圆弧的非线性变换

Question

看起来对圆弧进行非线性变换会产生扭曲。请参见下面的绿色和红色形状。这是预期的吗？我是否必须将路径操作限制为--、to和.. controls () ..？

\documentclass{standalone}

\usepackage{tikz}

\usepgfmodule{nonlineartransformations}
\usetikzlibrary{curvilinear,shapes.geometric,shapes.arrows}

\begin{document}
\makeatletter
\begin{tikzpicture}
  [
  bump/.style={semicircle, draw, fill=green},
  point/.style={single arrow, fill=cyan, single arrow head extend=1mm, minimum height=5mm},
  ]
  
  \draw [help lines] (0,0) grid (3,2);
  {
    \pgfsetcurvilinearbeziercurve
    {\pgfpoint{0mm}{20mm}}
    {\pgfpoint{11mm}{20mm}}
    {\pgfpoint{20mm}{11mm}}
    {\pgfpoint{20mm}{0mm}}
    \pgftransformnonlinear{\pgfpointcurvilinearbezierorthogonal\pgf@x\pgf@y}%
    \pgfsettransformnonlinearflatness{2pt} % very precise
    \draw (0,-30pt) grid [step=10pt] (80pt,30pt);

    % not working
    \fill [red] (0,-1) arc [radius=0.5, start angle=90, end angle=45];

    % working
    \fill [orange] (2,0) .. controls +(0,0.11) and +(-0.11,0) .. ++(0.2,0.2) .. controls +(0.11,0) and +(0,0.11) .. ++(0.2,-0.2) -- cycle;

    % working
    \node [single arrow, fill=cyan, single arrow head extend=2, minimum height=5mm, transform shape nonlinear] at (1.5,0) {};

    % not working
    \node [semicircle, draw, fill=green, transform shape nonlinear] at (1,1) {};
  }
\end{tikzpicture}
\makeatother
\end{document}