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Projections & Limitations

The Map Projection
The map on the screen uses the Web Mercator projection. While this projection maintains angles for navigation, it distorts scale near the poles, making regions like Greenland and Alaska appear larger than they are. Calculating the center based on these 2D screen coordinates would produce incorrect results.

Spherical Calculations
To prevent projection errors, calculations ignore the flat map. Instead, D3.js maps the country's coordinates onto a 3D sphere. This model is used to calculate the center of mass and handles countries that cross the 180° antimeridian line.

The Inscribed Circle Solution
Finding the deepest inland point (the pole of inaccessibility) requires casting a 2D grid over a shape. When a country crosses the 180° antimeridian, a standard 2D calculation treats its eastern and western territories as if they are separated by the width of the planet.

To resolve this, the system normalizes the longitudes of the country's geometry, shifting the coordinates to create a continuous shape. This allows the inscribed circle algorithm to calculate across the antimeridian and locate the pole of inaccessibility before the coordinates are mapped back to their geographic locations.