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Hi im using openstreetmap online api for getting the id from latitude an longitude(then i use this id to get the max speed limit of that road). now im using OsmSharp to do this job offline. in the first step how can i get the id from latitude and longitude ?

Elements are not indexed by their location so there is no built-in efficient way to retrieve them that way. You could either build your own collection using lat/lon as the key or enumerate every element and compare it's location to your target location.

Looking for elements by proximity was something I did a lot and needed to be efficient. My approach was to create two duplicate lists of elements, one sorted by lat and the other by lon. Each lookup-by-location was done by intersecting a range of candidates from the two collections.

The locations of a node is simple, the "location" of a way or relation takes a little math.

An example: https://github.com/blackboxlogic/OsmPipeline/blob/b93e9ecd7d5487d7c6879cac4144ab82a15f3f19/Fittings/Geometry.cs#L350

@blackboxlogic thanks for the idea, this's what I need