Hilbert curve sequence according to Ingress regional scoring grid?

Solution 1:

OK, the S2map presentation linked does a pretty good job of explaining things, but it lacks a good visualisation of the whole earth.

IITC now has a scoring cells plugin that'll give you a nice interactive map of all the cells, and http://ingress-cells.appspot.com/ will let you search individual cells and click to find out the names without touching IITC if you're wary of the Niantic TOS.

It's worth noting that the cells are only numbered along the hilbert curve at the lowest level, i.e. the final two digits - AM01 through AM16 are 'rows' reaching across the AM face (numbered north to south), and AM**-ALPHA through AM**-SIERRA are 'columns' reaching down the AM face, numbered west to east (n.b. this orientation changes for each face!). Therefore each face isn't really a complete Hilbert Curve

With that in mind:

• Where does the region s2 / hilbert curve start for the Americas face (AM)?
  • The curve 'starts' with AM01-ALPHA-00 approximately 800 miles West of the coast of california.
• Where does it end?
  • The highest numbered cell is AM16-SIERRA-15, approximately 500 miles ESE of Buenos Aires - note that this is NOT the SE corner of the Americas face (which is AM16-SIERRA-10) (see note earlier about cell numbering)
• How do the 6 faces line up?
  • Brian Tao's post here does a great job of showing the high level breakdown: https://plus.google.com/u/0/+BrianTao/posts/dSHWQVEwoNT
• Is there a good argument for a well-defined start to the whole curve? On which face?
  • As discussed above the cell numbering ISN'T really a complete curve. Not even along an entire face.

As for listing portals in 'cell order' - well that would be scraping the intel map and definitely a breach of the Niantic TOS ;-)

Postscript: Not all the NATO Phonetic Alphabet labels are used in 'column' names, here's the list:

ALPHA, BRAVO, CHARLIE, DELTA, ECHO, FOXTROT, GOLF, HOTEL, JULIET, KILO, LIMA, MIKE, NOVEMBER, PAPA, ROMEO, SIERRA

Excluded: Indigo, Oscar, Quebec - draw your own conclusions as to why!