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https://issues.apache.org/jira/browse/LUCENE-7970?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16174442#comment-16174442
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Ignacio Vera edited comment on LUCENE-7970 at 9/21/17 1:02 PM:
---------------------------------------------------------------
Hi [~karl wright],
Not sure if we have something to do here as I think current implementation
might be the best one to approximate the circle using one plane intersecting
the spheroid. I don't think I can assure that any other implementation would be
more precise.
Anyway, I was thinking what is needed to support circles in a spheroid and of
course it needs a totally different approach and eventually in some cases you
need to use brute force. I want to share what I think it would be a viable
solution if Geo3d ever needs to add precision to circles in spheriods like
WGS84:
The new shape should have two planes:
innerEllipse: plane cutting the spheriod producing the maximum ellipse
within the circle. Anything within this plane is within the circle.
outerEllipse: plane cutting the spheriod producing the minimum ellipse
contaning the circle. Anything not within this plane is not within the circle.
There is only one gray area between the two planes (within outerEllipse, not
within innerEllipse) where brute force will be needed.
I attach my implementation for such a shape. It seems to work for WGS84, except
for verly large and very small angles. I was unable to find the mathematical
model to generate those planes (is that possible to solve mathematically?).
Thanks!
was (Author: ivera):
Hi [~karl wright],
Not sure if we have something to do here as I think current implementation
might be the best one to approximate the circle using one plane intersecting
the spheroid. I don't think I can assure that any other implementation would be
more precise.
Anyway, I was thinking what is needed to support circles in a spheroid and of
course it needs a totally different approach and eventually in some cases you
need to use brute force. I want to share what I think it would be a viable
solution if Geo3d ever needs to add precision to circles in spheriods like
WGS84:
The new shape should have two planes:
innerElipse: plane cutting the spheriod producing the maximum ellipse
within the circle. Anything within this plane is within the circle.
outerElipse: plane cutting the spheriod producing the maximum ellipse
contaning the circle. Anything not within this plane is not within the circle.
There is only one gray area between the two planes (within outerEllipse, not
within innerEllipse) where brute force will be needed.
I attach my implementation for such a shape. It seems to work for WGS84, except
for verly large and very small angles. I was unable to find the mathematical
model to generate those planes (is that possible to solve mathematically?).
Thanks!
> Improve generation of circle plane
> -----------------------------------
>
> 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
>
>
> 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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