Introducing mercator projection

Article by Norbert Pachner (mathematics) and Wolfgang Stich (sample pictures).

For printing and viewing, almost all panorama stitching software provides as projection types for the stitching result 'cylindrical' and 'equirectangular' (or 'spherical'). When the VFOV (vertical field of view) of the result image is high (about more than 100°), the distortion becomes remarkable. High buildings e.g. look too stretched in cylindrical projection and too compressed in spherical projection.
Here an example with a VFOV of 150° (±75°):

equirectangular projection
equirectangular
the buildings look compressed 		cylindrical projection
cylindrical
the buildings look stretched

It seems, that a projection method between 'equirectangular' and 'cylindrical' would look better. And there indeed a projection method exists: the Mercator projection.
Unfortunally, no panorama software I know can calculate its output in Mercator projection.

Norbert Pachner now found a facility to convert cylindrical projection into Mercator projection by using the Panorama Tools Photoshop Plugin.
Below see the result:
Mercator projection
Mercator projection
the buildings look good, but the foreground is too big 		Mercator projection above the horizon line, equirectangular below the horizon
Mercator + equirectangular
buildings and foreground look good

... Hier die Verfahrensbeschreibung einfügen ...

Some other examples:

This example is a single fisheye foto, VFOV is 140° (±70°)
equirectangular projection
equirectangular
the tower looks too short 		cylindrical projection
cylindrical
the tower looks too long
Mercator projection
Mercator
the tower looks good



Even the extreme VFOV of 170° (±85°) can lead to acceptable results:

Mercator projection above the horizon line, equirectangular below
Mercator+equirectangular
the angels on the ceiling show good! 		equirectangular projection
equirectangular
cylindrical projection
cylindrica