How to clip some polygons to the boundary of another polygon?

Question

I have a Delaunay triangulation in a polygon with a hole (a so-called constrained Delaunay triangulation):

I'm able to construct the Voronoi cells by the duality principle. But some of them go outside the polygon (they go in the hole or outside the big perimeter):

How could I clip the Voronoi cells to the boundary of the big polygon? Maybe with the sf package, but I never used it.

(NB: the two pictures do not have the same scale.)

---

Edit

No sorry, that's not correct. Here is the picture with the Voronoi cells to which I added the big polygon:

So in fact I discarded the cells that go outside the polygon.

Will see if I can I change that but probably I will delete this question (and perhaps open a new one).

Answer 1

With {sf} you could try along the exemplary lines below. A polygon with hole can be used for clipping, too.

library(sf)

the_points <- st_multipoint(cbind(rnorm(10), rnorm(10))) 

the_voronoi <- 
  the_points |> 
  st_voronoi() |>
  st_geometry() |> 
  lapply(FUN = `[`) |>
  lapply(FUN = st_multipolygon) |>
  st_as_sfc() |>
  st_cast('POLYGON')

## create a polygon with hole(s) by supplying a list of
## matrices, all after the first matrix defining the holes:
the_clip_with_hole <- 
  3 * st_polygon(list(
    -.5 + cbind(c(0, 1, 1, 0, 0), c(0, 0, 1, 1, 0)),
    -.25 + .5 * cbind(c(0, 1, 1, 0, 0), c(0, 0, 1, 1, 0))
  )
  )



the_clipped_voronoi <- the_voronoi |> 
  st_intersection(the_clip_with_hole)

the_voronoi |> plot()
the_points |> plot(add = TRUE)
the_clipped_voronoi |> plot(col = 'red', lwd = 3, add = TRUE)

Converting the result of st_voronoi to a clippable multipolygon turned out some hazzle.

edit Alternative with {deldir}:

library(deldir)

the_points <- list(x = rnorm(10), y = rnorm(10))

## return Voronoi tesselation object (of class "deldir")
voronoi_object <- deldir(the_points)

corners <-  c(-1, 1, 1, -1, -1)

clip_with_hole <- 
  list(
    poly = list(x = .5 * corners,  y = .5 * rev(corners)),
    hole = list(x = .25 * corners, y = .25 * rev(corners))
  )

## return Voronoi polygons ("tiles") and plot
## original:
tile.list(voronoi_object) |> plot()
## clipped:
tile.list(voronoi_object, clipp = clip_with_hole) |>
  plot(lwd = 3, showpoints = FALSE, fillcol = rainbow(4), add = TRUE)