Opacity function applied to Graphics Objects

Question

I think this is a stupid/banal question, but I have searched the forum and I haven't find a solution (yet).

I need to apply a variable opacity function to a graphics object (say a rectangle). For instance the rectangle would have full opacity at its center and be more transparent near its edges, or have a gradient opacity along the x values.

I tried something like this but it obviously doesn't work:

Graphics[{{ColorFunction -> (Directive[Opacity[#1]] &), 
Rectangle[{0 - 0.25, -1}, {0 + 0.25, 1}]}, {Circle[]}}]

(here the unit circle is only a reference graphics object)

On the other hand a similar solution works for a Plot3D, like in the following example

Plot3D[Sin[x^2 + y^2], {x, -3, 3}, {y, -3, 3}, 
ColorFunction -> (Directive[Opacity[#3]] &), PlotPoints -> 40, 
Mesh -> None]

but I need to apply the opacity gradient to a graphics object. I'm sure there's a simple solution but I couldn't find it.

Any help?

Answer 1

Are you after something like this?

Graphics[{{
   Polygon[Tuples[{{0 - 0.25, -1}, {0 + 0.25, 1}}][[{1, 2, 4, 3}]], 
    VertexColors -> {RGBColor[0, 0, 0, 0], RGBColor[0, 0, 0, 1], 
      RGBColor[0, 0, 0, 1], RGBColor[0, 0, 0, 0]}]}, {Circle[]}}]

I wasn't sure which way you wanted the gradient to go.

A central gradient is a bit harder. The built-in gradient has some limitations:

mask = Texture[
   SetAlphaChannel[Image@SparseArray[{_, _} -> 0, {201, 201}], 
    ImageAdjust@Image[GaussianMatrix[100]]]];
Graphics[{mask, 
  Polygon[Tuples[{{0 - 0.25, -1}, {0 + 0.25, 1}}][[{1, 2, 4, 3}]], 
   VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}], {Circle[]}}]

Answer 2

With[{xmin = -0.25, xmax = 0.25, n = 20},
   Graphics[
    {Line[{{-1, 0}, {1, 0}}],
     Circle[],
     Blue,
     Table[
      {Opacity[#],
       Rectangle[
        {xmin + (m - 1) (xmax - xmin)/n, -1},
        {xmin + m (xmax - xmin)/n, 1}]},
      {m, n}]}]] & /@
 {(m - 1)/(n - 1),
  1 - Abs[2 ((n - 1)/2 - (m - 1))/n],
  Abs[2 ((n - 1)/2 - (m - 1))/n]}