Curious about creating an S2CellID from a FaceIJ and level

[CraigglesO]

I've been looking at the code for a while and curious if there is a creative way to go from FaceIJ+level to S2CellID and back again

To expound on this:

if The max level was say "2", then the maximum for I and J are "4".
The idea here is that I have an algorithm that sometimes uses IJ at various depths and I'm curious the easiest way to get to an S2CellID that complements the depth.

should I just bit shift the IJ to maxLevel, create an S2CellID then find its parent at the level I was originally in or do you have a superior alternative?

essentially I assume it is something like this before FromIJ:

I = I << (30 - level)
J = J << (30 - level)

then after getting the s2cell parent at level, heading back and after ToIJ:

i = i >> (30 - level)
j = j >> (30 - level)

while the math works from tests, I'm nervous there is something I am missing. The way I visualize it though, this seems to work.

[jmr]

You're looking for something like S2CellId::FromFaceIJ().parent()? Can you use that?

[CraigglesO]

Hey, sorry if I was not being clear enough. I'll try again.

FromFaceIJ then parent just ensures its a S2CellId as a specific level. But what I am interested in is working with IJ at various levels.

But I think the best way to explain this is to use different variables. Let's say X and Y.

So at level 0 we only have a face or just a singular cell. But at the next level (1) we have 2 cells in the X direction and 2 cells in the Y direction with 4 cells total.

My original fear was that after converting to IJ, I couldn't get the correct XY from IJ. but after more experimentation I know I can get the correct "XY" from "IJ" for sure now.

it really is just:

int IJtoXY (int i, int level) {
  return i >> (30 - level);
}

[CraigglesO]

However, I think it's interesting that from the main page here the top right is considered 2-2 whereas my IJtoXY would categorize the top right as 3-3.

[jmr]

I'm still not exactly sure what you're after. Do you want to "work with" (i, j), or convert to and from cell ids?

Did you read the coordinate descriptions here?

https://github.com/google/s2geometry/blob/master/src/s2/s2coords.h#L30

Maybe you want a shifted version of (si, ti)? You can do that.

[CraigglesO]

Let's put it this way. If it was you, looking at the page I linked in the prior comment, second image down.. how would YOU arrive at 2-2? It's clear it is using level 2 cells, but given a S2CellID, how would you arrive at that 2-2 number? for the top right cell at level/zoom 2.

[jmr]

looking at the page I linked in the prior comment, second image down.. how would YOU arrive at 2-2?

Using Python pseudo-code: [cell_id.child_position(level) for level in range(1, cell_id.level())]

This is equivalent to reading off pairs of bits from the cell id:

s2geometry/src/s2/s2cell_id.h

Line 66 in ad1489e

// - The id of a cell at level k consists of a 3-bit face number followed

s2geometry/src/s2/s2cell_id.h

Line 599 in ad1489e

return static_cast<int>(id_ >> (2 * (kMaxLevel - level) + 1)) & 3;

But if that's your question, I'm confused as to why you mention (i, j) above.

[CraigglesO]

Hey, that was a huge insight for me. I thought it was specifying an x-y but ti was actually just explaining consecutive cell positions in the image.
wow.

Ok, so I made some pictures to explain what I am doing:

I got a bit lazy and didn't fill it all in, but you can see what is going on. Sometimes I am interested in the "X-Y" pair positions from a S2CellID.

In the second image, the top right position has an XY of [3, 3]. However if I converted that S2CellID to IJ I would actually get [469762048, 469762048].

The reason is, no matter the S2CellID level, the I and J values will always be between [0, pow(2, 30) - 1].

I still believe my function is the correct/best method to get from an S2CellID to an XY at that cells level
if the level is 30, than XY and IJ will be the same, otherwise it "dives"

int IJtoXY (int i, int level) {
  return i >> (30 - level);
}

So:

1. convert S2CellID to a Face-I-J
2. convert the I and J to X and Y

Is this a bit more clear for what I want? I don't think s2geometry provides this function.

[jmr]

Yes, that will work. There's probably no function for that since it's just a shift.

What are you actually trying to do? Unless you're writing a tutorial about the coordinate systems, this is probably using the library at a lower level than necessary.

[CraigglesO]

Sorry, was a bit sick.

Javascript is a unique situation where I can:

1. Use "long" package and add a ton of storage overhead.
2. Use BigInt and see a 99% reduction in "number" performance.
3. Use Face-zoom(level)-x-y and manipulate data as numbers, then convert to BigInt as necessary.

3 has the nice advantage of speed and no package/size cost. But basically I was here to verify that the x-y solution was actually accurate, but in hindsight it was pretty obviously yes.

I appreciate your time though, this is really an absurdly impressive library.