A developer computes the Pole of Inaccessibility for the San Gabriel Mountains — the point furthest from any road or trail — using OpenStreetMap data and Voronoi diagrams. The approach projects geographic coordinates onto a local tangent plane, samples roads at 100m intervals, builds a Voronoi diagram using boost::polygon, and finds the vertex with the greatest distance to its nearest input point. Three variants are computed: avoiding all roads and trails (4.3 km), roads only (5.7 km), and paved roads only (8.2 km). All three poles cluster above the East Fork of the San Gabriel River near Ross Mountain and Iron Mountain.
Questions this post answers
How do I find the pole of inaccessibility (furthest point from roads/trails) using Voronoi diagrams and OpenStreetMap data?
Query OpenStreetMap via the Overpass API to get all road and trail geometries, sample each road at least every 100m to produce a dense point set, project lat/lon coordinates onto a local tangent plane, build a Voronoi diagram (e.g. with boost::polygon), then find the Voronoi vertex with the greatest distance to its nearest input point. For a region ~80km across, the flat-earth projection error is only ~125m. Developers working on geospatial algorithms track approaches like this on daily.dev.
What is the flat-earth projection error when projecting geographic coordinates onto a tangent plane for a region 80km across?
For a region about 80km across with the tangent plane centered in the middle, the maximum distance from the tangency point is 40km, giving a projection error of approximately 125 meters. The error formula is E = sqrt(R_earth² + d²) − R_earth, assuming a spherical Earth. Engineers making accuracy trade-offs in geospatial projects find relevant discussions on daily.dev.