# Rotated copies for spiral wireframe

coord[th_] = {Sech[th]*Cos[th + v], Sech[th]*Sin[th + v], Tanh[th]};
loxo45 = ParametricPlot3D[coord[th], {th, 0, Pi}, {v, .0, 2 Pi},
PlotLabel -> "3_D WirePlt", PlotStyle -> {Thick, Yellow},PlotRange -> All]


Using ListPlot3D or otherwise please help show how to avoid parallel lines and also the surface so that only the spirals are visible? (Like in ParametricPlot3D but with multiple rotated lines)

Try with this (play with Mesh):

loxo45 = ParametricPlot3D[coord[th], {th, 0, Pi}, {v, .0, 2 Pi},
PlotLabel -> "3 _D WirePlt", PlotStyle -> None, PlotRange -> All,
Mesh -> {0, 20}, MeshStyle -> {{}, {Red, Thickness[0.01]}}]


### Single-parameter ParametricPlot3D

ParametricPlot3D[Evaluate @ Table[coord[th], {v, 0, 2 Pi, 2 Pi/20}], {th, 0, Pi},
PlotStyle -> Directive[Red, Thick]]


### RotationTransform

line = ParametricPlot3D[coord[th] /. v->0, {th, 0, Pi}, PlotStyle->Directive[Thick, Red]];
Graphics3D[Table[GeometricTransformation[line[[1]], RotationTransform[a, {0, 0, 1}]],
{a, Range[0, 2 Pi, 2 Pi/20]}], Axes -> True]


If you wish make Lines into Tubes:

% /. Line -> (Tube[#, .02] &)


• very nice adds, +1 – José Antonio Díaz Navas Feb 6 '18 at 17:22
• Thank you @JoséAntonioDíazNavas. – kglr Feb 6 '18 at 17:27