Changes between Initial Version and Version 1 of Ticket #12427, comment 26
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- 2016-01-26T12:47:38+01:00 (10 years ago)
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Ticket #12427, comment 26
initial v1 3 3 > No, for example for two points on the equator, the shortest path is ''not'' to run along the equator! Due to the flattening of the earth, you can take a shortcut by making a slight curve towards one of the poles. :) 4 4 5 This is correct, but not fully relevant to our use case: You will always find two ''shorter arcs'' on the ellipsoid for ''any'' arc segment of a ''great ellipse'' through ''arbitrary but disjunct'' points {{{a}}} and {{{b}}}, unless that ''great ellipse'' matches one of the ''rotated ellipse'' instances (that define the ellipsoid of revolution).5 This is correct, but not fully relevant to our use case: You will find two disjunct geodesics on the ellipsoid for ''any'' arc segment of a ''great ellipse'' through points {{{a}}} and {{{b}}}, not only if they both lie on equator, but also if they are equally displaced for instance. 6 6 7 We do ''not'' define an osm way between {{{a}}} and {{{b}}} by the possibly two shortest arcs between them, but by a ''single arc''. That single arc is defined by the ''shortest path'' on the ''great ellipse'', not by any of the two true shortest arcs.Only for some subset of {{{a}}} and {{{b}}} the different arcs coincide.7 However, we do ''not'' define an osm way between {{{a}}} and {{{b}}} by the possibly two shortest arcs between them, but by a ''single arc''. That single arc is defined by the ''shortest path'' on the ''great ellipse'', not by any of the possibly two true shortest arcs. For some subset of {{{a}}} and {{{b}}} the different arcs coincide. 8 8 9 9 So, for your example, with respect to our application we measure a distance for, it would be wrong to associate the true shortest distance between {{{a}}} and {{{b}}} on ground with the distances of the ways drawn between {{{a}}} and {{{b}}} in JOSM. We indeed need to run along the equator to measure a meaningful distance of the line shown, defining a ''single arc'' on ground only. 10 11 {{{a}}} and {{{b}}} are associated a single "great ellipse" in ''any'' case, but the geodesic is not disamiguous for all cases.
