Four Projections of an Ultra-wide Image
St. Francis de Sales Church, Philadelphia, 120 x 90 degrees.  Photo by T K Sharpless, processed with Hugin.  Click images for larger views.

An 11mm ultra-wide angle lens on a 35mm camera would give a picture like the rectilinear view at upper left.  It is easy to see the distortion near the edges, if you compare it to the cylindrical view (lower left) which shows things at their natural angular widths.   The Pannini view (lower right) seems to blend the rectilinear and cylindrical projections. The edges are less stretched than in the rectilinear view; the bowing of horizontal lines is less than in the cylindrical view, though still objectionable to many eyes (van Gogh, however, might have drawn it just this way).  The Panini-General projection can straighten the horizontals, giving the image at upper right.  It covers the same angles as the rectilinear image, but looks as if it had been made with a longer focal length lens.  However, no real lens could have taken that picture.