[postgis-tickets] [PostGIS] #2913: ST_Azimuth and ST_Distance on geography antipodes or near-antipodes

[PostGIS]

#2913: ST_Azimuth and ST_Distance on geography antipodes or near-antipodes
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 Reporter:  mwtoews  |       Owner:  pramsey
     Type:  defect   |      Status:  new    
 Priority:  medium   |   Milestone:         
Component:  postgis  |     Version:  2.1.x  
 Keywords:           |  
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Comment(by mwtoews):

 Ok, I think I've unearthed the substance of this ticket. From (Vincenty
 1975a):
 > The inverse formulae may give no solution over a line between two nearly
 antipodal points. This will occur when λ is greater than π in absolute
 value.

 And similar, from Karney (2013):
 > Vincenty’s method fails to converge for nearly antipodal points.

 Furthermore:
 > Vincenty (1975a), who uses the iterative method of Helmert (1880, §5.13)
 to solve the inverse problem, was aware of its failure to converge for
 nearly antipodal points. In an unpublished report
 ([http://geographiclib.sourceforge.net/geodesic-papers/vincenty75b.pdf
 Vincenty 1975b]), he gives a modification of his method which deals with
 this case. Unfortunately, this sometimes requires many thousands of
 iterations to converge, whereas Newton’s method as described here only
 requires a few iterations.

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Ticket URL: <http://trac.osgeo.org/postgis/ticket/2913#comment:4>
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