Details
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Bug
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Status: Closed
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Major
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Resolution: Fixed
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1.1
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None
Description
Reversing 2D coordinates into long,lat that happen to be very near or right on North/South pole may produce "NaN" latitude, instead of +/- 90 degrees, because of an unhandled limit case and/or unavoidable rounding errors on the last bits of finite precision numbers.
In release 1.1, org/apache/sis/referencing/operation/projection/ObliqueMercator.java, lines 404-406
final double U = (V*cosγ0 + S*sinγ0) / T;
final double λ = -atan2( (S*cosγ0 - V*sinγ0), cos(y ) ) / B;
final double φ = φ(pow(H / sqrt((1 + U) / (1 - U)), 1/B));
Value for U is typically within ]-1, 1[ but can be
- exactly +/- 1.0 (theoretical bounds) which causes a division by zero on (1-U) or H/sqrt(...)
- slightly beyond +/- 1.0 (like 1.0000000000000002) owing to previous operations on finite-precision numbers. This then causes a NaN on the square root of a negative number.
Your code follows EPSG guidance notes and indeed, the latter makes no mention of that limit case (I looked at p.62 of 2019/09 revision). But it is noted in Snyder, 1987 (https://pubs.usgs.gov/pp/1395/report.pdf), from which EPSG guidance notes were most probably copied. See p.75, after equation 9-47. In the current case, we also have to cater for the "beyond +/- 1.0" case because of imprecisions.
Checking if abs(U) >= 1.0 then forcing φ to +/- pi/2 (and λ to any valid value) should thus be enough to fix this issue.
Should you need an actual case to reproduce the above issue, I stumbled upon it with the following transform:
Inverse_MT[
Param_MT["Hotine Oblique Mercator (variant A)",
Parameter["semi_major", 6378137.0, Unit["metre", 1]],
Parameter["semi_minor", 6356752.314245179, Unit["metre", 1]],
Parameter["Latitude of projection centre", 89.8, Unit["degree", 0.017453292519943295]],
Parameter["Longitude of projection centre", 179.8, Unit["degree", 0.017453292519943295]],
Parameter["Azimuth of initial line", -174.84239553505424, Unit["degree", 0.017453292519943295]]]]
While trying to reverse POINT(-905672.3035667514 -1.0011576308445137E7)
into long,lat, which gave POINT(41.98971287679859 NaN)