Rasterizing points, lines and polygons to raster with `st_rasterize`, using the default algorithms (top) and `options="ALL_TOUCHED=TRUE"` (bottom).

st_rasterize_example.R

library(stars)

multipoint = st_as_sfc("MULTIPOINT ((10 40), (40 30), (20 20), (30 10))")[[1]]
multilinestring = st_as_sfc("MULTILINESTRING ((10 10, 20 20, 10 40),(40 40, 30 30, 40 20, 30 10))")[[1]]
multipolygon = st_as_sfc("MULTIPOLYGON (((40 40, 20 45, 45 30, 40 40)),((20 35, 10 30, 10 10, 30 5, 45 20, 20 35),(30 20, 20 15, 20 25, 30 20)))")[[1]]

dat = c(st_sfc(multipoint), st_sfc(multilinestring), st_sfc(multipolygon))
dat = st_sf(dat, data.frame(value = 1, type = c("Points", "Lines", "Polygons")))
grid = st_as_stars(st_bbox(st_buffer(dat, 3)), dx = 3, dy = 3)

opar = par(mfrow = c(2, 3))
for(i in 1:3) {
  u = st_rasterize(dat[i, ], grid)
  plot(u, col = c(NA, "lightgrey"), key.pos = NULL, main = paste0(dat$type[i], " (default)"), reset = FALSE)
  plot(st_geometry(st_as_sf(u, as_points = TRUE)), pch = 4, col = "darkgrey", add = TRUE)
  plot(st_geometry(dat[i, ]), add = TRUE)
}
for(i in 1:3) {
  u = st_rasterize(dat[i, ], grid, options = "ALL_TOUCHED=TRUE")
  plot(u, col = c(NA, "lightgrey"), key.pos = NULL, main = paste0(dat$type[i], " (ALL_TOUCHED=TRUE)"), reset = FALSE)
  plot(st_geometry(st_as_sf(u, as_points = TRUE)), pch = 4, col = "darkgrey", add = TRUE)
  plot(st_geometry(dat[i, ]), add = TRUE)
}
par(opar)