The simplest approach is to check every single point. Compute the distance from the user's location to every restaurant in the database, keep the ones that are close enough, and throw away the rest.
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Crucially, this distribution of border points is agnostic of routing speed profiles. It’s based only on whether a road is passable or not. This means the same set of clusters and border points can be used for all car routing profiles (default, shortest, fuel-efficient) and all bicycle profiles (default, prefer flat terrain, etc.). Only the travel time/cost values of the shortcuts between these points change based on the profile. This is a massive factor in keeping storage down – map data only increased by about 0.5% per profile to store this HH-Routing structure!