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JNX scale values explained

Русская версия здесь.

JNX format description contains the following "standard" set of scale values, which is recommended to use in the hand-made JNX maps: 75, 149, 298, 597, 1194, 2388, 4777, 9554, 19109, 38218, 76437, 152877, 305758, 611526, 1223072, 2446184.

This set is an extension of the set used in BirdsEye subscription maps: 597, 1194, 4777 and 76437.
Still, there were no explanation of what these numbers mean.

Several days ago, I got a mail from Dmitry Sklyarov with quite logical reasoning.
Quote:

    I suspect, that so called "JNX scale" has a physical interpretation. This is a piece of the Equator which corresponds to a single raster point of a given zoom level, expressed in millimeters.

    Here's an explanation.

    The WGS-84 ellipsoid uses an equatorial radius of 6378137 meters. So, the length of the Equator is 2 * Pi * 6378137 = 40075016,685578 meters, or 40075016685,57849 millimeters.

    On "zero" raster level (z=0), which DigitalGlobe produces (and it is DigitalGlobe that provides the raster tiles for BirdsEye imagery), the whole globe fits in a single tile.
    Tile size if 256 * 256 pixels, that is, the linear size of a single equatorial pixel corresponds is 40075016685,578 / 256 = 156543033,928041 mm.
    It's difficult to decide to where the fractions should be rounded - to a closer integer, or possibly to a lower one.
    If we round to lower integers, then for z=0 we'll have a point size of 156543033 mm.
    At each successive level of the raster, the number of pixels in both directions is doubled, and the point size becomes twice as small.

    The following table contains hexadecimal and decimal scale values for all zoom levels provided by DigitalGlobe.
    A plus sign after a number mean that the value can be bigger by one, if we choose another type of rounding.
    zhexdec
    00x954A839156543033+
    10x4AA541C78271516+
    20x2552A0E39135758
    30x12A950719567879
    40x954A839783939+
    50x4AA5414891969+
    60x2552A02445984+
    70x12A9501222992
    80x954A8611496
    90x4AA54305748
    100x2552A152874
    110x12A9576437
    120x954A38218+
    130x4AA519109
    140x25529554+
    150x12A94777
    160x9542388+
    170x4AA1194
    180x255597
    190x12A298+
    200x95149
    210x4A74+

This means that JNX maps ideally should use the following set of scales: 74(75), 149, 298(299), 597, 1194, 2388(2389), 4777, 9554(9555), 19109, 38218(38219), 76437, 152874, 305748, 611496, 1222992, 2445984(2445985).
The values which differ from the "standard" scale set, are marked bold.

I haven't changed the format specification page yet, because almost all JNX tools use the "standard" JNX scale values, and the users can possibly have the maps with old scales. Moreover, the relative difference between the "standard" values and the corresponding "geographical" ones is less than one-hundredth of percent.

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