How it works
No light, cone or cylinder makes Mollweide's map, or Robinson's, or Equal Earth. They are
formulas for the whole sphere at once, and every one of them has to cut the globe somewhere
to lay it flat. The plain ones cut once, along the seam opposite the central meridian.
Unfold rolls the globe out into the map, and the seam opens at the back.
Goode's answer, in 1923, was to cut more. Each lobe of his homolosine gets its own central
meridian, so shapes near the middle of each lobe stay good, and the cuts go through the
oceans (or, for an ocean map, through the land). Interrupt slides every lobe's central
meridian from the map's own to the lobe's: at the left end it is one unbroken map with the
cuts drawn on it, at the right end the lobes have opened and straightened.
Gores take it to the limit: many narrow sinusoidal lobes, as on the paper strips glued
onto a globe. The octahedral butterfly is Cahill's 1909 map: the globe is projected from its
centre onto the eight faces of an octahedron around it, and the faces are unfolded around the
North Pole. Unfold shows both steps: the globe falls onto the octahedron, then the faces
open flat.
Each formula follows PROJ's own code (moll, goode,
igh, igh_o, imoll, imoll_o and the rest,
and gnom for each butterfly face), checked against PROJ.