Add lines to 3D Plot

Questions
,
1

How can I add lines that demarcate the different regions of the following 3D plot like [a > 0, c > 0], [a = 0, c > 0] etc.?

Plot3D[1/(1 + E^(-a - c)), {a, -8, 8}, {c, -8, 8}]

Thanks in advance!

2

You may find the follwing helpful.

(1) Drawing lines in 3D plots:
http://mathematica.stackexchange.com/questions/20479

(2) Various contour plot and marking planes inside 3D plots:
http://mathematica.stackexchange.com/search?q=planes+in+3D+plot

3

thanks for the references. I have looked at them but I still don’t know how to solve the problem.

To give you an idea of what I have in mind I have added the lines in paint to the diagram. What I want to know is how to make something similar in mathematica directly.

3Dplot.gif
3Dplot.gif581×456 42.7 KB

4 
pl1 = Plot3D[1/(1 + E^(-a - c)), {a, -8, 8}, {c, 0, 8}, 
   Mesh -> {{0}, {0}}, PlotStyle -> None, 
   MeshStyle -> Directive[Thick, Red]];
pl2 = Plot3D[1/(1 + E^(-a - c)), {a, -8, 8}, {c, 0, 8}, 
   MeshFunctions -> {#1 + #2 &}, Mesh -> {{0}, {0}}, 
   PlotStyle -> None, MeshStyle -> Directive[Thick, Red]];
pl3 = Plot3D[1/(1 + E^(-a - c)), {a, -8, 8}, {c, -8, 8}, 
   Mesh -> {{0}, {0}}, MeshFunctions -> {#2 &}, PlotStyle -> None, 
   MeshStyle -> Directive[Thick, Red]];
pl4 = Plot3D[1/(1 + E^(-a - c)), {a, -8, 8}, {c, -8, 8}, 
   PlotStyle -> Directive[Yellow, Specularity[White, 20]], 
   MeshStyle -> Opacity[.5], PlotPoints -> 40];


Show[pl3, pl1, pl2, pl4]

asdwqfsdg43t546y6rthb.jpg
asdwqfsdg43t546y6rthb.jpg499×405 70.7 KB

5

Another answer to the same question is cross-posted on MSE.

6

Thanks for the reply!

Sorry for crossposting (I did not anticipate that you would be so quick and effective in replying!)

Is it also possible to color the different regions?

7

Yes it is very easy for rectangular regions:

Plot3D[1/(1 + E^(-a - c)), {a, -8, 8}, {c, -8, 8}, Mesh -> {{0}, {0}},
  MeshStyle -> Directive[Thick, Gray], 
 MeshShading -> {{Yellow, Blue}, {Green, Red}}, PlotPoints -> 40]

ad234fg456h768j7.png
ad234fg456h768j7.png368×292 22.8 KB

But I am not sure about syntax for the custom regions. Maybe that MSE answer syntax is more suitable for that.