R Under development (unstable) (2024-03-16 r86144 ucrt) -- "Unsuffered Consequences"
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> suppressPackageStartupMessages(library(sf))
> bb = st_bbox(c(xmin=0, ymin=1, xmax=3, ymax=2))
> xx <- st_make_grid(st_as_sfc(bb), square = FALSE, what = "polygons")
> plot(xx, border = 'green', main = "pointy topped")
> x <- st_make_grid(st_as_sfc(bb), square = FALSE, what = "points")
> plot(x, add = TRUE)
> x <- st_make_grid(st_as_sfc(bb), square = FALSE, what = "corners")
> plot(x, col = 'orange', add = TRUE)
> plot(st_as_sfc(bb), add = TRUE, border = 'red')
> st_overlaps(xx) %>% 
+ 	lengths() %>% 
+ 	sum()
[1] 0
> 
> st_as_sfc(bb) %>%
+ 	st_difference(st_union(xx)) %>%
+ 	st_area()
numeric(0)
> 
> xx <- st_make_grid(st_as_sfc(bb), square = FALSE, what = "polygons", flat_topped = TRUE)
> plot(xx, border = 'green', main = "flat topped")
> x <- st_make_grid(st_as_sfc(bb), square = FALSE, what = "points", flat_topped = TRUE)
> plot(x, add = TRUE)
> x <- st_make_grid(st_as_sfc(bb), square = FALSE, what = "corners", flat_topped = TRUE)
> plot(x, col = 'orange', add = TRUE)
> plot(st_as_sfc(bb), add = TRUE, border = 'red')
> st_overlaps(xx) %>% 
+ 	lengths() %>% 
+ 	sum()
[1] 0
> 
> st_as_sfc(bb) %>%
+ 	st_difference(st_union(xx)) %>%
+ 	st_area()
numeric(0)
> 
> proc.time()
   user  system elapsed 
   0.56    0.09    0.64