\documentclass[a4paper]{article}

\usepackage{pgfplots}
%\usepackage{tikz}

\usepgfplotslibrary{fillbetween}



\begin{document}

\makeatletter
\def\showPathSegment#1#2{%
	\begin{tikzpicture}
		\draw[help lines] (0,0) grid[step=20pt] (200pt,100pt);

		\pgfsetcolor{blue}
		\pgfsetpathandBB{#2}%
		\pgfusepath{stroke}

		\pgfsetlinewidth{1pt}
		\pgfsetcolor{red}
		\pgfsetpathandBB{#1}%
		\pgfusepath{stroke}
	\end{tikzpicture}
}

\def\stripmoveto\pgfsyssoftpath@movetotoken#1\relax{%
	\def\pgfretval{#1}%
}

\def\prependmoveto\pgfsyssoftpath@movetotoken#1#2#3\relax{%
	\t@pgfplots@tokb=\expandafter{\pgfretval@L}%
	\t@pgfplots@tokc=\expandafter{\pgfretval@R}%
	\edef\pgfretval@L{\noexpand\pgfsyssoftpath@movetotoken{#1}{#2}\the\t@pgfplots@tokb}%
	\edef\pgfretval@R{\noexpand\pgfsyssoftpath@movetotoken\pgfretval\the\t@pgfplots@tokc}%
}%

\long\def\TEST#1{%
	\def\XXX{#1}%
	
	\stripmoveto#1\relax%
	\let\inputcurvewithoutmoveto=\pgfretval
	\pgf@split@curveto@softpaths\inputcurvewithoutmoveto{0.25}
	\prependmoveto#1\relax

	0.25 L:
	\showPathSegment\pgfretval@L\XXX

	0.25 R:
	\showPathSegment\pgfretval@R\XXX


	\pgf@split@curveto@softpaths\inputcurvewithoutmoveto{0.9}
	\prependmoveto#1\relax

	0.9 L:
	\showPathSegment\pgfretval@L\XXX

	0.9 R:
	\showPathSegment\pgfretval@R\XXX
}%

%\tracingmacros=2 \tracingcommands=2

% We use the polynomial f(x) -1/100 x^2 +2x .
% Values:
% x    f(x)
% 0    0
% 25   43.75
% 50   75
% 100  1
% 125  93.75
\TEST{%
	\pgfsyssoftpath@movetotoken{0.0pt}{0.0pt}%
	\pgfsyssoftpath@curvetosupportatoken{66.66666666666667pt}{133.3333333333333pt}%
	\pgfsyssoftpath@curvetosupportbtoken{133.3333333333333pt}{133.3333333333333pt}%
	\pgfsyssoftpath@curvetotoken{200.0pt}{0.0pt}%
}

\end{document}


