Consider a pseudosphere,
$\qquad \{x,y,z\} = \{\sin[u] \cos[v],\, \sin[u] \sin[v], \, \log[\tan[u/2]\}$.
Now I want to draw the figure.
ParametricPlot3D[
{Sin[u] Cos[v], Sin[u] Sin[v], Log[Tan[u/2]] + Cos[u]},
{u, -2 π, 2 π}, {v, -2 π, 2 π}]
Now I want to have the plot show the following:
All points with equal third coordinate has the same color.
A curve with constant third coordinate is shown on the surface. it is equal to $\cos(u)\cot(u) = 0$.
I don't know how to combine these requirements. I tried
ParametricPlot3D[
{Sin[u] Cos[v], Sin[u] Sin[v], Log[Tan[u/2]] + Cos[u]},
{u, -2 π, 2 π}, {v, -2 π, 2 π},
PlotStyle -> Thick,
Mesh -> 10,
MeshFunctions -> {ConditionalExpression[#, f'[#] == 0] &}]
but it didn't help.
Any help I get here will be appreciated!
MeshFunctions -> {#3 &}, ColorFunction -> (Hue[#3] &)
? $\endgroup$