Replacing unit `cm` to macro causes error in tikz-ellipse

Question

I wish to reproduce an object by drawing with tikz. My concept is measuring the coordinates of a raster image then reproduce the image with tikz \draw. Finally I wish replace absolute unit (cm or pt or etc) with a scale factor and integrate the object into a macro.

My MWE:

\documentclass{memoir}

\usepackage{xcolor}
\usepackage{tikz}
  \usetikzlibrary{shapes.geometric,positioning,calc,patterns}

\usepackage{tikzpagenodes}
\usepackage{calc}

\newcommand{\fsymbolI}[5]{%
\def\aII{0.013797449*#1 }
 \begin{tikzpicture}[rotate=#4,overlay, remember picture, -latex]%
  \node[shift={(#2,#3)}] at (current page.north west){%
   \begin{tikzpicture}[rotate=180,overlay, remember picture]%
    \begin{scope}[xshift=-11.7cm,yshift=1.1cm]%
    \draw[#5,-] (6.4cm,15cm) -- (6.4cm,15.6cm) -- (11.6cm,11.8cm) -- (11.6cm,4.1cm) arc (0:-90:5.1cm)  -- (6.4cm,4.1cm) -- (6.4*\aII,8.6*\aII) arc (270:360: 3.6cm and 2.1cm) -- cycle ;%
     \draw[#5,-] (5.8cm,10.7cm) ellipse (1.05cm  and 0.85cm);
    \end{scope}%
   \end{tikzpicture}%
  };%
 \end{tikzpicture}%
}

\begin{document}
 \fsymbolI{1cm}{0mm}{0mm}{0}{green}
\end{document}

works fine. But:

My idea is replace all the 'cm' with '*\aII' (defined in the macro fsymbolI by \def\aII{0.013797449*#1 }). Working fine except when I wish to change the 3rd param. of ellipse. So

\draw[#5,-] (5.8*\aII,10.7*\aII) ellipse (1.05cm  and 0.85*\aII);

works fine but

\draw[#5,-] (5.8*\aII,10.7*\aII) ellipse (1.05*\aII  and 0.85*\aII);

causes an error:

! Package PGF Math Error: Unknown operator a' oran' (in '1.05*0.013797449*1cm and 0.85*0.013797449*1cm ').

I've added a white space in definition '\aII' but it didn't sole the problem.

Any help will be welcomed.

Answer 1

Put the length expression into braces.

\draw[#5,-] (5.8*\aII,10.7*\aII) ellipse ({1.05*\aII} and 0.85*\aII);