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https://issues.apache.org/jira/browse/SIS-532?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Martin Desruisseaux closed SIS-532.
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> 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
> Assignee: Martin Desruisseaux
> Priority: Major
> Fix For: 1.2
>
>
> 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)
>
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