I am researching some applications of space filling curves in geospatial computation.
I'm familiar with the concept of space-filling curves as they apply to Euclidean spaces.
Currently major geospatial libraries (such as S2) map Euclidean space filling curves (such as the Hilbert curve) to a sphere for purposes of creating a spatial mapping from 1 dimension to all points on a sphere.
I'm making this post to ask if there are any known "native" sphere filling curves that are not constructed by mapping one or more Euclidean curves to a sphere but rather natively constructed using spherical geometry.
I'm particularly interested in curves that preserve locality like the Hilbert curve does (i.e. not a spiral).