Plot legend for filling

Question

I have a plot where several lines and curves intersect, and the regions between them are filled with red and blue. My code is

f[x_] = 2/(1 - 2 x^2); g[x_] = -(2/(1 + 2 x^2));
p1 = Plot[{g[x], -2}, {x, -2, -(1/Sqrt[2])}, 
   PlotStyle -> ColorData[97, "ColorList"][[1]], 
   Filling -> {1 -> {2}}, FillingStyle -> {Blue, Opacity[0.5]}];
pa = Plot[{g[x], -2}, {x, -2, -(1/Sqrt[2])}, 
   PlotStyle -> {Black, Black}];
p2 = Plot[{g[x], -2}, {x, -(1/Sqrt[2]), 1/Sqrt[2]}, 
   Filling -> {1 -> {2}}, FillingStyle -> {Blue, Opacity[0.5]}, 
   PlotStyle -> ColorData[97, "ColorList"][[1]]];
pb = Plot[{g[x], -2}, {x, -(1/Sqrt[2]), 1/Sqrt[2]}, 
   PlotStyle -> {Black, Black}];
p3 = Plot[{g[x], -2}, {x, 1/Sqrt[2], 2}, Filling -> {1 -> {2}}, 
   FillingStyle -> {Blue, Opacity[0.5]}, 
   PlotStyle -> ColorData[97, "ColorList"][[1]]];
pc = Plot[{g[x], -2}, {x, 1/Sqrt[2], 2}, 
   PlotStyle -> {Black, Black}];
p4 = Plot[{2, f[x]}, {x, -2, -(1/Sqrt[2])}, 
   Filling -> {1 -> {{2}, LightRed}}, 
   PlotStyle -> ColorData[97, "ColorList"][[1]]];
pd = Plot[{2, f[x]}, {x, -2, -(1/Sqrt[2])}, 
   PlotStyle -> {Black, Black}];
p5 = Plot[{f[x], 2}, {x, -(1/Sqrt[2]), 1/Sqrt[2]}, 
   Filling -> {1 -> {{2}, LightRed}}, 
   PlotStyle -> ColorData[97, "ColorList"][[1]]];
pe = Plot[{f[x], 2}, {x, -(1/Sqrt[2]), 1/Sqrt[2]}, 
   PlotStyle -> {Black, Black}];
p6 = Plot[{2, f[x]}, {x, 1/Sqrt[2], 2}, 
   Filling -> {1 -> {{2}, LightRed}}, 
   PlotStyle -> ColorData[97, "ColorList"][[1]]];
pf = Plot[{2, f[x]}, {x, 1/Sqrt[2], 2}, PlotStyle -> {Black, Black}];
line1 = Line[{{-(1/Sqrt[2]), -6}, {-(1/Sqrt[2]), 6}}]; 
line2 = Line[{{1/Sqrt[2], -6}, {1/Sqrt[2], 6}}]; 

It's horrible to look at, I know. It returns a nice plot though. What I would like to add to it are plot legends, as the red and blue regions indicate specific things. Can anyone help me?

Answer 1

Plot[{g[x], f[x], -2, 2}, {x, -2, 2}, PlotStyle -> Black, 
 Filling -> {1 -> {{3}, Opacity[0.5, Lighter @ Blue]}, 
             2 -> {{4}, Opacity[.5, Lighter @ Red]}}, 
 Exclusions -> None, 
 Frame -> True, Axes -> False, ImageSize -> Large, 
 PlotLegends -> Placed[SwatchLegend[{Lighter @ Blue, Lighter @ Red}, 
     Style[#, 16]& /@ {"legend 1", "legend 2"}], {.8, .8}]]

Note: We can also set the filling option as:

Filling -> {1 -> {-2, Opacity[0.5, Lighter @ Blue]}, 
  2 -> {2, Opacity[.5, Lighter @ Red]}}

We can set the position of the legend interactively using Locator:

DynamicModule[{pt = {.8, .8}}, 
 Plot[{g[x], f[x], -2, 2}, {x, -2, 2}, 
   PlotStyle -> Black, 
   Filling -> {1 -> {{3}, Opacity[0.5, Lighter @ Blue]}, 
      2 -> {{4}, Opacity[.5, Lighter @ Red]}}, Exclusions -> None, 
  Frame -> True, Axes -> False, ImageSize -> Large, 
  Epilog -> Dynamic @ 
   {Locator[Dynamic[pt], SwatchLegend[{Lighter @ Blue, Lighter @ Red}, 
       Style[#, 16] & /@ {"legend 1", "legend 2"}]]}]]

Answer 2

This can be merged into a single Plot call which will make adding legend with Epilog easier. Here's an example

f[x_] = 2/(1 - 2 x^2);
g[x_] = -(2/(1 + 2 x^2));
Plot[
  {
   g[x], f[x],
   -2, 2
   }, {x, -2, 2},
  PlotStyle -> Black,
  Filling -> {
    {
     1 -> {{3}, Append[LightBlue, .5]},
     2 -> {{4}, Append[LightRed, .5]}
     }
    },
  Epilog -> {
    Line[
     {
      {-(1/Sqrt[2]),
       f[-(1/Sqrt[2]) - $MachineEpsilon]},
      {-(1/Sqrt[2]),
       f[-(1/Sqrt[2]) + $MachineEpsilon]}
      }
     ],
    Line[
     {
      {(1/Sqrt[2]),
       f[(1/Sqrt[2]) - $MachineEpsilon]},
      {(1/Sqrt[2]),
       f[(1/Sqrt[2]) + $MachineEpsilon]}
      }
     ],
    Inset[
     Style["This is a thing", Red],
     {0, -4}
     ]
    },
  PlotRange -> {{-2, 2}, {-5, 5}},
  PlotLegends -> {
    "Function with a cusp",
    "Something like a cosecant"
    },
  Frame -> True,
  Axes -> False,
  ImageSize -> 600
  ] // bringLegendIn[#, Scaled[{1, 1}], {Right, Top}] &

where

bringLegendIn[plot_, where_ : Scaled[{.05, .95}], anchor_ : {Left, Top}] :=
    
  Show[#[[1]], 
     Epilog ->
      Join[
       Epilog /. Options[#[[1]], Epilog],
       {
        Inset[#[[2, 1]], where, anchor]
        }
       ]
     ] &@plot;