Fish-eye and Curvilinear Perspective

Fish-eye lenses are used in photography to capture angles larger than the normal field of view of cameras. This means that the lens captures more of a scene than a standard lens, at the expense of some distortion. Examples where this can be useful are security cameras and "peep-holes" outwards on doors.

The fish-eye lens causes barrel distortion. This means that objects far from the centre of the lens becomes mapped into a smaller surface than those at the centre, thus giving rise to a spherical appearance.

A similar effect is explained more formally by curvilinear or 5-point perspective. It was discovered as early as the Renaissance and has even been suggested as an alternative (and perhaps more accurate) way of representing the way our eye sees the 3D world. A simple demonstration is given by Scott McDaniel in his explanation of 5-point perspective.




One of the arguments for the use of curvilinear over linear perspective draws from the observation that objects which are farther away laterally in our field of view will look smaller and smaller. Imagine a box in the middle of your field of view. Now imagine that box being moved farther and farther towards the right edge of your vision. Objects farther away look smaller, thus lending strength to the argument of curvilinear perspective.
However, this argument breaks down if considering that our field of view is relatively limited for any fixed point of view. The objects which would supposedly look smaller towards the periphery would not be captured by our visual field, or at least not in any clarity.

While it's true that curvilinear perspective is able to squeeze in more information about a scene into any single drawing than normal linear perspective, thus giving the viewer a feeling of "being there", Bruce MacEvoy explains that this is due to the combination of multiple viewpoints. I.e. as if your eyes or head was moving and taking in more information about the scene than any one viewpoint could give. According to MacEvoy, a single viewpoint is best represented using linear perspective. The curvilinear perspective can be viewed as originating from superimpositions of multiple viewpoints.


More information about curvilinear perspective by Bruce MacEvoy.
MacEvoy has a very informative site on Elements of Perspective. The Perspective in the World-section explains what perspective really is and is well worth reading for a more in-depth understanding.