Graphical Parallel Projection - Isometric drawing

Isometric: from Ancient Greek ἰσομέτρητος (isométrētos, “equal in measure”), from ἴσος (ísos, “equal”) + μέτρον (métron, “measure”).

 There is a certain elegance to isometric drawings.

 What seems two-dimensional…

…can suggest something else.

And with a little shading…

…and turning…

…can look like the real thing.

And you can use that cube…

…to construct a cylinder.

And using a cylinder in a cube…

…rotated 90 degrees into each cube face…

…gives you a sphere with the same diameter as the cylinder.

 _________________________________________________

And what is this elegant technique good for? Let’s take a look.

In Joseph Gwilt's Civil Architecture, from 1825, we find a proportion study of Amien Cathedral in isometric form. The view is perfect for comparing the three-dimensional modularity of the cathedral’s structure.

Auguste Choisy was a professor of architecture at the École Nationale des Ponts et Chaussées, in Paris, from 1877 to 1901. He was an authority on ancient building systems, and wrote L'art de bâtir chez les byzantins and L'art de bâtir chez les romans. The drawings above are from those two books, and are all examples of isometric drawing. Note that Choisy has provided a scale for each axis, making each drawing quite informative as well as beautiful. (I’d dearly like to get my hands on copies of these books, but the timing isn’t right [I’m planning a move] and they would be expensive.)

This isometric of a work room by Walter Gropius (1923) is also highly informative and beautiful, but in a more abstract way than Choisy’s drawings. The see-through walls and ceiling allow a viewer to easily explore the design.

 R. Buckminster Fuller’s 1927 collage presentation of the Dymaxion House does a wonderful job of describing the complex geometry of the design. Placing the isometric drawing between the plan and the elevation makes the design easy to understand. However, I would hardly call the drawing beautiful, and the repeated geometry gets old really fast.

 This isometric of water wheel gears from the book Windmills & Watermills by J. Reynolds (1970) gives a wonderfully clear idea of the watermill setup. It would take a number of plans, elevations and sections to give as much information as this single isometric. And I, for one, think the drawing is gorgeous. 

 This isometric of a redevelopment plan for Rotebuhlplatz in Stuttgart, by Putz & Weber Architects, illustrates one of the obvious uses for isometrics: simple aerial views. Both this and the following two isometric studies are by Rob Krier; this aerial is from his book Urban Space (1979). 

 A sheet of isometrics illustrating column types in Rob Krier’s Elements of Architecture (1983). Surrounding the isometrics with scaled elevations and plans makes this example visually informative and practically useful.

 This sheet of rough isometric sketches is also from Elements of Architecture. In each case Krier juxtaposes the isometric with a simple plan. In spite of the roughness of the drawings, I find the approach quite elegant.

 Leon Krier is the younger brother of Rob, and a well-known neo-traditional architect in his own right. The above drawing of the School at St. Quentin in Yvelines, France, shows the simple elegance and clarity of the isometric. It also shows the quirky style of architecture practiced by the Kriers in the 70s and 80s.

 In the early 80s Leon Krier worked on the “New District of Tegel” in Berlin. The presentation drawings produced for the proposal included many bird’s-eye and worm’s-eye axonometrics. The lower drawing above is a simple projection drawing of a rectilinear grid of blocks, an iconic example of the isometric. The drawing above it is a curious inverted worm’s-eye view of a complex. In spite of its multiple grids and curves, I would label it an isometric, since the main grid of columns is close to the requisite 30-degree angle. In any case, it is a wonderful bit of frippery that I loved when I first saw it years ago.

 I have done quite a few isometrics in my time. This aerial of the Franklin & Marshall College master plan by Kliment Halsband Architects is perhaps the closest to a simple aerial. It was produced by making a computer model of the campus; printing out a hidden wire-frame view; and painting in the simple materials and modeling with airbrush. It would have been as easy to make an aerial perspective, but the look of an isometric was preferred by the client.

Just to summarize…

An isometric drawing takes a rectilinear object and draws it as if seen from 45 degrees off each axis, but with no foreshortening. Measurement along each axis is easy and accurate, but any other measurement (say a diagonal across a cube’s face) needs a different scale. The advantage, obviously, is being able to see the object in three dimensions while still being able to measure the most important parts.

Finally, isometric drawing, unlike plan or elevation projection, is easily done by computer modeling. My aerial drawing for Franklin & Marshall College involved a model which could be viewed either as a perspective or as a parallel projection. I simply turned off the perspective control to create the isometric drawing.

Computer modeling opens an easy and wide range of parallel projection views, but there are areas where hand drawing is still king. The following posts on elevation projection and plan projection drawing will explore two of them.

Graphical Parallel Projection - Introduction

When I started writing about perspective drawing nearly a year ago I noted that ancient and medieval artists were trying to make paintings that looked like 3 dimensional reality. They did this by drawing adjacent sides of a building using differently angled grids.

To quote from that first post describing the above image: “The fresco above from the Villa of Fannius Synistor allows every building to have its own vanishing point (or rather, every building has a rough approximation of a vanishing point).” The Roman era fresco could just as easily be a precursor of graphical parallel projections: the horizontal lines on one façade are (roughly) parallel to each other, and are different from all the (roughly) parallel lines on the adjacent façade.

This illuminated manuscript called Pericopes of Henry II (1002 – 1012 AD), shows a tower on the left of the center panel. It is a nice example of a proto parallel projection, with each façade having a consistent pattern of parallel horizontal lines.

In approximately the same time period Chinese artists were also struggling to depict rectilinear buildings on a flat surface. They avoided the single individual viewpoint and converging lines of Linear perspective practiced in Europe, but went beyond simple parallel projection. The Chinese handing of rectilinear objects is an immense subject on its own which involves the practicality of drawing, as well as philosophy and religion; and is something I myself will not get into here. OK… maybe in a future post.

All this suggests that graphical parallel projection was just a crude precursor to linear perspective; an inexact approximation of the perfect illusion.

So, once linear perspective was invented, what was the use of parallel projection drawings?

Well, one use was in aerial drawings of large areas such as cities or (in the case above) a palace complex. The viewpoint was typically so far away from the objects on the ground that perspective convergence could be ignored. This non-perspective view of a design for the Stuttgart Court by Thouret (1830) was much easier to layout than a perspective would have been. It looks like a realistic aerial perspective, but was produced with half the trouble.

Parallel projections are perfect for showing the 3 dimensional form of an object, and allowing the viewer to measure the drawing. Indeed, in the premodern design world, the whole point was to have a measurable drawing from which to build. Although it lacks a scale, Rob Krier’s Grand Staircase in Vienna’s Kunsthistorisches Museum is a good example. The complex drawing explains the stair’s shape and function, and would be a very useful addition to the typical plans, elevations and sections. The measurability of parallel projection drawings has made them a favorite of engineers over the years.

In the next three posts I’m going to explore the three most popular forms of graphical projection: Isometric, Plan Projection, & Elevation Projection. After that I plan on addressing the subject of graphic projection’s use in modern architectural presentation drawing. There are many ways to distort an object so as to reveal some aspect of it. There are also unlimited ways to distort an object so as to obscure the object. We “moderns” have gone a long way toward exploring all of the curious possibilities.

Note: I am not going to explore every sort of parallel projection drawing out there. Just tripping through the various names and subcategories is a bother. But if you are interested, Wikipedia does a good job of noting the taxonomy and the more esoteric variations.