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Rackstraw Downes, "At the Confluence of Two Ditches Bordering a Field with Four Radio Towers" (1995), 46 x 48 in. |
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Jean Fouquet, Arrival of Emperor Charles IV... 1455-1460. |
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360-degree panorama. Photo: Heiwa 4126 |
In many of his paintings, Downes uses a curvilinear perspective that's reminiscent of these photographic approaches. The painting below takes in more than 90 degrees.

Albertian perspective requires holding the head in one line of sight, what Downes calls a "head-in-a-vise" system. Downes' vistas often take in a 180 degree view, which would only be possible if you turned your head from one direction to another.
Such head-turning is in some ways more natural. It's what we do when we look around in a scene. Downes wants to capture this experience "empirically," a word he uses a lot. He's not terribly interested in following a strict geometric system, but would rather interpret the scene each time as he sees it.

Sometimes the resulting paintings have idiosyncratic features. For example, in the scene above, the horizon or eye level is below the center of the image. That would normally require it to be cupped upward in a concave fashion. But instead, Downes sees the horizon as bulging upward convexly. This would only happen in a photo if you pointed a super wide angle lens downward and cropped off the bottom half of the image.
Downes also makes the line of the building at left leaning straight outward, rather than curving back into the scene at the top like a parenthesis, as a normal wide angle perspective would require. These idiosyncrasies of perspective might strike different people in different ways.
To me this one has a queasy, funhouse feeling, and also the sense that the city scene is on the surface of a small spherical planet.

Downes lays out the case for his approach to perspective in an essay called "Turning the Head in Empirical Space," which appears in the back of his book Rackstraw Downes
Another good book is Rackstraw Downes: Onsite Painting, 1972-2008
10 Comments on Gurney Journey: Rackstraw Downes and the Rotating Viewpoint
That said, I think Downes and other people who employ curvilinear perspective (like Hockney's photo collages) invite us to see the world not as we remember it, but to kind of enter the mind of the artist and 'look around' with them. They portray the sense of being in a space, rather than an image of the space.. Bah it's a subtle distinction, but tons of fun to consider!
I think some artists have painted on concave surfaces so that when you stand at the right distance, the image sort of envelops you.. Anyone familiar with that illusion? I think Antonio Lopez did something that that..."
I do believe that straight lines must appear to curve as they move away from the center of our field of vision, but yes, our brains probably correct those curves, or we simply don't notice them because they are out of focus and the curves must be quite subtle.
As for painting on curved surfaces, Parmigianino did this most famously in his Self-portrait in a Convex Mirror, in which he painted the curving edges he saw in the mirror, and did so on a convex wooden panel. I love this painting, because both the subject and the surface are so perfectly married to the Mannerist aesthetic of distortion. In contemporary art, check out the drawings of the Oakes brothers, Ryan and Trevor, who typically work on concave surfaces."
https://youtu.be/4_lcb28fCz8"
https://s-media-cache-ak0.pinimg.com/originals/fc/93/87/fc938732aa153ec82d44b2d44eeb562f.jpg"
Thanks for the link Chris– I do like some of Hockney (as long as it's not his 'secret knowledge' :) I will take a look when I have a moment
Juan- yes that's what I was thinking of too! I think Antonio lopez also has some early work on curved surfaces as well.."
Because of that, all of these perspectives (including classical) are best understood as a two step process: projection onto a curved surface followed by a flattening of that surface. Of the infinite perspectives thus obtainable, two are "special": classical perspective, because the anamorphic surface is already a plane (hence, no flattening needed) so it is the only one that remains naturally anamorphic, and (360 degree) spherical perspective, since it captures the natural topology of vision, with every line having exactly two vanishing points (solving a perspective is all about solving vanishing points - the points of a line are a subset of the vanishing points of the plane defined by the line and the observer's point).
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This non-trivial occlusion makes drawing a sphere reflection very hard unless you calculate it with a computer (or you simply draw by looking at a real mirrored sphere, but that is not an option when drawing from imagination). Spherical perspective, on the other hand, can be drawn by ruler and compass quite simply (I explain how to draw it and compare it with reflections here: https://arxiv.org/abs/1511.02969).
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If you go with this dude's theories of five and six point perspective (aka a mirror ball, and a mirror ball from both sides) and understand your canvas crop from a camera's FOV metaphor (16mm = wide angle, 500 mm = zoom), can you argue 1, 2, and 3 point perspective all are just crops of a 5 point perspective shot, and the crop is so tight the lines falsely LOOK parallel? If our eyes weren't locked at this crop, and instead of turning your head to look up at a tall building it was naturally visible, would we no longer assume that building's lines are parallel as they zoom into the sky? "
That ‘Secret Knowledge’ stuff seems pretty straight forward and obvious to me.
I’m not sure I understand the difficulties some people have with Hockney’s thesis about lenses and curved mirrors. Does anyone have a link to a coherent critique? –RQ
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