How to hide and show graphics within Show (in Manipulate)

Question

There is a well documented way to "Dynamically Hide and Show Plots" (link). In the example 'Opacity' option is effectively used. Is there an efficient way to make the same functionality with "Show"? I can only see a way using "if" statement, but it looks somewhat cumbersome as it wants dummy Graphic[] as a placeholder. For instance:

Manipulate[    
 a = Plot[x, {x, 0, 1}];    
 b = Plot[1 - z, {z, 0, 1}];    
 Show[    
  If[cond1 == 1, a, Graphics[]],
  If[cond2 == 1, b, Graphics[]]
 ],
 Grid[
  {
   {Control[{{cond1, 1, ""}, {0, 1}}], "a"},
   {Control[{{cond2, 1, ""}, {0, 1}}], "b"}
  }
 ]    
]        

Another drawback is that unchecking 'a' causes Plot axes to disappear.
Any ideas?

Answer 1

Manipulate[a = Plot[x, {x, 0, 1}]; b = Plot[1 - z, {z, 0, 1}];
 Show[If[cond1 == 1, a, Graphics[]], If[cond2 == 1, b, Graphics[]], 
  Axes -> (cond1+cond2>=1), PlotRange -> {{0, 1}, {0, 1}}, AspectRatio -> 1/GoldenRatio], 
 Grid[{{Control[{{cond1, 1, ""}, {0, 1}}], "a"}, 
       {Control[{{cond2, 1, ""}, {0, 1}}], "b"}}]]

Change Axes -> (cond1 + cond2 >= 1) to Axes->True if you want to have the axes always visible.

You can get the same result by changing the PlotStyle of plots a and b based on the cond1 and cond2, respectivly.

Manipulate[ a = Plot[x, {x, 0, 1}, PlotStyle -> If[cond1 == 0, Opacity[0], Opacity[1]]];
 b = Plot[1 - z, {z, 0, 1}, PlotStyle -> If[cond2 == 0, Opacity[0], Opacity[1]]];
 Show[a, b, Axes -> (cond1+cond2>=1), PlotRange -> {{0, 1}, {0, 1}}, 
     AspectRatio -> 1/GoldenRatio], 
 Grid[{{Control[{{cond1, 1, ""}, {0, 1}}], "a"},
       {Control[{{cond2, 1, ""}, {0, 1}}], "b"}}]]

Alternatively, use a single plot with two curves:

Manipulate[Plot[{x, 1 - x}, {x, 0, 1}, 
   PlotStyle -> {If[cond1 == 0, Opacity[0], Opacity[1]], 
                 If[cond2 == 0, Opacity[0], Opacity[1]]},
   Axes -> (cond1+cond2>=1), PlotRange -> {{0, 1}, {0, 1}}, AspectRatio -> 1/GoldenRatio], 
 Grid[{{Control[{{cond1, 1, ""}, {0, 1}}], "a"}, 
       {Control[{{cond2, 1, ""}, {0, 1}}], "b"}}]]

If you have to use Show:

Manipulate[ab = Plot[{x, 1 - x}, {x, 0, 1}, 
   PlotStyle -> {If[cond1 == 0, Opacity[0], Opacity[1]], 
     If[cond2 == 0, Opacity[0], Opacity[1]]}];
 Show[ab, Axes -> (cond1 + cond2 >= 1), PlotRange -> {{0, 1}, {0, 1}}, 
      AspectRatio -> 1/GoldenRatio], 
 Grid[{{Control[{{cond1, 1, ""}, {0, 1}}], "a"},
       {Control[{{cond2, 1, ""}, {0, 1}}], "b"}}]]