With TikZ v3.00, you can use nonlinear transformations to do fantastic things. The problem here is the text since TikZ also puts the node text into a box and hopes for the best. And thus everything in the box gets affected by the same transformation that TikZ sees the box handle(for example add \hspace{3cm} to the node contents).
\documentclass[]{article}
\usepackage{tikz}
\usetikzlibrary{shapes.arrows}
\usepgflibrary{curvilinear}
\usepgfmodule{nonlineartransformations}
\tikzset{arrownode/.style={
shape=single arrow,
single arrow head extend=.75em,
single arrow head indent=.25em,
minimum width=3em,
draw,
}
}
\begin{document}
\begin{tikzpicture}
{
\pgfsetcurvilinearbeziercurve
{\pgfpoint{0mm}{30mm}}
{\pgfpoint{15mm}{30mm}}
{\pgfpoint{30mm}{15mm}}
{\pgfpoint{30mm}{0mm}}
\pgftransformnonlinear{%
\pgfpointcurvilinearbezierorthogonal%
{\csname pgf@x\endcsname}%
{\csname pgf@y\endcsname}%
}%
\node[arrownode,transform shape nonlinear=true] at (3,0) {why no rotation?};
}
\end{tikzpicture}
\end{document}
You can however switch to text decorations and I have not really looked carefully how Mark Wibrow coded the transformations but maybe you can make the text accept the current transformation matrix (I don't know yet). So if you replace the above node with
\node[arrownode,transform shape nonlinear=true] (a) at (3,0) {\phantom{Why not rotating?}};
\path[decoration={text along path,
text={Why not rotating?},
text align=center,
raise=-0.5ex
},postaction={decorate}](a.west) -- (a.east);
you will get
Notice that the point you place the node matters since the transfomation is nonlinear so in this example if you put your node further, the more pronounced the effect will be. And you can see the top white space coming in from the transformed canvas Play around with the bezier curve coordinates and you'll get ridiculous results :)
