Drawing toroid with TikZ using perspective projection

toroid-v2.tex

\documentclass{standalone}
\usepackage{tikz}
\def\camtheta{60}
\def\camphi{70}
%\def\p{((3+cos(16*\t))*cos(\t))}
%\def\q{((3+cos(16*\t))*sin(\t))}
%\def\r{sin(16*\t)}
%\def\w{\p*sin(\camtheta)*cos(\camphi) + \q*sin(\camtheta)*sin(\camphi) + \r*cos(\camtheta)}
\def\rot{32} % # of toroid revolution.
\def\dist{20} % distance of camera and origin
\def\bigr{4} % radius of big circle
\def\smallr{0.5} % radius of small circle
\begin{document}
	\begin{tikzpicture}
		\draw[domain=0:360, smooth, samples=200, variable=\t]
		plot (
			{((\bigr+\smallr*cos(\rot*\t))*cos(\t)*sin(\camphi) - (\bigr+\smallr*cos(\rot*\t))*sin(\t)*cos(\camphi)) / ((\bigr+\smallr*cos(\rot*\t))*cos(\t)*sin(\camtheta)*cos(\camphi) + (\bigr+\smallr*cos(\rot*\t))*sin(\t)*sin(\camtheta)*sin(\camphi) + sin(\rot*\t)*cos(\camtheta)-\dist)},
			{((\bigr+\smallr*cos(\rot*\t))*cos(\t)*cos(\camtheta)*cos(\camphi) + (\bigr+\smallr*cos(\rot*\t))*sin(\t)*cos(\camtheta)*sin(\camphi) - sin(\rot*\t)*sin(\camtheta)) / ((\bigr+\smallr*cos(\rot*\t))*cos(\t)*sin(\camtheta)*cos(\camphi) + (\bigr+\smallr*cos(\rot*\t))*sin(\t)*sin(\camtheta)*sin(\camphi) + sin(\rot*\t)*cos(\camtheta)-\dist)}
		);
	\end{tikzpicture}
\end{document}