HatchFilling exports as non-vector graphics

Question

As of version 12.1, there is an interesting new function to perform object pattern filling: HatchFilling

It works great, but it seems that any graphics containing this symbol export as non-vector graphics.

For example,

Export["rectangle.pdf", Graphics[{HatchFilling[], Rectangle[]}]]

Will create a PDF file with a lossy image, instead of vector graphics.

Is this a bug?

Is there an alternative to this function that can seamlessly fill a graphics object e.g. Rectangle[] with this kind of pattern and export as a vector graphics?

Answer 1

You can use RegionPlot and the options MeshFunctions + Mesh + MeshStyle

RegionPlot[Rectangle[], Mesh -> 50, 
 MeshFunctions -> {#1 + #2 &, #1 - #2 &}, 
 MeshStyle -> {Directive[Thin, Blue], Directive[Thin, Red]}, 
 PlotStyle -> None, BoundaryStyle -> None, Frame -> False]

Add the option MeshShading -> {{White, Cyan}, {Orange, White}} to get

RegionPlot[Rectangle[], Mesh -> 15, 
 MeshFunctions -> {#1 + 2 #2 &, # - 2 #2 &}, 
 MeshStyle -> {Directive[Thick, White], Directive[Thick, White]}, 
 PlotStyle -> None, 
 MeshShading -> Dynamic[{{RandomColor[], RandomColor[]}, {RandomColor[], 
     RandomColor[]}}],
 BoundaryStyle -> None, Frame -> False, ImageSize -> Large]

RegionPlot[Annulus[], Mesh -> {50, 20}, 
 MeshFunctions -> {Sin[# + #2] &, Norm[{# , # - #2}] &}, 
 MeshStyle -> {Directive[Thick, White], Directive[Thick, White]}, 
 PlotStyle -> None, 
 MeshShading -> Dynamic[{{RandomColor[], White}, {White, RandomColor[]}}], 
 BoundaryStyle -> None, Frame -> False, ImageSize -> Large]

RegionPlot[Disk[], Mesh -> 20, 
 MeshFunctions -> {# + #2  RandomReal[{1, 1.2}] &, 
     # + #2 RandomReal[{-1.2, -1.}] &}, 
 MeshStyle -> {Directive[Thick, White], Directive[Thick, White]}, 
 PlotStyle -> None, 
 MeshShading -> Dynamic[{{RandomColor[], White}, {White, 
     RandomColor[]}}], BoundaryStyle -> None, Frame -> False, 
 ImageSize -> Large]

Block[{z = u + I v, pa = PadeApproximant[Exp[z], {z, 0, {5, 0}}]}, 
 RegionPlot[Abs[pa/Exp[z]] > 1, {u, -4, 4}, {v, -4, 4}, 
  ImageSize -> Large, PlotPoints -> 100, Mesh -> 70, 
  MeshFunctions -> {#1 + #2 &, #1 - #2 &},
  MeshShading -> {{White, Cyan}, {Orange, White}}, 
  MeshStyle -> {Directive[AbsoluteThickness[1], Blue], 
    Directive[AbsoluteThickness[1], Red]}, PlotStyle -> None, 
  BoundaryStyle -> None, Frame -> False]]

See also: This answer to a related Q/A

Answer 2

I have written a quick and dirty function to fill rectangular shapes with lines. It is not generalizable, it only works with rectangular shapes and for angles less than 90 degrees, but maybe it can be useful for someone.

RectangleLineFill[min_, max_, step_, angle_] := {
   Table[Line[{
      {i, min[[2]]},
      {Min[(max[[2]] - min[[2]])/Tan[angle] + i, max[[1]]], 
       min[[2]] + (Min[(max[[2]] - min[[2]])/Tan[angle] + i, 
            max[[1]]] - i)*Tan[angle]}
      }], {i, min[[1]], max[[1]], step}],
   Table[Line[{
      {min[[1]], i},
      {Min[(max[[2]] - i)/Tan[angle] + min[[1]], max[[1]]], 
       i + (Min[(max[[2]] - i)/Tan[angle] + min[[1]], max[[1]]] - 
           min[[1]])*Tan[angle]}
      }], {i, min[[2]] + step, max[[2]], step}]
   } /. {Line[{x_, y_}] -> If[x == y, Null, Line[{x, y}]]}

Usage example:

Graphics[{Red, RectangleLineFill[{0, 0}, {3, 2}, 1/10, 45 \[Degree]]}]