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https://issues.apache.org/jira/browse/LUCENE-7970?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16177378#comment-16177378
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Karl Wright commented on LUCENE-7970:
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I also had another look at the logic in the proposed "complex circle". The
real problem I see is the intersects() methods. The code in the patch does not
actually reliably determine intersection of a plane and an exact circle within
the specified bounds, and that's in fact rather hard. Computing the distance
from the plane to the center of the circle isn't going to work.
You could do this with a lagrangian multiplier, but the problem with that is
that the Vincenty formula is iterative and is thus not describable as a
differentiable function.
That means that instead of an analytic solution, an iterative numeric solution
will be needed that finds the intersection of the exact circle edge on the
surface of the ellipsoid with the given plane. Coming up with such a thing
will require a far more in-depth understanding of the Vincenty algorithm than I
have at this time. Maybe an idea will come to me but so far I am not so
inspired.
> Add a Geo3d shape that models an exact circle, even when the planet model is
> not a sphere
> -----------------------------------------------------------------------------------------
>
> Key: LUCENE-7970
> URL: https://issues.apache.org/jira/browse/LUCENE-7970
> Project: Lucene - Core
> Issue Type: Improvement
> Components: modules/spatial3d
> Reporter: Ignacio Vera
> Assignee: Karl Wright
> Attachments: LUCENE_7970.patch, LUCENE-7970.patch,
> LUCENE-7970-proposed.patch, LUCENE-7970_testBearingPoint.patch
>
>
> Hi [~Karl wright],
> How circles are currently build do not behave very well when the planet model
> is not an sphere. when you are close to the border in WGS84 you might get
> false positves or false negatives when checking if a point is WITHIN. I think
> the reason is how the points to generate the circle plane are generated which
> assumes a sphere.
> My proposal is the following:
> Add a new method to PlanetModel:
> public GeoPoint pointOnBearing(GeoPoint from, double dist, double bearing);
> Which uses and algorithm that takes into account that the planet might not be
> spherical. For example Vincenty's formulae
> (https://en.wikipedia.org/wiki/Vincenty%27s_formulae).
> Use this method to generate the points for the circle plane. My experiments
> shows that this approach removes false negatives in WGS84 meanwhile it works
> nicely in the Sphere.
> Does it make sense?
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