A different geometry

One of the challenges of the kind of painting I do is avoiding arbitrary decisions, or at least minimizing them. Representational painters don’t have that problem to the same degree, because the need to maintain a likeness puts some constraints on the sorts of liberties they can take. (Which is not to minimize the problems of representational painters, by the way, just to say they don’t experience this particular problem as much.)

Not that I feel a need to have a fully articulated rationale for every element of my compositions. Sometimes “it just feels right” is acceptable. But too much of that and my paintings could easily devolve into sheer caprice, so I’m always pleased when I can draw what I hope is an interesting composition out of the geometry of the rectangle.

I’ve written about geometry several times before in this blog, with a heavy emphasis on the Golden Section, a ratio beloved of early modern painters. However that’s not to say there aren’t other compositional geometries, and in fact a quick perusal of Bouleau’s The Painter’s Secret Geometry reveals that the Golden Section occupies a minority position in the history of the discipline. All of which serves to provide some context for the topic of this post, wherein I draw back the curtain and reveal the geometric underpinnings for one of my latest paintings, which represents something of a departure from my usual approach.

As I’ve noted before, my paintings typically begin with a thumbnail sketch, usually executed with a black fountain pen. Sometimes they go through several versions, other times they get translated into paintings right away. Geometry usually gets applied in the intermediate stage, while the sketch is being transferred to the canvas. I’ve described that whole process in a previous post, so I won’t go into any more detail here. What was different this time is that the geometry and the composition kind of arose organically as the sketch was evolving, rather than being applied after the sketch was done. And as I’ve already implied, the Golden Section wasn’t the framework I used this time.

Instead the fundamental lines of the composition were derived from another well known compositional strategy, which Bouleau calls ‘rabatment’, creatingĀ  a square within the larger rectangle by mapping the short side onto the long side. The strategy is so well known that Wikipedia has it covered if you need a better description.

When you’ve got a composition as simple as this one, the main challenge is to keep it from being boring. One of the best ways to add interest is to avoid putting everything on the midline. But then you run into a different problem: once you leave behind the obvious central placement of objects where do you put them? The options are literally infinite.


The diagonals of the larger rectangle and the internal square provided the solution. Their intersection with each other provides the off-centre centre point of the circle that is the focal point of the composition, and their intersection with the rabatment line provides the basis for the framing rectangle. I was particularly pleased that I could also use the centre point of the larger rectangle to derive one of the points on the circle’s circumference, and the diagonal of the larger rectangle could be used to derive the bottom of the internal frame.

You couldn’t do this with just any rectangle, of course. If you used a square everything would be back at the midline, and if the rectangle was too long you’d get other kinds of distortions. Interestingly, the size that seemed to work best was in the 16″x20″ ballpark, an aspect ratio I use quite frequently.

Of course, once the composition had been worked out I still had to paint the thing. There were a couple of considerations there. Compositionally the main issue was painting it in such a way that diagonal balance was maintained even though the compositional weight skewed a bit to the left. I leave it to you to determine how well that was achieved.

The other consideration was that I was determined to make it work with cerulean blue, a colour I love but have had problems working with in the past. Hey, as noted above, I don’t need to have a fully worked-out rationale for everything.