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https://issues.apache.org/jira/browse/LUCENE-7970?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16178096#comment-16178096
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Karl Wright commented on LUCENE-7970:
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Hi [~ivera], I think I have a solution.
Basically, all we need to do is find a set of planes which, together, describe
the actual circle to within MINIMUM_RESOLUTION. And this is
straightforward, because we can use a "divide and conquer" approach, where we
start with a small number of planes (2), and then
divide each plane into two if it turns out that a single plane has too great a
degree of error.
I haven't yet coded this but I suspect this will yield a small number of planes
for common planetoids like WGS84. Stay tuned.
> 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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