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https://issues.apache.org/jira/browse/LUCENE-6196?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14292567#comment-14292567
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Karl Wright commented on LUCENE-6196:
-------------------------------------
The full point formulas for (x,y,z) for min/max z are as follows:
{code}
z = DC +/- sqrt(D^2*C^2 + 1 - C^2 - D^2)
y = -B[D+Cz] / [A^2 + B^2]
x = -A[D+Cz] / [A^2 + B^2]
{code}
For rectangles, and any shape that uses only planes going through the origin,
this is all that I need. But for shapes using other planes, I need a similar
formula for min/max longitude. Working on that now.
> Include geo3d package, along with Lucene integration to make it useful
> ----------------------------------------------------------------------
>
> Key: LUCENE-6196
> URL: https://issues.apache.org/jira/browse/LUCENE-6196
> Project: Lucene - Core
> Issue Type: New Feature
> Components: modules/spatial
> Reporter: Karl Wright
> Assignee: David Smiley
> Attachments: ShapeImpl.java, geo3d.zip
>
>
> I would like to explore contributing a geo3d package to Lucene. This can be
> used in conjunction with Lucene search, both for generating geohashes (via
> spatial4j) for complex geographic shapes, as well as limiting results
> resulting from those queries to those results within the exact shape in
> highly performant ways.
> The package uses 3d planar geometry to do its magic, which basically limits
> computation necessary to determine membership (once a shape has been
> initialized, of course) to only multiplications and additions, which makes it
> feasible to construct a performant BoostSource-based filter for geographic
> shapes. The math is somewhat more involved when generating geohashes, but is
> still more than fast enough to do a good job.
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