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Related to this issue: meilisearch/meilisearch#1872
Fix the whole computation of distance for any “geo” operations (sort or filter). Now when you sort points they are returned to you in the right order.
And when you filter on a specific radius you only get points included in the radius.
This PR changes the way we store the geo points in the RTree.
Instead of considering the latitude and longitude as orthogonal coordinates, we convert them to real orthogonal coordinates projected on a sphere with a radius of 1.
This is the conversion formulae.
Which, in rust, translate to this function:
Storing the points on a sphere is easier / faster to compute than storing the point on an approximation of the real earth shape.
But when we need to compute the distance between two points we still need to use the haversine distance which works with latitude and longitude.
So, to do the fewest search-time computation possible I'm now associating every point with its
DocId
and its lat/lng.