Perspective Squared: Some Classic Angles (Part One)

November 2, 2018 | Brent

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Every year the Toronto Reference Library hosts classes from OCADU researching aspects of perspective, found imagery and collage. It's a great way to show off some of the resources available through our Picture Collection, as well as some of the books available through the Toronto Reference Library Arts Department. This post is an attempt to go over some of the milestones in the discussion of perspective in art and hopefully point students towards some helpful (and maybe inspiring?) material.



Perspective is one of the building blocks of drawing. But paradoxically, the visual markers used to indicate distance and dimension are so ubiquitous that they are difficult to notice. Once they are noticed, they can become grating. Look at too much one-point perspective and the world appears to be continually receding away while somehow at the same time constantly trying form a pyramid ready to poke you in the eye.



Of course there are more complex means of rendering linear perspective as well as multiple other visual conventions used to indicate depth, from cast shadows to the color shifts of atmospheric perspective to changes in relative size and more.  

Perspective from Basic to Creative

Perspective Drawing

Drawing Perspective

It’s tempting to think that perspective is only interesting when its rules are violated or ignored whether it be through anamorphic distortions or the "fish eye" distortions caused by the panorama mode on the iPhone camera

Hogarth’s famous frontispiece is meant to be instructional, a means of chiding artists who don’t know the rules, but on the other hand, it’s also a gleeful violation of them.


Piranesi’s carceri famously hide impossible angles which seem to make his imaginary prisons inescapable.

Image result for ISBN: 3822850942

Much of Escher’s work—with its endless regressions, ambiguities of scale and impossible objects – concerns perspective puzzles, so it’s always a pleasant surprise to see a straightforward bravura demonstration.

  Amazing World of MC Escher

That said, some of his most famous work seems like arch parodies of Piranesi.

But until recently such impressive mathematical feats would feel out of place within a High Modernist or even a Post-Modernist context. Within the last century of painting, especially since the advent of cubism, the assumed stage of the painting flattens out and stays that way, even after the figurative revivals of the seventies and eighties. Paintings are self consciously marks arranged on a canvas, continuing through the all over composition of the New York School through to a different type of all over post-modern composition in which images still appear to float independently on the plane.





The paintings all gesture towards the flatness of the canvas but they all certainly have depth as well. It's just that they occupy a shallow space like a shadow box.

But that's not to say that mathematical perspective is irrelevant by a long shot. David Hockney’s History of Pictures is mostly a catalogue of different approaches to rendering depth.


Mathematical perspective is an essential component of commercial video games, CGI animation, virtual reality and CAD rendering as well as 3D printing and design.

Videogames and Art

CAD for the Workshop

  3D Printing for Artists Designers and Makers

And while architecture generally gets most of the attention, rendering three dimensional objects can also be incredibly tricky.

Lorenz Stöer’s deapan renderings – from Geometria et Perspectiva (1567) – of geometric figures posed amongst ruins made of curlicues seem like sly parodies of the Durer above. 



Wenzel Jamnitzer and Jost Amman's Sechs Oktaeder (1568) are brilliant collections of polyhedra. 


The same goes for Max Brückner’s shelves of paper polyhedrons featured in his book Vielecke und Vielflache: Theorie und Geschichte (1900).

Readers with more patience and better math skills than I can make their own polyhedra out of paper.

How to fold it

A plethora of polyhedra in origami

Unit polyhedoron origami

or wood:

  Wooden Puzzles



Crafting wood logic puzzles


OK now that you've mastered rendering polyhedra in CAD, paper and wood, why not browse through Part Two Perspective Squared: Some Personal Angles?