Hi Karl Wright,
Current implementation of GeoExactCircle seems to work well for planet models with low flattening (~|0.025|). When flattening increase shapes start becoming invalid because of the cutting angle of the circle plane which results on the center of the circle ending up on the wrong side of the plane.
I propose a new version of GeoExactCircle that tries to overcome this problem by creating a new plane for a circle sector in such cases. The new plane is built built for each sector when needed by using two points from the circle edge and the center of the world. The plane is such that it is built as close as possible to the circle plane of the sector. Points from the circle plane must not be within the new plane and the center of the circle must be within the plane.
This approach seems to work well up to planets with flattening up to around ~|0.1|. I think after that the cutting angles of circle planes can be so thin that the apporach is not valid.
Therefore I propose to add this new approach and limit the creation of such circles to planet models with flattening lower than |0.1|. Probably a limitation that does not affect most of the realistic cases.
In addition this new version forces a minimum of 4 sectors in a circle. The issue on
LUCENE-8071 came up again for circles of any radius so we should enforce it for all circles.