Changes between Version 2 and Version 3 of Ticket #12427, comment 36


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Timestamp:
2016-01-28T10:43:45+01:00 (10 years ago)
Author:
cmuelle8

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  • Ticket #12427, comment 36

    v2 v3  
    66 If a and b are moved ever closer together on equator, there must be a time when the shortest geodesic north, the one south and equator ''all'' have ''minimum curvature'' (wrt to the bi-gon surface), and hence the same length. Beyond this step the area grows in size and hence is not of interest anymore. It's like climbing a hill, once you reach a certain height, it's shorter crossing the top to descend to the same height you would otherwise reach on equidistant paths around it.
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    8  However, figure 15 in the wiki article I think to be incorrect. Imo the cut locus should be an ''area'' (the figure shows it as a red line). It should be more like a bi-gon. You can combine two arbitrary geodesics chosen from disjunct hemiellipsoids (as defined by that red line), i.e. shorten a longer geodesic on one hemiellipsoid H1 and lengthen a geodesic of the other hemiellipsoid by the same amount into H1. It seems as if the author of this figure was focused on specific pairs only.
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    108> I don't get what you mean by maximum curvature. The curvature is different at each point along the curve. You could take some kind of average along the line, but then it is far from obvious why this would give great ellipses.
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