I am trying to plot a few points on the following picture in Mathematica:

ParametricPlot3D[
   {{u, v, (Cos[u] + Cos[v])/3}, {u, -1, (Cos[u] + Cos[0])/3}, 
   {5, v, (Cos[4] + Cos[v])/3}}, {u, -4, 4}, {v, 0, 8}, Axes -> False, 
 Boxed -> False, BoxRatios -> {8, 8, 1.5}]

Mathematica graphics

(they should just look like dots on the surface)

What I was trying to do is enter the coordinates of the points manually on another graph using ListPointPlot3D, and then combine them using Show. But for some reason that isn't working. Suggestions?

Also, I would like to add small vectors tangent to the surface in the x directions for the points I have plotted, but I have no idea on how to do that, so suggestions would be very much appreciated!

wolfram-mathematica
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