# Isometric Exercises

That hexagonal envelope in my recent post about letters to Amy got me to digging out other images I’ve done over the years in isometric projection. Wikipedia defines it as “a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings. It is an axonometric projection in which the three coordinate axes appear equally foreshortened and the angles between any two of them are 120 degrees”.

The cube illustration should make it clear. All three visible sides of the cube are equally foreshortened and the near corner where they meet exactly overlaps the opposite corner. Because the cube is viewed as if from an infinite distance, all parallel lines remain parallel throughout the picture and do not converge on a vanishing point.

Isometric projection has a long history. Far Eastern art used a parallel line system approximating isometric until perspective was introduced from the West. Isometric has been popular in engineering and architectural drawing because measurements along each of the three major axes are at the same scale. More recently, isometric images turn up frequently in video games and online graphics. My new book Extreme Perspective! includes a chapter explaining how to draw isometrics as well as related parallel drawing systems.

(Sometimes the term “isometric” is applied in error. Rand McNally’s Isometric Map of Manhattan is actually another kind of architectural drawing known as a plan oblique, or axonometric. The telltale difference is that the city streets meet at right angles and form rectangular blocks, not the rhomboidal ones you would see in a true isometric).

I learned about isometric as part of studying perspective, and I use it on occasions when perspective is not required. I like the simple construction (no vanishing points) as well as its godlike point of view. This flyer for the theater company Bad Neighbors is an early example.

Isometric is a natural for comics- the insistent diagonal lines automatically tie the design of a page together, and because there is no perspective distortion at the edges, a single scene can be extended across multiple panels. It is a particular godsend in 24 Hour Comics where time is of the essence. The yard sale story with Mugg is a sequence from my second 24 Hour Comic, which is collected in the book 24 Hour Comic All-Stars. The all-isometric story Now Open The Box from 2008 is viewable on the Top Shelf website.

I have also used isometric for illustration assignments, such as this Modern Love piece for the New York Times (another yard sale!). The Mathemakitty illustration for Cricket Magazine was set up in CGI, and even though ease of construction was not a factor (I could have set my virtual camera up anywhere and simply traced the rendering) I chose to take an angle that resulted in an isometric view because it seemed “mathematical”. By the way, I am proud of the extra care I took in this piece- in addition to details called for in the text, like “isosceles ears” and “triangle nose,” I added a few mathematical touches of my own, like an Escher-style cat tessellation for the wallpaper, a Fibonacci spiraled tail, a Moebius strip of yarn, and a bell around the cat’s neck with the silhouette of a bell curve.