I am having trouble plotting curves on surfaces. I have searched for similar examples and I have tried both Plot3D and ParametricPlot3D commands and experimented with Epilog and MeshFunctions (et.c) without success.

Goal: to plot a curve and a line segment (or, it could be a vector) on a surface. The curve follows the surface.

The Sin[x] function is a reasonable surface although my surface I am using is constructed via a ParametricPlot3D command from an Interpolation function generated from data numerically computed by an external program. But, if I know how to do this with Sin[x] via ParametricPlot3D I can do it with my Interpolation function.

Here is a Sin[x] function plotted using:

enter image description here

Notice that a surface and a curve is plotted, the curve being the $2\sin{x}$ value along $y=2$. I have not yet figured out how to highlight the curve with different color or thickness but that is not may main question. I would like to have this $2\sin{x}$ curve run from points $(2.3,2)\rightarrow (4.0,2)$ only and of course highlighted by a different color. Another line (on the surface) would extend from points $(2.3,2)$ to $(4.0,4)$.



Your problem was that your line did not depend upon $y$. ParametricPlot3D functions use both variables and produces fundamentally two-dimensional surfaces when you have two variables.

  {x, y, 2 Sin[x]},
  {x, 2 + y/50, 2 Sin[x]}
 {x, 0, 3 π}, {y, 0, 6},
 PlotStyle -> {{Opacity[0.5], Pink}, {Black}}]

Best is to make the plot of the line a function of just one variable:

a = ParametricPlot3D[
   {x, y, 2 Sin[x]},
   {x, 0, 3 π}, {y, 0, 6},
   PlotStyle -> {Opacity[0.5], Pink}];
b = ParametricPlot3D[{x, 2, 2 Sin[x]},
   {x, 0, 2 π},
   PlotStyle -> Blue];
Show[a, b]

enter image description here

  • $\begingroup$ I attempted to mark as answer but it is not working for some reason. But, this worked and I am kicking myself (not too easy to do though) because I did not realize the solution you posted -- I should have. $\endgroup$ – K7PEH May 24 '16 at 17:59
  • $\begingroup$ I now see that the answer mark is posted -- had to refresh the page though. $\endgroup$ – K7PEH May 24 '16 at 18:00

You can also use the options Mesh and MeshFunctions with a single ParametricPlot3D:

a = 2; b = 2 Pi;
ParametricPlot3D[{u, v, 2 Sin[u]}, {u, 0, 3 Pi}, {v, 0, 6}, 
 MeshFunctions -> {# &, #2 &, ConditionalExpression[#2 - 2, a <= # <= b] &},
  Mesh -> { 15, Range[0, 6, .5], {{0, Directive[Thick, Red]}}}]

Mathematica graphics


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.