Hello!

I'm interested in using PostGIS's support for trajectories to solve a problem 
I'm working on. I have a collection of 3D spatiotemporal trajectories 
(representing spacecraft orbits) that I'm needing to query for any close 
approaches among any pair of trajectories.  For my problem, a close approach 
occurs when the distance between two trajectories at the same time/measure 
falls below a threshold; a close approach can occur multiple times between a 
pair of trajectories. Naively, the problem can be solved by calculating 
pairwise distances for each epoch, resulting in ~ n^2/2*t distance calculations 
(where t is the number of timesteps), but I'm trying to avoid the n-squared 
problem. 

I started reading through the docs and was attracted to 
ST_ClosestPointOfApproach, however I'm interested in more than just the point 
of minimum distance between the trajectories -- it would be ideal to have 
multiple closest points of approach.

Is it possible to use PostGIS to perform this type of query?

On a related note, is it possible to index trajectory geometries such that a 
Cartesian product can be avoided when querying for close approaches between any 
pairs of trajectories?

Thanks for any insight you can share!

Cheers!
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