Circle to Polygon to Sphere

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I'm going to map some triangles from a circular world map to a spherical one, where longitude is angle around the pie and latitude is distance from the center. Vastly distorted at the edges, but I can see everything. I'm going to wrap the world div polygon shape around the outside of my triangle mesh. I can get a circumference, diameter and radius and size the world div based on rounding up radius.

The world sphere is 11096.66 km across, 5548.33 km in radius, 336 pixels across, 386.84 m. km^2