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    Re: What Three Words at sea
    From: Frank Reed
    Date: 2018 Jun 30, 01:07 -0700

    Earlier, I wrote:
    "This is easily resolved in practice. The "3m" grid that they specify is closely matched by (and probably identical to) tenths of a second of arc in latitude. So 41°27'00.0" is at the center (or corner) of one square and 41°27'00.1" is the center of the next square to the north. In longitude you lay out the squares in proportion to the cosine of the latitude. So if you're at 60°00'00.0" N and 10°00'00.0" E, the next square to the northeast would still be just a tenth of a second up but two tenths to the east. Its coordinates would be 60°00'00.1" N 10°00'00.2" E. That lets you cover the whole globe with the only tiling defect occuring within a few meters of the maritime dateline (and since this system can afford to over-specify locations, that can be handled by a one tile overlap."

    I've run some experiments, and their system mostly works as I described here except that the widths vary a tiy bit in typical latitudes and significantly at the very highest latitudes. Their tiles completely cover any band at any latitude. in order to do this, they have to vary the width slightly and eventually, near the poles, drop the whole idea of having a particular width for the tiles. It's still true that the normal tile scaling is proportional to the cosine of the latitude, as you would expect. They don't make it easy to see the very high latitude tiling in their standard tools since they really don't expect anyone to use this at the poles! But we can probe the API and figure it out. The last band of latitude begins a tenth of an arcsecond south of the north pole at latitude 89°59'59.9". That's ten feet from the pole. But before reaching this latitude, the division of longitude tops out at 2.5 minutes of arc. That means that this last band contains 8640 separate slices. They are effectively triangles ten feet long with apexes at the north pole and each less than a tenth of an inch at the base. All of these narrow triangles are treated as unique tiles in the global map, and each is assigned "three words", just like the "normal" 10 foot by 10 foot squares in lower latitudes. In fact, for the last five nautical miles to the pole (3000 rings of latitude when divided at a tenth of a second of arc), every latitude band is divided into 8640 slices. This all yields a tiny inefficiency, and it also seems to imply that the "squares" end up over twenty feet wide. So if you open a donut shop five miles from the north pole, your customers might confuse you with the coffee shop next door.

    Frank Reed

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