Clarify x/y vs p/q

[cdeil]

@michitaro - I'm still in the process of reading the HEALPix papers, using your code to try to fully understand.

This list of variable names and descriptions is very helpful:
https://github.com/michitaro/healpix/blob/master/src/index.ts#L4

You do sometimes use x/y, but those are not defined in the list.
Note that you have tu2fpq and fxy2tu, so maybe x/y and p/q are the same?

Is it possible to make the notation more consistent; or to clarify what x/y are in that list?

[michitaro]

I have added note about x and y.
2d3aaef

Note that you have tu2fpq and fxy2tu, so maybe x/y and p/q are the same?

Both x/y and p/q are along with north-west/north-east axis, but p/q run on [0, 1] while x/y run on [0, nside).

[cdeil]

Is it useful / needed to have both x/y and p/q?

tu2fpq is only called once, in tu2fpq:

export function tu2fxy(nside: number, t: number, u: number) {
    const { f, p, q } = tu2fpq(t, u)
    const x = clip(Math.floor(nside * p), 0, nside - 1)
    const y = clip(Math.floor(nside * q), 0, nside - 1)
    return { f, x, y }
}

And you're not offering a fpq2tu.

Is this extra clip in tu2fxy really needed?

If it's possible without loosing functionality, I'd suggest removing the p/q coordinate system and moving the content of tu2fpq into tu2fxy and only use fxy.
(the other way would also be possible, but fxy is used in many places, seems the preferred coordinates in this package.

[michitaro]

I'd suggest removing the p/q coordinate system and moving the content of tu2fpq into tu2fxy and only use fxy.

OK. let's do so.

Is this extra clip in tu2fxy really needed?

Ah..., they seem to be not needed.
I was caring the case where p == 1 or q ==1, but p and q always < 1.
It's OK to remove them.