Confirmation of grid algorithm
csbrown opened this issue · comments
The h3 docs cite [1] as a reference for the icosahedral discrete global grid system algorithm h3 employs. That paper mentions a number of algorithms, notably one they call the "Icosahedral Snyder Equal Area aperture 3 Hexagon (ISEA3H) Geodesic DGGS." This algorithm seems also to be implemented in an R package by Sahr and Barnes.
Does H3 employ the ISEA3H algorithm? If not, is there a publication describing the algorithm that H3 uses to generate its DGGS? If so, is there a publication or other documentation of the parameters provided to the ISEA3H algorithm to generate the various levels and orientations of the H3 grids?
Cheers
[1] Sahr, Kevin, Denis White, and A. Jon Kimerling. "Geodesic discrete global grid systems." Cartography and Geographic Information Science 30.2 (2003): 121-134.
No, H3 does not use the ISEA3H algorithm. The base algorithm is described on the page you linked - I don't think we have more in-depth documentation. Key differences between H3 and ISEA3H include:
- The aperture - 3 in ISEA3H and 7 in H3
- The grid projection - ISEA uses the Snyder Equal Area projection, while H3 uses a gnomonic projection. This means that H3 is not truly equal-area - see this table or this visualization to understand area variation across the grid - but projection is somewhat faster and cell boundaries are proper spherical polygons, with great-arc edges.
@sahrk may have more details here.
So H3 is using an Aperture 7 subdivision with gnomonic projection for each icosahedron face. It is derived from @sahrk's DGGRID but there was no explicit effort to maintain compatibility between the two (the requirement for H3's index to bitpack all of the relevant data into a 64-bit integer essentially required that incompatibility).
H3 does not implement ISEA3H, but I don't remember the exact terminology.
@nrabinowitz and @dfellis hit all the high points. ISEA3H is a pure aperture 3 grid; H3 has an unindexed initial aperture 3 and 4 (to form the base cells) followed by the indexed pure aperture 7 grid. H3 uses a polyhedral face-centered gnomonic. Both are created on icosahedrons, but the orientation relative to the earth is different. ISEA3H uses an orientation which is symmetrical about the equator, while H3 uses Bucky Fuller's Dymaxion orientation that places icosahedral vertexes (and thus the 12 pentagonal cells) in water.
If you're interested in a more detailed description and taxonomy of these types of grids, a better reference (which didn't exist yet when we created H3) would be:
Sahr, K. 2019. Central Place Indexing: Hierarchical Linear Indexing Systems for Mixed-Aperture Hexagonal Discrete Global Grid Systems. Cartographica: The International Journal for Geographic Information and Geovisualization, 54(1):16-29.