This blog is dedicated to my kids who often complain they
will never use their GCSE maths in ‘the real world’. It’s also to remind me to
keep on squirrelling away that apparently useless information...
A family friend studies drawing and painting at the Barcelona Academy of Art. She’s being taught – or re-taught as she was already an artist – to paint in the way of the grand masters; a tradition of realism that goes back to the renaissance. Being from the polar opposite world of computer rendering I’m continually blown away by her work and whenever she describes her techniques I’m like the HMV dog. I always hope that some of her analogue wisdom might add some different dimension to my own, digital, work.
Now call me stupid, but there was one thing she told me that seems so obvious I don’t know why I never worked it out. She paints from life, from models or sculptures, and will always position her easel the exact distance required to create a 1:1 relationship between her canvas and the subject. To fit the subject onto, say, an A3 canvas she’ll stand right next to a marble bust but might be several feet away from a human figure. Then all she has to do is transcribe everything like-for-like, without having to scale anything up or down.
This stuck in my head even though I had no actual use for the information at the time.
Then, working on the planning application for Herzog de Meuron’s Blavatnik School of Government in Oxford, I was asked to produce some verified views: accurate photomontages that showed the new design in relation to landmarks when viewed from a distant vantage point. Some residents were worried that the proposals unusual form would distract from the historic skyline. The scheme looked very small on the photomontages, even accounting for the ‘standard’ lens we used to closely approximate the human eye’s angle of view. Even when we produced a set with a zoom lens to mimic the eye’s ability to focus in on details.
Both these approaches were in keeping with the industry standard method for creating accurate visual representations (or AVRs... It’s not clever unless it has an acronym). Still, the residents naturally wanted us to produce a set of large blow-ups, complaining the scheme wasn’t clear enough on the photomontages for them to judge its impact on the vista. Was it the case that, if they couldn’t make out the scheme in the images, then perhaps the design wasn’t a problem in real life? It fell on us to come up with a credible way to put their minds at rest.
I remembered my artist friend and her easel, and wondered what size you would need to print a standard lens photograph, and how far you’d have to stand from it, so that the scale of it matched its real-world scale. The answer lay in some surprisingly simple trigonometry. See Figure 1.
So if our photograph was taken on a medium format camera with a 47mm lens, that gave us a horizontal view angle of around 54-degrees which we usually cropped to 40-degrees. Printed at A1 – 831mm wide – if you stood 1140mm from the print it would cover a 40-degree portion of your vision and everything in the image should be the same “size” (subtend the same angle) as the real world as seen from the camera’s position.
We printed the verified views to size and our client hung them for the residents with instructions to debate from the prescribed distance, and... the Blavatnik School of Government is a fantastic building which you can still see to this day. In actual fact, there is a statue of me outside it in commemoration of my genius and my project-critical input.
Only one of those assertions is true.
Still, here’s the generalised equation if you’re interested:
Viewing distance from image=Half image width/TAN(half
It’s thrown up some surprising (to me) ‘did you knows’. Did you know that a 40-degree photo printed at A3 and held at arm’s length (approx. 57cm) will match the perspective of the real world? As will an A4 print of an iPhone photo held at just under an A4’s length from your face?
These days, I print renders at A4 (with a 30-degree view) and use them on site walk-arounds to help determine where a proposal will appear when it’s built. Everybody is delighted and impressed when I repeatedly shove images in their faces at exactly the right distance for the perspective illusion to spring into life.
I don’t know why this technique of printing to scale isn’t used by more people more often; in site visits or brochures or on hoardings. I like to think of it as a kind of digital trompe l’oeil or a printed projection map. Or an Augmented Reality head-up display. Old school.