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uber
Add documentation page highlighting irregularities of the H3 grid
This might help to address frequent questions about:
- Pentagons
- Distortion vertices
- Variations in area and edge length
I would suggest adding a h3IsNotHexagon() function as it is not just pentagons.
Another point I want to add (but I don’t think that demand any change in the current H3 system) is a paper which hints that Fuller’s orientation is sub-optimal https://www.researchgate.net/publication/331105808_Optimal_orientations_of_discrete_global_grids_and_the_Poles_of_Inaccessibility
@billyauhk Per the conversation on #168, the cells in question are topologically hexagons. This is the distinction that matters for most traversal algorithms, directed or undirected edges, etc. The extra distortion vertices only matter when you're treating the cell as a polygon for rendering, area calculation, etc. As the code currently stands, we can't easily offer h3IsNotHexagon in the way that you mean, since the only way to determine this is to actually run it through h3ToGeoBoundary (as opposed to h3IsPentagon, which is a bitwise operation).
@nrabinowitz Really thanks for the clarifications and hope these all go into the upcoming documentation updates.
I just made an exploration notebook about this topic https://observablehq.com/@fil/h3-oddities
Comments welcome
@Fil That is really nice work! I think it's a very clearly written and accurate description. I was a little surprised by the abruptness of the area change at the hexes crossing the icosahedron edges, but it makes sense, they're getting the worst case distortion from both faces.
Thank you Kevin! I have updated the marks I'm using — it should clarify that the red and black colors denote polygons that have extra "distortion vertices", not high distortion per se.
In fact I'm play/working on a DGGS in which I draw a regular lattice of points on a Dymaxion projection, then lift them back to the sphere (& the cells are their Voronoi). Not exactly the system you described in the 1998 paper, but probably quite close.
@Fil This is amazing! There should be a link to this in the documentation. I was trying to wrap my head around Uber's oddities for some time now and suddenly virtually everything became clear thanks to your observable. Thank you for making that.
