# Hilbert curve sequence according to Ingress regional scoring grid?

The new regional scoring grid for Ingress (Regional Scoring - This Changes Everything - DeCode Ingress) is based on an S2 (Hilbert curve) global grid as used in Geometry on the Sphere: Google's S2 Library and an encoding described in request: regional scoring cell borders · Issue #741 · jonatkins/ingress-intel-total-conversion.

That allows every point in the world to be mapped to a point along the Hilbert curve, and begs existential questions like:

• Where does the region s2 / hilbert curve start for the Americas face (AM)?
• Where does it end?
• How do the 6 faces of the cube line up?
• Is there a good argument for a well-defined start to the whole curve? On which face?

And, for extra credit, to go to the limit, the whole enchilada: what is the sequence of all Ingress portals by Hilbert curve order (adding additional levels as necessary)? :)

• I think this question would be better served on the math stackexchange site... Commented Feb 1, 2014 at 20:39
• Agreed. While Ingress is a game, we don't do graphs. ;P Commented Oct 13, 2014 at 15:21
• But of course most mathematicians don't play Ingress, and would have no idea how to gather the Ingress-specific data needed to answer this. And I figure other mathematicians on that site could care less about the answer. I still think we have some sufficiently savvy Ingress players who happen to be interested enough in the math to work it out, and any Ingress player can understand the fun of knowing the answers. Commented Oct 14, 2014 at 2:35

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?
• 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!

• Thanks! I added the links you couldn't, and fixed the SE corner - really AM16-SIERRA-10 - in an edit which will hopefully show up oon.... Commented Dec 24, 2014 at 14:57
• If you follow the hilbert curve, the AM face only has one real exit, and thus actually ends at AM16-ALPHA-15, and then exits to ST01-ALPHA-00. Next is the exit from ST16-ALPHA-15 to AF01-ALPHA-00. The goal is to see if that curve can be followed all the way thru the 6 faces, and what that suggests for the other questions. So I voted you up for making nice progress, but am still looking for answers in line with the hilbert curve itself by you or whoever in order to accept an answer. Commented Dec 24, 2014 at 16:56
• Thanks for the edits. I still don't believe the hilbert curve is strictly 'followed' by the cell numbering. I'll play around with some layouts and see what I can come up with regarding general S2 curve layouts on the cube/sphere though Commented Dec 26, 2014 at 22:31