Hilbert R-tree for spatial Index

[Vedic Chawla]

Hi PostGIS community,

I was doing a feasibility study/survey for optimal Geospatial Index when I
came across this concept.

Currently, POSTGIS uses R-tree on top of GiST to implement Geospatial
Index. and there has been this GSOC Task[1] to implement Z sort to make
this indexing faster, This should also have the effect of Increasing MSU,
and making query faster as this would benefit from the same concept as
Packed Hilbert R tree[2] used by FlatGeoBuf[3]. I would suggest that we use
Hilbert ordering instead of Z sort, as PostGIS has since switched its sort
to Hilbert and it is also used by flatgeobuf.
We can probably do both too.

Extending upon that we can also implement Dynamic Hilbert R-Tree[4] if we
store Largest Hilbert Value for each of the Nodes.

I would love to know your views on this!
Regards
Vedic

[1] : https://trac.osgeo.org/postgis/wiki/GoogleSummerCode2021
[2] : https://en.wikipedia.org/wiki/Hilbert_R-tree#Packed_Hilbert_R-trees
[3] : https://github.com/flatgeobuf/flatgeobuf?tab=readme-ov-file
[4] : https://en.wikipedia.org/wiki/Hilbert_R-tree#Dynamic_Hilbert_R-trees
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