Stereographic Projections
A stereographic projection is a projection of the sphere onto an infinite plane. It has a whole range of nice properties, that makes it ideal to present equirectangular panoramas:
* it is conformal: all angles are conserved so (local) shapes are preserved.
* it is azimuthal: the direction from the center of the projection is the true one. This property also holds for the simple "polar panoramas" you can do with photoshop.
* it maps the whole sphere minus one point, so you can show as much detail as you want
* it is very easy to create: all you need is hugin and an equirectangular panorama.

Here is what the steps look like: 1 2 3
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