You could also use package pict2e:
\documentclass{article}
\usepackage{eso-pic}
\usepackage{pict2e}
\begin{document}
\AddToShipoutPictureFG{%
\AtPageLowerLeft{%
\Line(\LenToUnit{\paperwidth},0)(0,\LenToUnit{\paperheight})%
}%
}
Text\newpage Text
\end{document}


Code:
\documentclass{scrbook}
\newcommand*\snum{10}% number of segments
\KOMAoptions{DIV=\snum}
\usepackage{eso-pic}
\usepackage{pict2e}
\usepackage{xcolor}
\usepackage{ifthen}
\usepackage{calc}
\newcounter{segment}
\newlength\circletextwidth
\setlength\circletextwidth{\paperwidth*\ratio{\paperwidth}{\paperheight}}
\usepackage{blindtext}
\begin{document}
\AddToShipoutPictureFG{%
\AtPageLowerLeft{%
\ifodd\value{page}%
\setcounter{segment}{1}
\whiledo{\value{segment}<\snum}{%
\Line
(\LenToUnit{\value{segment}\paperwidth/\snum},0)%
(\LenToUnit{\value{segment}\paperwidth/\snum},\LenToUnit{\paperheight})%
\Line
(0,\LenToUnit{\value{segment}\paperheight/\snum})%
(\LenToUnit{\paperwidth},\LenToUnit{\value{segment}\paperheight/\snum})%
\stepcounter{segment}%
}%
\linethickness{2pt}%
\moveto(\LenToUnit{\paperwidth/\snum},\LenToUnit{2\paperheight/\snum})%
\lineto(\LenToUnit{\paperwidth-2\paperwidth/\snum},\LenToUnit{2\paperheight/\snum})%
\lineto(\LenToUnit{\paperwidth-2\paperwidth/\snum},\LenToUnit{\paperheight-\paperheight/\snum})%
\lineto(\LenToUnit{\paperwidth/\snum},\LenToUnit{\paperheight-\paperheight/\snum})%
\closepath
\textcolor{red}{\strokepath}%
\textcolor{blue}{%
\Line(\LenToUnit{\paperwidth},0)(0,\LenToUnit{\paperheight})%
\Line(0,\LenToUnit{.5\paperheight})(\LenToUnit{\paperwidth},\LenToUnit{\paperheight})%
}
\else
\linethickness{2pt}%
\moveto(\LenToUnit{2\paperwidth/3-2\circletextwidth/3},\LenToUnit{2\paperheight/3-2\paperwidth/3})%
\lineto(\LenToUnit{2\paperwidth/3+\circletextwidth/3},\LenToUnit{2\paperheight/3-2\paperwidth/3})%
\lineto(\LenToUnit{2\paperwidth/3+\circletextwidth/3},\LenToUnit{2\paperheight/3+\paperwidth/3})%
\lineto(\LenToUnit{2\paperwidth/3-2\circletextwidth/3},\LenToUnit{2\paperheight/3+\paperwidth/3})%
\closepath
\textcolor{red}{\strokepath}%
\moveto(\LenToUnit{.5\paperwidth},\LenToUnit{5\paperheight/\snum})%
\circlearc[1]{\LenToUnit{.5\paperwidth}}{\LenToUnit{2\paperheight/3-\paperwidth/6}}
{\LenToUnit{.5\paperwidth}}{0}{360}%
\textcolor{green}{\strokepath}%
\textcolor{blue}{%
\Line(0,0)(\LenToUnit{\paperwidth},\LenToUnit{\paperheight})%
\Line(0,0)(\LenToUnit{\paperwidth},\LenToUnit{.5\paperheight})%
}%
\fi
}%
}
\Blindtext[20]
\end{document}
Changing \snum to 8
\newcommand*\snum{8}
results in
