How can I use and understand (R-) leaflet's crsClasses?

Question

Edit after input below and e.g. here: leaflet has to make a compromise between "understandable for non-gis-experts" and "correct gis-handling". What I understand now, leaflet focussed on easy handling, thus, projections cannot really be implemented.

Originial question: My goal is to display "real" densities correctly, that is in events/m^2. At the moment I am struggeling with leaflet's projection's. What do I have to do, to display all crsClasses correctly? My data generates uniform random points on the shere.

I guess I miss to transform the data?

library(leaflet)
n <- 10000
z <- 2*runif(n) - 1
phi <- 2*pi*runif(n) - pi
x <- sin(phi)*sqrt(1 - z^2)
y <- cos(phi)*sqrt(1 - z^2)
theta <- acos(z)
# lat / lng
lat <- theta*180/pi - 90
lng <- phi*180/pi

# Working fine:
# plot3D::polygon3D(x, y, z)
rgl::plot3d(x, y, z)
# rgl::plot3d(sin(phi)*sin(theta), cos(phi)*sin(theta), cos(theta)) # the same...

# EPSG:3857, also known as "Google Mercator" or "Web Mercator", the first in the following list
crsClasses <- c("L.CRS.EPSG3857", "L.CRS.EPSG4326", "L.CRS.EPSG3395", "L.CRS.Simple", "L.Proj.CRS")
epsg3857 <- leafletCRS(crsClass = crsClasses[1])
leaflet(options = leafletOptions(
  crs = epsg3857, worldCopyJump = FALSE)) %>%
  addTiles() %>%
  addProviderTiles(providers$OpenStreetMap, group = "OSM") %>%
  addProviderTiles(providers$Stamen.TonerLite, group = "Toner Lite") %>%
  addLayersControl(baseGroups = c("OSM", "Toner Lite")) %>%
  addCircleMarkers(lat = lat,
                   lng = lng,
                   radius = 1, 
                   stroke = FALSE,
                   fillOpacity = 0.7)

Using crsClasses[1] ... looks ok, but I don't understand why this corresponds to worldCopyJump = FALSE.

Using crsClasses[2] ... looks strange

crsClasses[3...6] also look strange. It is really hard to find good tutorials for a GIS-newbie

References:

• rstudio
• geocompr

Comment after input from IvanSanchez: Is the following strategy correct?

• Using crsClass L.CRS.EPSG4326, the map changed, but the data remained unchanged. Thus, I also have to transform the data. This means I have to use new <- sp::spTransform(x, CRSobj, ...). It looks like
  • I have to figure out the EPSG code, here you already told me (and you could guess) it is EPSG:4326. Is there a systemtic way to get that result?
  • I need to transform (lat, lng) to an a proper object. From ??spTransform: "x ... object to be transformed" and "CRSobj ... object of class CRS". The help leads to sp::CRS(projargs, doCheckCRSArgs=TRUE). But then I get stuck...
  • Call the new lat/lng in addCircleMarkers().
• As you pointed out, I should look for equal-area projection for densities
  • From here I would look for a Lambert azimuthal equal-area (LAEA), as they recommend. From here, I would guess, I take the EPSG:3575(??) for Europe, but perhaps the "WGS 84 / North Pole LAEA Europe" is wrong?
  • The I am lost: ...find (or build) base maps for that projection. I think this means for the map and the data?

Can you provide a guidline through that jungle or at least to one of the cases above? Or do you have a good reference to learn how to do that properly?

From the Leaflet docs:

crs ... Coordinate Reference System to use. Don't change this if you're not sure what it means.

But unfortunatelly, they don't tell you, where to look if you need to change.

Answer 1

My goal is to display "real" densities correctly, that is in events/m²

You should use an equal-area projection, then.

but I don't understand why this corresponds to worldCopyJump = FALSE.

The worldCopyJump is an interaction option, and not a visualization option. Let me quote Leaflet's reference, emphasis mine:

With this option enabled, the map tracks when you pan to another "copy" of the world and seamlessly jumps to the original one so that all overlays like markers and vector layers are still visible.

In other words: That option only impacts the behaviour of the map when the user pans the map around so that the map's center crosses the antimeridian. It doesn't have any other effect. It doesn't make multiples copies of the data as Leaflet.RepeatedMarkers does, and it doesn't magically reposition your data so it looks nicer.

Using crsClasses[2] ... looks strange

You're using a map with a EPSG:4326 coordinate system, but the background tiles are still in EPSG:3857. As explained elsewhere, Leaflet does not reproject raster data (unlike OpenLayers does in some very specific scenarios). If you change the map's CRS, you are in charge of changing the map's tile source(s) as well.

EPSG:4326 is the coordinate system for the equirectangular projection, based on the CRS84 geoid.

It has the property that the extents of the earth look like a rectangle of ratio 2:1; Leaflet makes the assumption that a tile server serving tiles in EPSG:4326 has two tiles for the zoom level zero. Compare that with the assumption Leaflet makes about EPSG:3857 having just one square tile at zoom level zero.

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Do not change the CRS blindly and expect things to work. Choose a map projection, find its EPSG code, then find (or build) base maps for that projection.