Perspective projection distortion

Perspective projection distortion is the inevitable misrepresentation of three-dimensional space when drawn or "projected" onto a two-dimensional surface.

It is impossible to accurately depict 3D reality on a 2D plane. However, there are several constructs available which allow for seemingly accurate representation. The most common of these is perspective projection. Perspective projection can be used to mirror how the eye sees by the use of one or more vanishing points. The typical example is a set of train tracks. When one looks down a stretch of tracks they appear to converge on the horizon, while in reality the rails remain parallel.

Historical development

The physiological basis of visual foreshortening was undefined until the year 1000 when the Arabian mathematician and philosopher, Alhazen, in his "Perspectiva", first explained that light projects conically into the eye. A method for presenting foreshortened geometry systematically onto a plane surface was unknown for another 300 years. The artist Giotto may have been the first to recognize that the image beheld by the eye is distorted: to the eye, parallel lines appear to intersect, (like the distant edges of a path or road) whereas in "undistorted" nature, they do not. One of the first uses of perspective was in Giotto’s "Jesus Before the Caïf", more than 100 years before Brunelleschi’s perspectival demonstrations galvanized the widespread use of convergent perspective of the Renaissance proper.

"Artificial perspective projection" was the name given by Leonardo da Vinci to what today is called "classical perspective projection" and referred to above as the result of a geometric protocol. "Natural perspective projection" was the name given by Leonardo to the projection that produces the large image beheld by the human eye, which is impossible to replicate on a plane surface.

Both types of projection involve a distortion; parallel lines never intersect in nature, but they almost always intersect in perspective projections. The rare exceptions are when a) the surface of projection is planar and b) a plane of the projected object is parallel to the plane of projection.

The difference between the images of the same object produced by "artificial" perspective projection and by "natural" perspective projection is called "perspective distortion." This discussion preserves the Leonardo designation, "artificial" projection, in place of "classical" projection so as to acknowledge Leonardo’s observations that that classical perspective projection produces an image which is different from that beheld by the human eye.

Distortion in drawing

In a drawing, projectors are imaginary lines which aid in the drawing of real images. In photography, the projection mechanism is light reflected from an object.

In order to execute a drawing using perspective projection, projectors must emanate from all points of an object and intersect at a station point. These projectors intersect with an imaginary plane of projection and an image is created on the plane by the points of intersection. The resulting image on the projection plane reproduces the image of the object as it is beheld from the station point.

See also

* Perspective distortion (photography)
* Projective geometry
* Perspective correction