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].

[asinghvi17]

It's definitely possible, some of the the same considerations as spherical geometry apply, so some of the polygon processing code could work out of the box.

But it would probably be useful to see some concrete usecases first to understand what the problems that have to be solved are!

[asinghvi17]

http://www.boeing-727.com/Data/fly%20odds/distance.html is useful for the intersection_point implementation for spherical lines

[asinghvi17]

https://github.com/ryanketzner/sphericalpolygon and its associated paper are pretty interesting for fast point in polygon on the sphere...but they require a known point inside the polygon. Maybe we can automatically generate that, somehow?

[asinghvi17]

http://www.edwilliams.org/intersect.htm has some nice stuff