The cylindrical perspective is also known as "panorama view". It is applied in situations, where the image needs to show information about a wide range of horizontal angles, ultimately over the full circle. A typical application is for use in QuickTime animations or similar presentation formats.
A cylindrical perspective is a combination of a normal perspective in vertical direction, with an angular fisheye in horizontal direction. The consequence of this approach is, that the image can show a wide range of horizontal angles, while still avoiding the image distortion that most other projectiosn would exhibit in that case. The vertical angles are of course still bound to the limitations of a normal perspective.
The maximum horizontal opening angle is 360 degrees, the maximum vertical angle is less than 180 degrees. Note that due to the special geometry, neither the specification of a diagonal angle, nor of the focal length for this projection would make much sense.
One of the most interesting properties of this projection is the fact that vertical lines in the scene (more precisely: lines that are parallel to the axis of it's virtual cylinder) will always be vertical in the image.
The diagram below illustrates the three dimensional properties of a cylindrical perspective.
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Hemishpherical Fisheye 