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https://issues.apache.org/jira/browse/LUCENE-8066?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16265823#comment-16265823
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Ignacio Vera commented on LUCENE-8066:
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Yes, the circle is divided into sectors and therefore there is no dependency
between the concavity/convexity of the circle planes. I agree we should add a
check to make sure the center of the circle is WITHIN the circle plane. Luckily
it seems it is always true for WSG84.
Just for the record, I haven seen test failing when the circle is close to
Math.PI (I think the limit for WSG84 is 0.9995 * Math.PI) but I think that is
because Vincenty's formula does not converge close to antipodals points. We
might need to do something in that case and it probably depends on the planet
model.
Thanks!
> Another approach to Exact circle
> --------------------------------
>
> Key: LUCENE-8066
> URL: https://issues.apache.org/jira/browse/LUCENE-8066
> Project: Lucene - Core
> Issue Type: Improvement
> Reporter: Ignacio Vera
> Assignee: Karl Wright
> Fix For: 6.7, master (8.0), 7.2
>
> Attachments: LUCENE-8066.patch
>
>
> Hi [~daddywri],
> I was thinking in the limitation of convexity for circle planes and I worked
> out another approach that overcome this limitation. There is a condition,
> circle lanes must contain the center of the circle which is probably always
> true for planets like WGS84 which are not too far from the sphere.
> The idea is create a short of polygon for every slice using the center of the
> circle (like an orange) and therefore you can treat them separately. I
> attached what I developed, it seems to pass all tests regardless of the
> radius.
> Let me know what you think and if I am missing something.
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