How to apply cross-hatching to a polygon using the grid graphical system?

Several functions in R's base graphical system, including rect() and polygon(), support cross-hatching via their angle= and density= arguments:

x = c(0, 0.5, 1, 0.5)
y = c(0.5, 1, 0.5, 0)
par(mar=c(0,0,0,0))
plot.new()
polygon(x, y, angle=45, density=10)

How might I apply similar cross-hatching to a polygon drawn by the grid graphical system's grid.polygon() function:

library(grid)
grid.newpage()
grid.polygon(x,y)

I've looked in the documentation for ?grid.polygon and ?gpar, and have skimmed through Paul Murrel's book on R graphics, and have so far come up empty. Am I missing something obvious? If not, is there some simple hack which will make this possible?

As of R 4.1.0, grid got the pattern function which allows to repeat any other grob as a filling:

library(grid)

# Note that using absolute coordinates like "cm" for
# x and y does not work
cross <- grobTree(
  linesGrob( x=unit(c(0,1),"npc"), y=unit(c(0,1),"npc")),
  linesGrob( x=unit(c(0,1),"npc"), y=unit(c(1,0),"npc")))

cpat <- pattern(cross,
  width = unit(1,"cm"),
  height = unit(1,"cm"),
  extend = "repeat")

rect <- rectGrob(
  width = unit(5, "cm"),
  height = unit(5, "cm"),
  gp= gpar(fill = cpat))

grid.newpage()
grid.draw(rect)

(This answer was helped by this blog post)