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From "Martin Desruisseaux (JIRA)" <j...@apache.org>
Subject [jira] [Created] (SIS-467) Unsupported geodesics
Date Tue, 16 Jul 2019 13:45:00 GMT
Martin Desruisseaux created SIS-467:
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             Summary: Unsupported geodesics
                 Key: SIS-467
                 URL: https://issues.apache.org/jira/browse/SIS-467
             Project: Spatial Information Systems
          Issue Type: Bug
          Components: Referencing
    Affects Versions: 1.0
            Reporter: Martin Desruisseaux


The {{GeodesicOnEllipsoid}} class tries to implement the equations published in Charles F.
F. Karney, 2013. [Algorithms for geodesics|https://doi.org/10.1007/s00190-012-0578-z], SRI
International. Those algorithms were already implemented in [GeographicLib|https://geographiclib.sourceforge.io/],
which we use as a reference implementation in our tests but not in the main code in order
to keep the amount of Apache SIS dependencies low. We also want close integration with the
rest of SIS framework (automatic conversion of input/output coordinates), keep some intermediate
values for computing Bezier curves, _etc._ However our current implementation has the following
limitations (maybe because of misunderstanding on our side). The GeographicLib source code
may be examined for understanding what we are doing wrong, but the relationships between that
source code and the formulas are not easy to establish.

h2. Nearly antipodal geodesics on equator
Apache SIS does not have a solution for geodesics on equator when the difference of longitude
is ∆λ > (1 - _f_)⋅π (close to 180°). This issue is discussed in Karney (2013) below
equation 44, but we have not yet understood what is the appropriate action. Even if equation
57 can be use for computing α₁ in such case, we still have equations 11 and 12, for example
σ = atan2(sinβ, cosα⋅cosβ), producing 0 because sinβ = 0, which result in a geodesic
distance of 0. We surely do something wrong, but I haven't understood what yet. Current SIS
implementation throws {{IllegalStateException}} in such case.




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