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https://issues.apache.org/jira/browse/LUCENE-7663?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15843639#comment-15843639
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Michael McCandless commented on LUCENE-7663:
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bq. This approach can also be used to priorize rectangles, for top-k search.
Oh we also have a nearest neighbor implementation for points:
{{LatLonPoint.nearest}}. Seems like these papers could help that too?
> Improve GeoPointDistanceQuery performance
> -----------------------------------------
>
> Key: LUCENE-7663
> URL: https://issues.apache.org/jira/browse/LUCENE-7663
> Project: Lucene - Core
> Issue Type: Improvement
> Reporter: Erich Schubert
> Priority: Minor
>
> GeoPoint queries currently use only the bounding box for filtering.
> But the query circle is only roughly 80% of the bounding box, so we could be
> roughly 20% faster. Furthermore, the current approach requires splitting the
> box if it crosses the date line.
> > Schubert, E., Zimek, A., & Kriegel, H. P. (2013, August). Geodetic distance
> > queries on r-trees for indexing geographic data. In International Symposium
> > on Spatial and Temporal Databases (pp. 146-164).
> The minimum spherical distance of a point to a rectangle is given ("Algorithm
> 2: Optimized Minimum Distance Point to MBR"). Rectangles whose minimum
> distance is larger than the query radius can be skipped. The authors used the
> R-tree, but it will work with any bounding box, so it can be used in
> CellComparator#relate.
> It's not very complex - a few case distinctions, and then either Haversine
> distance, or cross-track-distance. So the cost ist comparable to Haversine.
> This could be added as GeoRelationUtils.pointToRectMinimumDistance, for
> example.
> This approach can also be used to priorize rectangles, for top-k search.
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