How can one generate plots having regions filled with vector hatching?

Question

I'm using Mathematica 13.3, I want to have a vector output image from all of my plots using hatch filling.

For a test code:

RegionPlot[Sin[x] Sin[y] > 1/4, {x, -10, 10}, {y, -10, 10},
 PlotStyle -> {RGBColor["#0077BB"], HatchFilling[]},
 BoundaryStyle -> Thickness[0.01]]

But the output ALWAYS contains bitmap fractures...clearly visible after zooming. How it can be solved with hatch filling.

Answer 1

• Export such drawing to pdf is not a vector format pdf file. We use Mesh to draw such hatchfilling instead.

plot = RegionPlot[Sin[x] Sin[y] > 1/4, {x, -10, 10}, {y, -10, 10}, 
  BoundaryStyle -> Thickness[0.01], PlotStyle -> None, Mesh -> 80, 
  MeshFunctions -> {#2 - #1 &}, 
  MeshStyle -> {RGBColor["#0077BB"], AbsoluteThickness[1.5]}]
Export["test.pdf", plot] // SystemOpen

• For 20 Degree slope, since the equation of such lines are y=Tan[20 Degree] x +b ( where b is variety), so we can set MeshFunctions -> {#2 - Tan[20 Degree] #1 &} to change the angle of lines.

Clear[plot];
plot = 
 RegionPlot[Sin[x] Sin[y] > 1/4, {x, -10, 10}, {y, -10, 10}, 
  BoundaryStyle -> Thickness[0.01], PlotStyle -> None, Mesh -> 200, 
  MeshFunctions -> {#2 - Tan[20 Degree] #1 &}, 
  MeshStyle -> {RGBColor["#0077BB"], AbsoluteThickness[1]}];
Export["test.pdf", plot] // SystemOpen