How to make dot in the defined bigcupdot automatically change size?

Question

I searched in the TSE and found a solution to define the \bigcupdot. As you see the size of the dot in the \bigcupdot is fixed no matter whether it's in display style or not. I tried to use \ifx command to make the dot automatically change its size but failed! Who can fix the following codes? Any help is welcome.

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\makeatletter
\providecommand*{\bigcupdot}{%
  \mathop{%
    \vphantom{\bigcup}%
    \mathpalette\@bigcupdot{}%
  }%
}
\newcommand*{\@bigcupdot}[2]{%
  \ooalign{%
    $\m@th#1\bigcup$\cr
    \sbox0{$#1\bigcup$}%
    \dimen@=\ht0 %
    \advance\dimen@ by -\dp0 %
    \sbox0{%
    \ifx\displaystyle\scalebox{1.7}{$\m@th#1\cdot$}\else
    \ifx\textstyle\scalebox{1.4}{$\m@th#1\cdot$}\else
    \ifx\scriptstyle\scalebox{1.2}{$\m@th#1\cdot$}\else
    \scalebox{1.1}{$\m@th#1\cdot$}\fi\fi\fi
    }%
    \advance\dimen@ by -\ht0 %
    \dimen@=.5\dimen@
    \hidewidth\raise\dimen@\box0\hidewidth
  }%
}
\makeatother
\begin{document}
[ \bigcupdot a=\biguplus mn]
\end{document}

Answer 1

You can parametrize the scaling factor:

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}
\makeatletter
\providecommand{\bigcupdot}{%
  \mathop{%
    \vphantom{\bigcup}%
    \mathpalette@bigcupdot{}%
  }%
}
\newcommand{@bigcupdot}[2]{%
  \ooalign{%
    $\m@th#1\bigcup$\cr
    \sbox0{$#1\bigcup$}%
    \dimen@=\ht0 %
    \advance\dimen@ by -\dp0
    \sbox0{\scalebox{@dotscale{#1}}{$\m@th#1\cdot$}}%
    \advance\dimen@ by -\ht0
    \dimen@=.5\dimen@
    \hidewidth\raise\dimen@\box0\hidewidth
  }%
}
\newcommand{@dotscale}[1]{%
  \ifx#1\displaystyle 1.7\else\ifx#1\textstyle 1.4\else
  \ifx#1\scriptstyle 1.2\else 1.1\fi\fi\fi
}
\makeatother
\begin{document}
$\displaystyle\bigcupdot$
$\textstyle\bigcupdot$
$\scriptstyle\bigcupdot$
$\scriptscriptstyle\bigcupdot$
\end{document}