Spherical geometry

[tiemvanderdeure]

It could be useful to have some spherical geometry (read: geometry on the Earth surface).

In this pull request I implemented a formula to calculate the area of any spherical polygon, which of course sits awkwardly in Rasters.jl.

Some things we might want to implement are (please suggest more):

• Shortest distance between two points on a sphere
• Bearing
• Polygon area

This page has some relevant math

[rafaqz]

Turf.jl also has a bunch of code for this we could use.

[rafaqz]

Distance between points and lines on a sphere would also be useful
https://stackoverflow.com/questions/1299567/how-to-calculate-distance-from-a-point-to-a-line-segment-on-a-sphere

[rafaqz]

Could be good to standardise with Distances.jl
https://github.com/JuliaStats/Distances.jl

This also integrates with
https://github.com/KristofferC/NearestNeighbors.jl

for fast calculations of e.g. distances between vectors of points,

Like finding minimum spherical distances between raster pixels and points in an arbitrary collection of features/geometries is only this much code already:

points = GeometryOps.flatten(GI.PointTrait, rivers) do point
    SVector(deg2rad(GI.x(point)), deg2rad(GI.y(point)))
end |> collect

bt = BallTree(points, SphericalAngle())
targets = map(DimPoints(mask_raster)) do p
    SVector(deg2rad.(p))
end |> vec
nearest = nn(bt, targets)
dist = Raster(nearest[2], dims(mask_raster))
Rasters.rplot(dist)

But it could be nice to make this a bit easier for people, and have a spherical_distances function that does the conversion to spherical coordinates automatically, as well as handling the conversions between packages for people.

Distances to lines and polygons on a sphere will of course be harder than this, but it would be good to have those too.

[asinghvi17]

Just to chime in, there seem to be two other packages which look at spherical (specifically Earth spherical :D) coordinates: GeographicLib.jl (unregistered but pure Julia) or Proj.jl's geodesic API. I would guess that we could offer one or all of those as references as well, at least in the docs!

[JeffreySarnoff]

Hello. While doing this -- how about Hyperbolic Geometry [has applications in AI/ML].