i, total=\t}] 
    [brown, opacity=1, every node/.style={black, opacity=1}] 
    \foreach \s in {1,...,\t}{(i-\s) circle (3pt)
        node [above left, red] {#3}};
}

\begin{document}
\begin{tikzpicture}
\Rectangle[fill=green!30]{Bottom}{\Width}{\Height}{\NumberOfVerticalLines}
\begin{scope}[rotate=20, xshift=1cm, yshift=-0.75cm, fill opacity=0.5]
    \Rectangle[fill=blue!60]{Top}{\Width}{\Height}{\NumberOfVerticalLines}
\end{scope}

\ShowIntersection{\PathNameTopA}{\PathNameBottomA}{aa}
\ShowIntersection{\PathNameTopA}{\PathNameBottomB}{ab}
\ShowIntersection{\PathNameTopB}{\PathNameBottomB}{bb}
\ShowIntersection{\PathNameTopB}{\PathNameBottomC}{bc}
\ShowIntersection{\PathNameTopC}{\PathNameBottomC}{cc}
\ShowIntersection{\PathNameTopC}{\PathNameBottomD}{cd}
\ShowIntersection{\PathNameTopD}{\PathNameBottomD}{dd}
\ShowIntersection{\PathNameTopD}{\PathNameBottomE}{de}
\ShowIntersection{\PathNameTopE}{\PathNameBottomE}{ee}
\end{tikzpicture}
\end{document}
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