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I'm looking for a solution to snap my GPX tracks to OSM roads. Mapbox Map Matching API actually does this, but sometimes snaps to wrong roads. In this wrong case I want manually edit snapped track by dragging its vertices. When dragging vertices they should be snapped to OSM roads as well.

what could be good solution to implement this kind of task?

I do not want to download and store OSM data locally. If it is possible also not to use routing engines.

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I am not sure whether the following is more to your aim besides the mapbox solution, but you can have a closer look at the OSM based map matching feature of Graphhopper,

See this blog posting, or the sourcecode at github.

Also in the graphhopper user forum there is a sub section about map matching, so you can search or ask there.

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