Sstrhsrtj

I'd like to reproduce the following 3d image using pgfplots

the battery doesn't need to be there, just the closed path and the axis.

I haven't been able to find any examples of 3d paths that are not expressible as parametric functions, but that are user-defined, seemingly random paths. Any idea on how to achieve this?

This is just a quick attempt to produce some curve that somewhat resembles the one on your screen shot. Obviously, you do not necessarily need a parametrization, you could also draw a smooth curve through a set of known coordinates. However, as I know neither parametrization nor coordinates, this is a quick example that should give you an idea how things may look like.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

begin{document}

tdplotsetmaincoords{70}{130}

begin{tikzpicture}

begin{scope}[tdplot_main_coords]

pgfmathsetmacro{Radius}{3}

draw[-latex]   (0,0,0) --  (1.5*Radius,0,0) node[pos=1.1]{$x$};

draw[-latex]   (0,-1.5*Radius,0) --   (0,1.5*Radius,0) node[pos=1.05]{$y$};

draw[-latex]   (0,0,0) --  (0,0,1.5*Radius) node[pos=1.1]{$z$};

draw[double] plot[variable=x,domain=360:0,samples=181] 

({Radius*cos(x)},{Radius*sin(x)},{2.5+Radius*cos(2*x)/2});

draw (0,0,0.75*Radius) -- (0,0,1.45*Radius);

end{scope}

end{tikzpicture}

end{document}

Sure enough, you can draw a 3D curve it with pgfplots as well.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

begin{document}

begin{tikzpicture}

begin{axis}[axis lines=middle,view={135}{45},xlabel=$x$,

ylabel=$y$,zlabel=$z$,clip=false,xtick=empty,ytick=empty,ztick=empty]

pgfmathsetmacro{Radius}{3}

addplot3[double,domain=360:0,samples=181,samples y=1] 

({Radius*cos(x)},{Radius*sin(x)},{2.5+Radius*cos(2*x)/2});

end{axis}

end{tikzpicture}

end{document}