The full 3D-view in xyt-space

To get an idea how this worked, simply look at the full 3D-view in xyt-space and consider the
views form the top, and the sides -- feel free to rotate the graphic - it is a 3d-picture!

>	with(plots): s0:=spacecurve([cos(t),sin(t),t],t=0..3*Pi,color=black,thickness=1): s1:=spacecurve([0.97*cos(t),0.97*sin(t),t],t=0..Pi,color=red): s2:=spacecurve([cos(t),sin(t),t],t=2*Pi..3*Pi,color=blue): s12:=display([s0,s1,s2],axes=boxed,thickness=4): display(s12,topview);