Changes between Initial Version and Version 1 of Ticket #12427, comment 20


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Timestamp:
2016-01-25T07:43:19+01:00 (10 years ago)
Author:
cmuelle8

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  • Ticket #12427, comment 20

    initial v1  
    22
    33* in 3D space there exist planes intersecting both points (a) and (b) on the ellipsoid's surface
    4 * adding a third point (c), let it be the center of the ellipsoid, a definite plane out of the former is picked
     4* using a third point (c), let it be the center of the ellipsoid, a definite ''plane P'' out of the former is chosen
    55
    6 * all of the following are guaranteed to lie in that same plane
     6* all of the following are guaranteed to lie in ''plane P''
    77 * a non-spherical, possibly [https://en.wikipedia.org/wiki/Isosceles_triangle non-isosceles] triangle given by (a), (b), (c)
    88 * a "great ellipse" for (a) and (b) which we do not know an [https://en.wikipedia.org/wiki/Eccentricity_(mathematics) eccentricity] for
    … …  
    1212* eccentricity and circumference of the "[https://en.wikipedia.org/wiki/Great_ellipse great ellipse]" are a function of (a) and (b) and thus varying
    1313
    14 For the recursion of {{{curvatureDistance}}} to work flawlessly, the partial sums must calculate lengths of
    15 "great ellipse"-segments which '' lie in that same plane''. But actual ratio of partial lengths is ''not'' important.
     14For the recursion of {{{curvatureDistance}}} to work flawlessly, partial sums must calculate lengths of
     15"great ellipse"-segments which lie in ''plane P''. But actual ratio of partial lengths is ''not'' important.
    1616
    1717A bisecting ray {{{br}}} from (c) intersecting the chord ''will'' also intersect the "great ellipse".
    … …  
    2323Let the recursion step be {{{return thres > ret ? ret : r(a, m, ret)+r(m, b, ret);}}},
    2424then a ray that strictly intersects at the middle is not needed. Using {{{br}}} to simply find a
    25 "middle" point ''guaranteed'' to lie on the "greate ellipse" will suffice. Any split ratio will do.
     25point ''guaranteed'' to lie on the "greate ellipse" will suffice. Any split ratio will do.
    2626
    2727{{{thres}}} is not {{{eps}}} - it needs to be chosen in a different way, reasonably large,
    28 acknowledging that below a certain threshold distance, ''all'' true distances of arbitrarily
    29 chosen (a) and (b) do not differ from the threshold more than {{{eps}}}.
     28acknowledging that for results below a certain threshold distance, ''all'' true distances
     29of arbitrarily chosen (a) and (b) do not differ from {{{thres}}} distance more than {{{eps}}}.