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Both "mapbox" and "maplibre" offer Web Mercator and ‘Globe’ projections:

Globe projection (default)

tmap_mode("maplibre")
#>  tmap modes "plot" -> "view" -> "mapbox" -> "maplibre"
#>  rotate with `tmap::rtm()`switch to "plot" with `tmap::ttm()`

tm_shape(metro) + tm_bubbles(size = "pop2030", fill = "red")

Mercator projection

tmap_mode("maplibre")
#>  tmap modes "plot" -> "view" ->
#> "mapbox" -> "maplibre"

tm_shape(metro) + tm_bubbles(size = "pop2030", fill = "red") + tm_crs(3857)

In addition, "mapbox" offers a couple of other projections:

Other projections

Pseudo-cylindrical

tmap_mode("mapbox")

tm_shape(metro) + tm_bubbles(size = "pop2030", fill = "red") + tm_crs("+proj=eqearth")
tm_shape(metro) + tm_bubbles(size = "pop2030", fill = "red") + tm_crs("+proj=wintri")

Conic

tm_shape(metro) + tm_bubbles(size = "pop2030", fill = "red") + tm_crs("+proj=eqearth")
tm_shape(metro) + tm_bubbles(size = "pop2030", fill = "red") + tm_crs("+proj=eqearth")