rotating and positioning of repeating parts in tikz

Question

This is related to my question: using tikz to draw a flattened polyhedron and is similar, but in my interpretation not the same as the question:Rotate a path around a point.

The following MWE shows what I want as an output, but I was hoping there was an easier way, something like: draw the second trapezium by y-shifting it up so that cordinate A1 is at B2 and then rotating so that C2 is at D1. Do such elegant transformations exist? My aim is to then be able to repeat this many times to get an arch of such trapeziums.

\documentclass{article}

\usepackage{tikz}

\newcommand{\trapezium}[1]{%
\coordinate[label=A#1] (A#1) at (0,0);
\path (A#1)--++(-90:2) coordinate[label=B#1] (B#1);
\path (B#1)--++({-10}:1) coordinate[label=C#1] (C#1);
\path (A#1)--++({10}:1) coordinate[label=D#1] (D#1);
\draw (A#1)--(B#1)--(C#1)--(D#1)--cycle;
}


\begin{document}

\begin{tikzpicture}
\trapezium{1}

\begin{scope}[yshift=57,rotate around={20:(A1)}]
\trapezium{2}
\end{scope}

\end{tikzpicture}

\end{document}

Answer 1

I followed Thruston's tip (the question being: Transform defined coordinates in TikZ) and found an interesting solution from Mark Wibrow. The code below borrows heavily from there.

\documentclass{article}
\usepackage{tikz}

\makeatletter
\newif\iftikztransformnodecoordinates
\tikzset{transform node coordinates/.is if=tikztransformnodecoordinates}


\def\tikz@parse@node#1(#2){%
    \pgfutil@in@.{#2}%
    \ifpgfutil@in@
        \tikz@calc@anchor#2\tikz@stop%
    \else%
        \tikz@calc@anchor#2.center\tikz@stop%
        \expandafter\ifx\csname pgf@sh@ns@#2\endcsname\tikz@coordinate@text%
        \else
            \tikz@shapebordertrue%
            \def\tikz@shapeborder@name{#2}%
        \fi%
    \fi%
    \iftikztransformnodecoordinates%
        \pgf@pos@transform{\pgf@x}{\pgf@y}%
    \fi
    \edef\tikz@marshal{\noexpand#1{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}%
    \tikz@marshal%
}

\begin{document}

\begin{tikzpicture}

\coordinate (A1) at (0,0);
\path (A1)--++(-90:2) coordinate (B1);
\path (B1)--++({-10}:1) coordinate (C1);
\path (A1)--++({10}:1) coordinate (D1);

\draw (A1)--(B1)--(C1)--(D1)--cycle;

\foreach \n/\m in {1/2,2/3,3/4,4/5,5/6}{%
\draw [transform node coordinates, rotate=20, shift={(0,2)}] 
(A\n) coordinate (A\m)-- (B\n) coordinate (B\m) -- (C\n) coordinate (C\m) -- (D\n) coordinate (D\m) -- cycle;
}


\end{tikzpicture}

\end{document}

Answer 2

Your code was not far away from a easy solution.

I've changed trapezium's origin to bottom left corner (B1). If you want to draw another one on top of it, shift its origin to A1 and rotate it proportionally to trapezium slope (in your case 20 degrees for every new trapezium).

The code used to clip an image with trapezium border has been borrowed from JLDiaz answer to TikZ: Drawing regular hexagons with pictures inside

\begin{scope}[shift={(A1)}, rotate=20]
\trapezium{2};
\end{scope}


\documentclass[tikz]{standalone}

\usepackage{mwe}

\newcommand{\trapezium}[1]
{
    \path (0,0) coordinate[label=B#1] (B#1) --++(90:2) coordinate[label=A#1] (A#1);
    \path (B#1)--++({-10}:1) coordinate[label=C#1] (C#1);
    \path (A#1)--++({10}:1) coordinate[label=D#1] (D#1);
    \draw (A#1)--(B#1)--(C#1)--(D#1)--cycle;
    \begin{scope}
        \clip (A#1)--(B#1)--(C#1)--(D#1)--cycle;
        \node{\includegraphics{image-A}};
    \end{scope}
}

\begin{document}

\begin{tikzpicture}
   \trapezium{1}
   \begin{scope}[shift={(A1)}, rotate=20]
      \trapezium{2};
   \end{scope}
   \begin{scope}[shift={(A2)}, rotate=40]
      \trapezium{3};
   \end{scope}
   \begin{scope}[shift={(A3)}, rotate=60]
      \trapezium{4};
   \end{scope}
\end{tikzpicture}
\end{document}

Just for fun I've also tested with a TiKZ 3 pic

\documentclass[tikz]{standalone}

\usepackage{mwe}

\tikzset{
    pics/trapezium/.style={
       code = {
        \path (0,0) coordinate[label=B#1] (B#1)--++(90:2) coordinate[label=A#1] (A#1);
        \path (B#1)--++({-10}:1) coordinate[label=C#1] (C#1);
        \path (A#1)--++({10}:1) coordinate[label=D#1] (D#1);
        \draw[clip] (A#1)--(B#1)--(C#1)--(D#1)--cycle;
        \node{\includegraphics{image-A}};
        }
    }
}


\begin{document}

\begin{tikzpicture}
\path pic[rotate=0] {trapezium=1};
\path (A1) pic[rotate=20] {trapezium=2};
\path (A2) pic[rotate=40] {trapezium=3};
\path (A3) pic[rotate=60] {trapezium=3};
\end{tikzpicture}

\end{document}

Both codes produce: