Staight line Mesh

How to see (t,u) junction/nodes with a dot or a small circle connected by straight line in Mesh in 3D, but not as arcs generated by a large number of small steps of t and u.The command should, if possible modify existing ParametricPlot3D without use of Table and ListPlot3D. TIA

ParametricPlot3D[ { u Cos[t], u Sin[t],  1.2 u  }, { t, 0, 2 Pi}, {u, 1, 1.5},
Mesh -> { 25, 5}]


• @george2079 Thanks for image. Feb 12, 2015 at 16:47

I am not sure I understand your question fully. Does this do what you are looking for?

ParametricPlot3D[{u Cos[t], u Sin[t], 1.2 u}, {t, 0, 2 Pi}, {u, 1, 1.5},
Mesh -> Full, MaxRecursion -> 0, PlotPoints -> {25, 5}]


It will not draw arcs, just straight lines between mesh points. The mesg corresponds to the sampled points precisely (thanks to Mesh -> Full), so the mesh density is now controlled by PlotPoints. MaxRecursion -> 0 prevents automatically refining the mesh.

If you wish to include small dots at the mesh line intersections, I don't believe it will be possible to avoid generating them using Table.

• Thanks, Mesh-> Full plots nothing more than chosen sample points. Feb 12, 2015 at 17:09
• @Narasimham There's also Mesh -> All which shows the edges of the polygons (always triangles!) making up the object. Mesh -> Full will instead show just the rectangular mesh, not a triangular one. Both of them just use the sample points. Feb 12, 2015 at 17:11
• +1, Mesh -> Full is definitely better. I forget that here is a difference between Full and All. Feb 12, 2015 at 17:35

Straight mesh lines can be obtaining by specifying corresponding plot points with zero max recursion. Then points can be drawn with post-processing (/. ... :> ...)

n1 = 10;
n2 = 3;
ParametricPlot3D[{u Cos[t], u Sin[t], 1.2 u}, {t, 0, 2 Pi}, {u, 1.0,
1.5}, Mesh -> {n1, n2}, PlotPoints -> {n1 + 2, n2 + 2},
MaxRecursion -> 0, NormalsFunction -> None, PlotRange -> All,
BoundaryStyle -> Darker@Gray, MeshStyle -> Darker@Gray] /.
l : Line@p_ :> {Thickness[0.005], l, Sphere[p, 0.05]}


Here I also add NormalsFunction -> None to draw flat surface pieces.