Changes between Version 4 and Version 5 of Ticket #12427, comment 27


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Timestamp:
2016-01-26T11:55:01+01:00 (10 years ago)
Author:
cmuelle8

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  • Ticket #12427, comment 27

    v4 v5  
    99
    1010The intersection of the planes with the ellipsoid yield a maximum of three different arcs.
    11  If the arcs obtained by intersecting the last two planes are unequal, I suggest these to be the true shortest arcs.
     11 If the arcs obtained by intersecting the last two planes are unequal, I suggest these to "enclose" the geodesic.
    1212
    1313 If the normals ''do'' intersect, and {{{IP}}} is ''neither in'' equatorial plane ''nor on'' polar axis, all three arcs will be equal ''and'' be the true shortest arc between the points. The same applies if {{{IP}}} lies ''uncentered'' in equatorial plane, but at least one of the normals lies not.
    1414 (The great ellipse through the points coincides with the rotated ellipse defining the ellipsoid in these cases.)
    1515
    16  If both normals lie in equatorial plane, {{{IP}}} coincides with the center of the ellipsoid. Other two points, displaced from the center along the polar axis in proportion to the eccentricity need to define planes ''P2'', ''P3'' in this case. The surface normals are not helpful to find the true shortest arcs left and right to equator in this case. Similar applies if {{{IP}}} lies ''on'' polar axis.
     16 If both normals lie in equatorial plane, {{{IP}}} coincides with the center of the ellipsoid. Other two points, displaced from the center along the polar axis in proportion to the eccentricity need to define planes ''P2'', ''P3'' in this case. There will be two geodesics and two true shortest arcs left and right to equator in this case. Similar applies if {{{IP}}} lies ''on'' polar axis.
    1717
    1818Put unspecific, first is the general case, second for points with no difference in longitude and third for those with no difference in latitude.