Poles of Inaccessibility in the San Gabriel Mountains

The author took on the challenge of finding the 'Pole of Inaccessibility' in the San Gabriel Mountains, defining it as the spot furthest from any road or trail. This endeavor is a prime example of applying computational geometry and open-source tools to solve a specific, real-world geographic puzzle.

• The approach begins by importing road and trail data from OpenStreetMap, which is then projected onto a locally flat tangent plane for simplified 2D geometric processing.
• A key component of the methodology is the construction of a Voronoi diagram, where the Pole of Inaccessibility is identified as the Voronoi vertex that maximizes the distance to its nearest input point (road/trail).
• The implementation is modular, featuring separate scripts for querying OSM data, massaging it into suitable planar coordinates with sufficient density, and then performing the core Voronoi calculation using the boost::polygon library.
• The final computed planar coordinates are then converted back into human-readable latitude and longitude.
• The author conducted analyses for three distinct definitions of 'accessibility': avoiding all roads and trails, avoiding roads only, and avoiding only paved, drivable roads.

Ultimately, the analysis successfully located the various poles of inaccessibility, all situated above the East Fork of the San Gabriel River near Ross Mountain and Iron Mountain, with the most remote point being over 8 kilometers from the nearest paved road. This project showcases an elegant solution to a niche problem, employing robust technical methods.