How to force the RegionPlot to shade a narrow region?

Question

I have an interactive demonstration, which (very simplified to leave out unnecessary details) looks as follows:

    Manipulate[
 Show[{
   Plot[{x, a*x}, {x, -1, 1}, PlotRange -> {-1, 1}],
   RegionPlot[x < y < a*x, {x, -1, 1}, {y, -1, 1}]
   }], {a, 0.5, 1.5}]

On the screen I see this: .

I draw the arrow to point out a defect in the shading: the shading does not cover a narrow triangle in the vicinity of the coordinates origin, though it should.

More than that. The degree of shading varies as I move the slider.

I could, of course, use the option "Filling" in the Plot statement and remove the RegionPlot at all. I need, however, the filling to show the region where one of the lines is above the other. It seemed that the RegionPlot is in this case a more natural choice.

Can you imagine a workaround with the RegionPlot, or I should inevitably go to Filling in the Plot statement?

Answer 1

You can play with PlotPoints, MaxRecurrsion etc. but this will slow you down. I think RegionPlot just doesn't fit here well.

I would use Filling, notice that I've change the order of functions in Plot so the White filling is on top.

Manipulate[
  Plot[{a*x, x}, {x, -1, 1}, PlotRange -> {-1, 1}, PlotStyle -> {Red, Blue}, 
                             Filling -> {2 -> {Bottom, White}, 1 -> {Bottom, Orange}}, 
                             BaseStyle -> Thick]
  , {a, 0.5, 1.5}]