Affects Version/s: None
Fix Version/s: None
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.