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https://issues.apache.org/jira/browse/LUCENE-8136?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16338256#comment-16338256
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Karl Wright commented on LUCENE-8136:
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I'm still pressed for time, BUT it occurs to me that the code is computing a
normal vector given three points: the origin, and two other given points. The
problems arise when the two other points are very close together. This causes
numerical instability because the two sides we are working with are so much
larger than the differences between them.
However, we can recenter the entire problem to one of the other two points when
that happens, and then the problem should be more numerically stable. The
trick is to know when to do that. I'll do some experiments to see if I can
come up with some code that works better for this case.
> Planes constructed with two points are wrong when points are close
> ------------------------------------------------------------------
>
> Key: LUCENE-8136
> URL: https://issues.apache.org/jira/browse/LUCENE-8136
> Project: Lucene - Core
> Issue Type: Bug
> Components: modules/spatial3d
> Reporter: Ignacio Vera
> Assignee: Karl Wright
> Priority: Major
> Attachments: LUCENE-8136-RandomTest.patch,
> LUCENE-8136-RandomTest.patch
>
>
> Whenever a plane is constructed with two points (and the center of the
> planet), and those points are close to each other,it might happen that the
> final plane does not contain all points used for the construction. The issue
> seems to happen when the resulting magnitude of the normal vector of the new
> plane (calculated using cross product) is lower that 1e-5.
> This is a follow up of issue LUCENE-8133.
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