[jira] [Created] (SIS-532) NaN from unhandled case in reverse Oblique Mercator calculations

["Emmanuel Giasson (Jira)" <ji...@apache.org>]

Emmanuel Giasson created SIS-532:
------------------------------------

             Summary: NaN from unhandled case in reverse Oblique Mercator calculations
                 Key: SIS-532
                 URL: https://issues.apache.org/jira/browse/SIS-532
             Project: Spatial Information Systems
          Issue Type: Bug
          Components: Referencing
    Affects Versions: 1.1
            Reporter: Emmanuel Giasson


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 can be
 * exactly +/- 1.0 (theoretical bounds) which causes a division by zero on (1-U) 
 * 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.

When U tends toward +/- 1.0, the reciprocal with H tends towards 0, giving {{φ = pi/2.}} This limit case is not mentioned in EPSG guidance notes (I looked at p.62 of 2019/09 revision), but it is 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. 

Checking if abs(U) >= 1.0 then forcing {{φ}} to pi/2 (and {{λ}} to any valid value) should be enough to fix the bug.

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)


 



--
This message was sent by Atlassian Jira
(v8.20.1#820001)