How to find location of position of nodes in TikZ graph automatically to use?

Question

I'd like to find out if it is possible to automatically find position of a node in the picture, to use in order to draw additional objects to connect to it or from it without having to manually keep tracking of physical coordinates.

For example, I wanted to make a second x-y axis, rotate it, the make point inside this frame (relative to it) and then wanted to draw a line from (0,0) to this point. Since I rotated the second frame, it is hard to keep track myself of all the physical locations of all the objects I draw in the rotated frame.

It will be useful, if I can get TikZ to do that for me. To make it clear what I mean, here is a MWE:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\fbox{
  \begin{tikzpicture}
   %first frame, the base frame
   \draw [->] (0,0) -- (1,0) ;
   \draw [->] (0,0) -- (0,1) ;

   %second frame, rotate it by 45 degrees relative to the base
   \draw[rotate around={-45:(2,2)}] [->] (2,2) -- (3,2) ;
   \draw[rotate around={-45:(2,2)}] [->] (2,2) -- (2,3) ;

   %draw a point, relative to the second frame
   \draw[rotate around={-45:(2,2)}] [->] (2,2) -- (2.5,2.5) ;
   \draw[rotate around={-45:(2,2)}] [fill=red] (2.5,2.5) circle(.25ex);

   %now, I want to draw an arrow from (0,0) to the circle above.
   %I can't just do this below, since frame 2 has rotated
   %\draw [->,color=red] (0,0) -- (2.5,2.5) ;    
\end{tikzpicture}
}
\end{document}

I need now to draw an arrow from (0,0) to the red circle but I do not know the coordinates of the circle now, relative to the picture, since frame 2 is rotated. I'd have to calculate it. I know its coordinates relative to frame 2.

Is there a way to label it, and use the label to automatically find its coordinates relative the base frame (i.e., the drawing itself)?

Answer 1

Yes. You can add a named coordinate, which is a special type of node, at the red dot, and use this instead of explicit coordinates.

This is described in chapter 17 Nodes and their shapes of the manual.

\documentclass[tikz,border=2mm]{standalone}
\begin{document}
  \begin{tikzpicture}
   %first frame, the base frame
   \draw [->] (0,0) -- (1,0) ;
   \draw [->] (0,0) -- (0,1) ;

   \begin{scope}[rotate around={-45:(2,2)}]
   %second frame, rotate it by 45 degrees relative to the base
   \draw[->] (2,2) -- (3,2) ;
   \draw[->] (2,2) -- (2,3) ;

   %draw a point, relative to the second frame

   \draw [->] (2,2) -- (2.5,2.5) ;
   \draw[fill=red] (2.5,2.5) circle(.25ex) coordinate (red dot);
   \end{scope}


   \draw [->,color=red] (0,0) -- (red dot) ;    
\end{tikzpicture}
\end{document}