A quick, fast and dirty python script to generate rough isochrone lines using OSRM

Map example

The map used to produce this image can be found here on umap.

Description

For a given place p and duration d, we want to generate a line linking points that are at a travel time d from p using the road network.

• Put it simple: kind of like drawing "circles" on a map with travel time on roads replacing usual euclidean distance.

• Put it formally: we seek the convex envelope of the set S of points q such that d(p, q) <= d.

Quick?

The script was written in a few hours' time to produce a rough result on a bunch of cities so don't expect too much refinements here.

Fast?

Starting from p, we just look around in different directions. For each of them, we find a spot at distance d from p. This search is performed dichotomically with several OSRM requests so it's quite fast. Examples show in addition that it's not necessary to explore loads of directions to get a rough picture.

Dirty?

We just use a bunch of points around p on the map, whose relevance is determined by OSRM requests. The real thing would be to get into the graph structure of the road network and perform some kind of deep search.

Usage

The script handles list of durations and locations to generate a geojson file for each isochrone line. You need an up and running OSRM server at hand to handle the requests.

For example, to compute isochrone line at 20 and 40 minutes for Paris and Lyon, use:

python isochrone_line.py --duration 20 40 --loc 48.8565056,2.3521334 45.7575926,4.8323239

Limitations

• Using a few points around just gives an outline of the convex enveloppe of the above mentioned set S. But using more points doesn't necessarily provide more precision as it tends to emphasize local discontinuities. So in all cases, the obtained lines remains rough approximations.

• Moreover the set S of points q such that d(p, q) <= d is arc-connected but has no reason to be convex so looking for a single point in each direction is quite an approximation: for a given direction, there is actually no guarantee concerning the uniqueness of a point q such that d(p, q) = d.