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.

What perspective?

If you've ever tried to draw a very wide-angle shot in linear one-point perspective, you would notice how objects further away from the central vertical axis will look increasingly distorted. This is an effect which has caused great puzzlement to perspective beginners, such as myself.


This grid illustrates the wide-angle distorted effect in one-point perspective. The squares closer to the centre look perfectly in perspective, but the squares at the very end look strangely stretched.

Art classes, and even most perspective tutorials often seem to address the Hows of perspective-drawing, but rarely the When and Why.
As it turns out, the perspective you should use (most commonly one-, two-, three-point) depends entirely lot on what you're trying to draw and the viewpoint you're viewing the scene from.
For example, if you're viewing a house from quite a close distance and only seeing two corners of the house, the situation calls for one-point perspective.

On the other hand, if you stand back and view three corners of the house simultaneously, two-point perspective might be more appropriate.


If the vanishing points are placed too close to each other in two-point perspective a distortion effect will become apparent. Just as in the case of the breakdown of one-point perspective in wide-angle shots, two-point perspective is also situation-based.
In theory, the two vanishing points symbolizes the extreme peripheral limit of the field of view of our eye. An object which is very "large" in relation to the spacing of the vanishing points would mean that we are viewing the object from very up close. When we get too close to an object it will fill our entire field of view so that we can no longer see the it in it's entirety. I believe that's why a large object will appear distorted if it is "squeezed" into the field of view.

In the first wide-angle example, what would seem like a simple case of one-point perspective might actually be better represented using 5-point, or curvilinear perspective.


Tomorrow: Fish-eye view & Curvilinear perspective