THE PERSPECTIVES

Quick: how many perspective drawing systems are there? You might immediately answer “two…no wait, three.” Ching, for example, lists the one and two point system. If you get adventurous, you might go for a three point system.

Turns out that there are many alternate perspective systems. Below is a compendium with a brief description of each, if only to demonstrate that the potentials and possibilities exceed what we are spoon fed in Ching, Lauseau, etc. Most of these systems incorporate time. They are a solution for the blinder like limits of Representational Spacetime. Most strive for a holistic, 360 degree knowledge depiction. Many look like they were drawn by Byzantines. And they are all perspectives, with vanishing points!

Linear: typically termed the One Point perspective
-also termed Central Convergent Perspective by Fernando Casas
-also Frontal Perspective
-can also be a two point
-see Ching, et al.

4, 5 and 6 Point Perspective:
-requires curved lines to connect the vanishing points
-also called Curvilinear Perspective
-geometry related to the human visual field, which is curved
–Dick Termes uses a 6 point system for representations on spheres
-relates to Hyperbolic Projection

Fish Eye: Michael Moose
-commonly termed 5 point perspective

Byzantine Perspective (Also called Reverse Perspective)
-essentially inverts the foreground with the background
-see Goodman, p 15.
–Wikipedia entry with description

Flat Sphere Perspective: Fernando Casas
-see every direction at once
-spherical image surface is flattened onto finite plane
-contiguous projection of 360 degrees of vision

Tetraconic Perspective: Kenneth Adams (1)
-provides simultaneously a view of all that can be seen in all directions from a point in space
-a cubical room is assumed to be filled by an imaginary sphere, and the projection system builds from there
-each image below is a tetraconic perspective

Mercator Perspective: Emilio Frisia
-applies the rules of Mercator Mapping to a perspective projection system

Planisphere: Emilio Frisia
-similar to the Mercator Perspective
-holistic (representational) image of entire space is produced.

Divergent Perspective: Howard & Allison
-studied how adults draw a basic cube
-determined that the majority do not draw in a cohesive projection system
-they called this divergent perspective
-turns out most adults draw a cube just like a Byzantine would

Equirectangular Perspective
–António Bandeira Araújo
-used for VR Panoramas
-shows an expanded 360 degree view in one drawing

Choisey One Point: Kurt Ofer
-combines the Choisey projection method with the one point linear perspective

Frontal Perspective – Arnheim 1956 p. 265.
“One side of the solid lies in a frontal plane. All lines meant to recede perpendicularly to the frontal plane (orthogonals) are drawn at an oblique angle, which is constant throughout the picture.”

Equilibrium Perspective – Teshurah Naumann
In their words: “A method of enhancing a sense of depth on a flat canvas regardless of the geometrical perspective; an additional dimension of distance, concave or convex surfaces in a flat image. This phenomenon is natural to human vision and perception but inconceivable to a camera and photographs that flatten the photographed space.”

Sundial Perspective – Veltman
In their book, The Sources of Linear Perspective, Kim Veltman reports that sundials work as a result of the principals of linear perspective. That makes sense, given the center of the sun is the vanishing point, and the light rays are projected onto the dial. p 43.

Synthetic Perspective – White (added 3June22)
Integration of the visual cone with a spherical surface concave to the eye.
Four main characteristics: p208,
-all straight lines (unless they pass thru point closest to eye) are curvelinear
-increasing distortion and foreshortening of forms in all directions (from this center point)
-the center point conincides with the vanishing point
-object size is dictated by the visual angle

Atmospheric Perspective – Cooper (added 7August22)
The farther away a form is, the less distinct, and the blurrier it is. p111. The farther away a form is, the more atmosphere that you need to look thru to see the form. Japanese screen paintings typically use a lightening of the tones as a way of indicating depth. Western artists have typically used bluing as a way of indicating atmosphere.

Artificial Perspective – Gibson (added 9September22)
“The theory of projection on a transparent picture place to a station point is a Renaissance discovery that is properly called artificial perspective.” p271.

Natural Perspective – Gibson (added 9September22)
“The theory of the ambient optic array from an environment to a point of observation should be called natural perspective.” p271.
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An obvious question: are any alternate perspective systems being taught? Are students being made aware that there is more than one way to pluck a chicken? Or, is the two point perspective being taught, in analogue, even though the machine will produce draughters with exactly two vanishing points? When I was teaching, I had to teach students how to assemble a two point perspective in analogue, and I hated it. Entirely wide open space times have already been devised and are in use, and all we can think to spend precious time teaching is a two point projection?

Possibly this will be of inspiration to you. If you want to do something really wild and crazy, try incorporating Byzantine Perspective. Or see how 5 vanishing points might work for your drawing. Or see what happens if you employ Equilibrium Perspective as an alternate perspective. Of course, since our drawings are transparent, we achieve holistic 360 degree knowledge in the most elegant way imaginable.

If any reader knows of an alternate perspective projection system that is not listed here, please let me know. My intent is to update this page, as necessary.

1. Adams, Kenneth. Tetraconic Perspective For A Complete Sphere of Vision. LeonardoVol. 9, No. 4 (Autumn, 1976), pp. 289-291. MIT Press.
2. Moose, Michael. Guidelines for Constructing a Fisheye Perspective. LeonardoVol. 19, No. 1 (1986), pp. 61-64. MIT Press.
3. Casas, Fernando R. Flat-Sphere Perspective. Leonardo, Vol 16, No1. pp 1-9, Great Britan. 1983.
4. Goodman, Nelson. Languages of Art. Bobbi-Merrill Company. New York. 1968.
5. White, John.  The Birth and Rebirth of Pictorial Space.  Harper & Row.  New York.  1967.