Plot3D: Plot a piecewise function with different colors when plotting multiple function

Question

I am plotting two functions in two variables and one of them is a piecewise function as given below. I am trying to get different colors for each of the sub-function of the piecewise function.

func1 = -(Subscript[n, 1]^2 + Subscript[n, 2]^2) + 100
cb1[[1]] = 1.1245;
cb2[[1]] = 0.7153;
p1 = 
 Plot3D[{func1, 
   Piecewise[{{cb1[[1]] + 100, 
       Subscript[n, 1] <= 5 && Subscript[n, 2] <= 5}}, cb2[[1]]] + 
    75}, {Subscript[n, 1], 0, 10}, {Subscript[n, 2], 0, 10}, 
  AxesLabel -> Automatic]

The entire piecewise function is in color blue as shown in the figure. Is there a way to have sub-functions in different colors? Also, is there way to have the origin on the bottom left?

Answer 1

func1 = -(n1^2 + n2^2) + 100
pw = Piecewise[{{cb1[[1]] + 100,n1 <= 5 && n2 <= 5}}, cb2[[1]]] + 75;

plt2 = Plot3D[pw,
  {n1, 0, 10}, {n2, 0, 10}, 
  MeshFunctions -> {#3 &}, 
  Mesh -> {{100}}, 
  MeshShading -> {Opacity[.6, Red], Opacity[.6, Green]}, 
  ExclusionsStyle -> Opacity[.6, Blue],
  BoundaryStyle -> None];

Show[Plot3D[func1, {n1, 0, 10}, {n2, 0, 10}, AxesLabel -> Automatic], plt2]

Alternatively, construct two functions from your Piecewise function:

pwe = PiecewiseExpand[pw];
{pw1, pw2} = {ConditionalExpression @@ pwe[[1, 1]], 
   ConditionalExpression[pwe[[2]], Not @ pwe[[1, 1, 2]]]};

Plot3D[{func1,  pw1, pw2}, {n1, 0, 10}, {n2, 0, 10}, 
   AxesLabel -> Automatic, 
  PlotStyle -> {Automatic, Opacity[.5, Red], Opacity[.5, Green]}]