Perspective drawings by V. Pellegrin, 1873, and Ernest Norling, 1929

Fig. 1

Okay, I get it. Perspective is boring. Especially arcane drawings from some 19th century manual by the Professor of Topography at some Military School. True, the text (which you can read here) is as thick and dense as Dermot Malone who beat me up when I was a kid, but the drawings are amazing. Take the first one (Fig. 1), for example.

It shows how to draw a square in perspective (lmno), a column in perspective (m1, n1, q1, p1), and how to draw shadows cast in perspective (v2, u2, p2) ... all in one tiny little drawing. Note that the shadows also recede. Not only do they stretch back towards the horizon, but they have their own distance point at F1, which is a theoretical point that would be way under the ground somewhere. You know where to place the shadows by marking the intersection points between lines going back from the column towards the horizon, and lines cast by the sun (above and behind) that pass through the top corners of the column (p1, q1, u1, v1) and recede to F1. Simples.

Now you can delete this email and go about your day. See you in another couple of months with some more useless info. Bye!

I admit; some might be a tad complicated. But they still look cool.

Continuing from Figure 1, this shows an obelisk in perspective and how to construct appropriate shadows.

Maybe these next ones are a bit easier to follow. They're by Ernest Norling from Perspective Made Easy (1929). Maybe I should have posted these first, but they're not as cool-looking as Pellegrin's. And besides, nobody's made it this far into the post anyway.

A New Perspective on Rubens

Rubens painted a set of massive canvases (including two measuring 28 x 20 feet and two others at 40 x 10 feet) for the ceiling of the Banqueting House at Whitehall in 1630. Despite boasting to his customer, James I, that he was “by natural instinct better fitted to execute very large works than small curiosities,” he seems to have made a bit of a mess of the linear perspective. In one of the panels (above), the seated figure of the King, his retinue and even the putti floating above with the royal coat of arms, are all painted as you would expect in di sotto in su painting; they're all foreshortened from below. The columns, however, are parallel to the picture plane which is incorrect.

I took the liberty of sketching on top of Rubens painting (below) using the correct viewpoint (according to linear perspective, at least), such that the columns and the figures appear to recede towards the same - singular - vanishing point.   

This discrepancy in Rubens' paintings was first noted by 18th century painter James Highmore, who published his "Critical Examination of paintings on the Ceiling at the banqueting-Hall at Whitehall," in  1754. Below, on the right, is the row of columns as Rubens painted them, and to the left appears Highmore's engraving of the corrected view. Highmore points out that Rubens used up to three (!) vanishing points in each of the panels. Why? We'll never know. Certainly, he wasn't especially used to painting on ceilings. I leave it up to the viewer to decide which version of the scene is the better view.

Here they are again, side by side for easier comparison.

The Academic Tradition on Hockney's claims of "cheating" in Classical Painting

Bouguereau (1825-1905), The Flagellation

Everyone loves a secret, but there's more than a whiff of sour grapes to Hockney's assertions about the use of Camera Lucida among the great draughtsmen of the past. The underlying arrogance of his "if I can't do it then nobody can" premise appears to have informed his theories, and blinded him to the possibility that yes, in fact, they were just that bloody good at drawing.

Ingres, Lethier family portrait drawing

Kirk Richards in The Classical Realism Journal points out that it may just be Gladwell's "10,000 hours" theory in action among the likes of Bouguerau, Alma-Tadema, et al. No one's denying that optical aids were available (and most likely used) by artists, and yet Hockney seems to think he's pulled back the curtain to reveal the "secret." At this point Hockney's eureka revelations are old news, but it gives us the opportunity to read a quote or two that serve as a rebuttal and give insight into the meticulousness of the Academic methods of 19th century practitioners.

Chardin, the attributes of painting

"Hockney [in his New Yorker article] alludes to the probability that [Jean-Baptiste Siméon] Chardin used optical aids. Of several artists, including Chardin, he says, "Suddenly they all seem to be able to render the image, just like that, onto the canvas itself." Suddenly? Just Like that? Chardin speaks forcefully to this claim:

"They put a crayon in our hands when we are seven or eight years old. We begin to draw from models of eyes, mouths, noses, ears, then of feet and hands. For a long period our backs are bent over our portfolios in front of the Hercules or the torso, and you have not seen the tears brought on by this Satyr, this Gladiator, the Venus de Medici, this Antaeus ... After we have spent days and worked nights by lamplight before stationary and inanimate forms they confront us with life and suddenly, the labor of all the preceding years seems to count for nothing .... One must teach the eye to see nature, and how many have not seen it and never will! It is the torment of our lives. We are kept working five or six years from the living model before they turn us over to our own genius, if we have any ... He who has not realized the difficulties of this art does in it nothing worthwhile." [source]

David Hockney, camera lucida drawing of Ray Charles White

Dawn signaled the start of a long, sweaty and mostly tedious day for apprentices in Classical ateliers. Grinding pigments, mixing size, unloading heavy materials, stretching canvases. The busy work of the studio spilled out onto the streets of Florence. And that was just the beginning. It took years before an apprentice did any actual painting. As far as Cennini was concerned, thirteen years apprenticing was a necessary and reasonable tenure:

"To begin as a shop boy studying for one year, to get practice in drawing, . . . next to leam how to work at all branches which pertain to our profession... for the space of a good six years. Then to get experience in painting . . . for six more years. If you follow other systems, you need never hope that [the apprentices] will reach any high degree of perfection."

Kelly Borsheim, sight-size charcoal portrait

The traditional sight-size method (above) evidently trumps Hockney's own attempts at drawing a portrait using his own optical aid, a small spherical lens not much bigger than an eyeball attached to the end of a metal rod. Sure, you could use a lens as a short cut, but it should be evident from Hockney's drawing above that a lens is no substitute for solid drawing skills and could never, on its own, replace them.

According to Charles H. Cecil, “When properly understood, sight-size is not a mere measuring technique, but a philosophy of seeing. The method was used by many of the finest painters in oil since the seventeenth century, including Reynolds, Lawrence and Sargent.”

As Degas once said, "Make a drawing. Start all over again. Trace it. Start it and trace it again. [...] You must do over the same subject ten times, a hundred times. In art nothing must appear accidental, even a movement. " He also once said that, "Painting is easy, until you learn how."

Enter the Vault

Definitely not a bad Italian restaurant. 

Arches appear in trompe l'oeil murals with predictable regularity. I don't know how many times I've sat in a bad Italian restaurant, staring at an appallingly painted Bay of Naples through some row of wonky arches. Overcooked pasta, bad wine, swirly stucco and a gilded gorilla on a glass pedestal staring me out as I go to the bathroom. We've all been there. With even the smallest of effort, however, these murals could be made better. Not good exactly, but better. 

To begin with, I'd argue that the arch is not the best structure to imply depth. A single row of arches in the foreground, perpendicular to the line of sight and revealing a landscape behind (for example), creates two distinct planes. We are made aware of the picture plane itself, as signified by the arches, and we are made aware of the plane of the background. A distant landscape exists very much on a flattened plane. Murals painted according to this standard model are distinguished by two discrete planes, foreground and background, usually painted without much physically linking them. It's a very static and finite solution to creating depth.

The vault, on the other hand, creates a continuous bridge between the foreground and middle distance. It may even appear to extend towards us, implying a continuous ceiling right over our heads. The painting above provides both examples in one. An arch revealing a scene (on the left), where the illusion of depth is created almost exclusively through use of value, and the receding vault (on the right), which uses both value and linear perspective to create its spatial illusion of depth. The scene on the left appears static, while the one on the right is dynamic.

[Oddly, the light on the background building seen through the window comes from the right, while the light on the vaulted corridor comes from the left.]

Replica of Ghiberti's Baptistry Doors at Trinity Lutheran Church in Hicksville (!)

The number of architectural structures that inherently suggest depth is quite small. If you want to create the illusion of three dimensions in an architectural mural or large-scale painting, you're pretty much limited to the vault. 

A barrel vault may even extend all the way to the background spatially, as in the wonderful Baptistry doors by Ghiberti. The carefully delineated outline of a vault is all that's needed to suggest great depth, despite the actual relief being no more than an inch or so. The action stops at the altar, but or eye travels all the way to the back of the nave.

Massaccio's Trinity

Massaccio's Trinity is a perfect example. The arch does nothing to create depth besides delineating a plane, it's the vault that creates the illusion that wows everyone.

The original "cassetted" vault: Temple of Maxentius

"The cassetted vault was well known from the Roman temple of Maxentius and other buildings. It became one of the great themes of humanistic architecture. Masaccio used it in his Trinity, generally accepted as the first extant work in perspective. Borromini's use of a variant nearly two centuries later in the Palazzo Spada attests to the enduring fascination of this illusionistic form."" [Kim Veltman, The Sources of Perspective]

Architects such as Borromini,  Scamozzi and Bramante, understood that architectural trompe l'oeil was best served by the vault, using it to spectacular effect in their illusionistic built environments.

An arch is more of a decorative frame. It sits in the foreground as a mute barrier. Arches serve as portals, a decorative meme intended to entice us to walk through into the scene beyond. Taken on their own, however, they serve to isolate the viewer from the scene, acting more like a simple barrier than, say, a pathway running sinuously from us and disappearing into a landscape. A long barrel vault is the architectural equivalent of a forest path in landscape painting. Paths are irresistible. They trigger an irresistible urge to explore and see what lies around the corner.

Arches are not. I see an arch in a painting and I feel like there's going to be a red velvet rope with a bouncer telling me I'm not on the list. Whatever drama is unfolding in the painting above, we’re clearly not part of it, just as I'm viscerally aware that I am not invited to Veronese’s Feast at the House of Levi. I'm a spectator, not a participant. On the other hand, Raphael’s School of Athens makes me want to march right up those steps to join those conversations in the crowded vault.

Veronese’s Feast at the House of Levi

Veronese circumvents the static nature of the single row of arches in the foreground by plonking a second row directly behind it. This implies a vault running perpendicular to us between the rows of arches, and creates depth. If the architecture is to run perpendicular to the line of sight, then it's a handy little trompe l'oeil trick to simply place a second row. Notice (below) how much depth is implied by adding the second row of columns. 

Colonnades running away from the viewer, along the lines of sight, imply great depth. "By the end of the (Fifteenth) Century, artists such as Bramante realized that the representation of colonnades was particularly suited for perspectival purposes because these permitted one not only to look into but even look straight through a space." [Veltman]

From Antiques in Italian Interiors, Vol II

And, of course, the last word goes to Raphael. As if there was any question on the matter. He pretty much closes the argument. How tempting it is to march up those steps and enter the vault, listening in on the conversations of all those great thinkers. Notice too, how Raphael has chosen to position his key players at the precise point of greatest implied depth in his painting. He knew that we are viscerally drawn to the "deepest" spot, and planned the hierarchy of his incredible painting accordingly. Another example of how depth is intrinsic to composition.

A Few Thoughts on Rosa Bonheur's Use of Space in "Horse Fair"

Rosa Bonheur's fantastic "Horse Fair" is a massive canvas that caused quite a stir when it first appeared at the Salon in France back in 1853. Standing in front of the painting today at the Met, the effect of the circling horses was dizzying. I could almost hear the commotion and clatter of hooves. The visceral sense of "being there" is accentuated by the way Bonheur constructed her painted space. 

Solution 1: Objects on the same perpendicular plane get smaller to the left and right

The panoramic sweep of her canvas seems to adhere to this Hyperbolic perspective grid. Imagine that these black silhouetted figures are all standing in a perfectly straight line from left to right. I've exaggerated the effect a bit in the illustration, but to the real-world viewer it would appear that they shrink towards the horizon line as they get further away from us. We know that the line they are standing on is straight, but it appears curved in reality. 

Our brains do lots of similar tricks, lining up our reality with what it knows to be true rather than what it actually sees. Imagine you arrived late to a movie and you're sitting in the front row of the theater, squashed all the way over on the furthest seat to the right. A giant square shape appears on the screen. Your brain knows for certain that that's a square, despite the fact that it looks nothing like one from your current vantage point. 

You can see the same effect in this stitched-together panoramic photo I took of Storm King seen from Breakneck Ridge. It's not a bend in the Hudson river you're looking at here. It's just that it adheres to the same "optical" grid as Bonheur's painting whereby objects in the center appear larger (because they're closer) than objects to the distant left or right. This happens when we try and squeeze anything beyond about 60º (our normal - undistorted - field of vision) into the frame. In this case, the extreme distortion of the river is due to the 180º view.

Solution 2: Objects on the same perpendicular plane stay the same size

Linear perspective takes a simpler solution to the problem of how to represent objects in space. Its solution is Euclidean in that its geometry is based on straight lines. The standard approach would have us portray as the same size any objects on the same plane, perpendicular to the viewer. This works just fine when we stick to portraying a scene that's within the undistorted 60º field. 

When painting especially wide scenes we are faced with a dilemma. Maybe we just paint everything the same size (as in Solution 2 above) and let reality do the shrinking for us. If you've ever stood in front of Veronese's gigantic canvas in the Louvre you'll know that he had no need to artificially reduce the scale of his figures in paint. The outer figures are so far away from the viewer that they naturally appear smaller.

Fish-eye distortion isn't just for large canvases

 It's not that painters didn't understand the problem. It seems that they simply found this fish-eye distortion unattractive, so (for the most part) they chose to ignore it and paint everything in straight line grids.

Pierre Puvis de Chavannes chose to ignore the issue. He painted incredibly long paintings, where each figure was the exact same size. His "Allegory of the Sorbonne," painted as a mural in 1889, reads as a long decorative frieze rather than a painted depiction of actual space, and that's not just because it contains all those allegorical figures (symbolizing Eloquence, Poetry and Drama etc).

"The Allegory of the Sorbonne," Pierre Puvis de Chavannes

De Chavannes' broad panorama is a simplified depiction of reality in that he chose to present all the figures the same size as each other. In reality, if we were positioned directly in front of the central figure of the Virgin, then all the figures to the left and right would appear to get smaller the further away from us they were.

Unless we happened to be witnessing the scene through a pair of binoculars, that is. Then we'd be at a sufficient distance away from the action that it would indeed tend to appear as De Chavannes portrayed it: a flattened frieze with very little variation in depth, scale or value. But de Chavannes knew what he was doing, of course. He knew this was a mural, and was not meant to be experienced from a single, fixed viewpoint, like Bonheur's painting. He knew that people would be milling around the Sorbonne, experiencing his painting from various angles.

"The Triumph of Aemelius Paulus," by Carle Vernet

A third solution is also possible: Why not just kind of blend the first two solutions together? You know: fake it a bit?

Carle (Antoine Charles Horace) Vernet did just that. He painted "The Triumph of Aemelius Paulus" in 1789, as a bravura performance of pre-Revolution pro-Empire sentiment. Vernet painted the architecture in perfectly straight, horizontal lines, but his painting avoids the stiff frieze-like nature of De Chavannes. How? He manages to inject a little hyperbolic perspective into the scene in two ways. 

Central figures are close to the bottom of the canvas, and have strong value contrasts, thus appearing closer

Firstly, the central figures are lower on the canvas than those to the left or right. This simple trick makes them appear closer (even though the are the same size as those to the left or right. It also approximates the optical effect we would have if viewing this scene in reality, in that figures to our distant left and right would appear closer to the horizon (and thus further away). 

I say he "approximates" because, in reality those peripheral, distant figures would also appear to be smaller. Vernet, however, defers to the same unnatural rules of linear perspective as Pierre Puvis de Chavannes in that he presents these peripheral figures the same size (Linear perspective tells us that figures on the same plane should be painted the same size).

Figures on the right are higher up and less "contrasty", making them seem further away

The second little trick he pulls to avoid de Chavannes' "frieze" trap is to reserve his strongest values for the central figures. Although the figures to the far left and right are painted the same size as those in the center, they appear to be further from us because they are painted with a narrower range of values. While he does use strong lights, his darks are greyed-out. This pushes the figures back in space.

Anyway, there you have it. A few thoughts I had while strolling through the Met the other day. A comment by Annabel Armstrong on my last post got me thinking about this subject. One of the great benefits of working on an apartment literally across the street is that I get to spend my lunch break with this stuff.

Gustave Caillebotte: Mystery in the Making

Le Pont de l'Europe, Gustave Caillebotte 1886

Every time I walk down the street, the most instinctive, primal part of my brain asks two questions of each person I pass:

1: "Is this person a potential threat?"

2: "Is this person a potential mate?"

The first question may just be a throwback to growing up in Dublin, where every approaching kid in the lane by the railroad tracks was a potential threat to this skinny art kid. It was always tense and nervy. The second is, well, just human nature. It's a fleeting nod to my simian side, and I don't have to act on it to recognize its existence. I'm a believer that we are animals first, and humans second. But maybe that's just me, I don't know.

Anyhoo: If the answer to both questions is "no," then I feel nothing and go about my day. But if the answer is "yes" to either one (and if I'm being honest), then there's a momentary charge in the air. Even the mutt in the painting seems to feel it. The point is; I believe that Caillebotte created his painting, "Le Pont de l'Europe," to deal specifically with this instant of primal recognition. The mystery that's endured speculation is; to which question is he answering "yes?"

The dress code may be different, but "Le Pont De l'Europe" depicts that same scene from the railroad tracks of my childhood, except that here it's a flaneur from nineteenth century Paris instead of some scumbag from Dublin. 

Le Pont de l'Europe from Le Gare St. Lazare, 1868 [source]

The area around the railway station, Le Gare St. Lazare, was pretty seedy around the time. The protagonist (let's assume it's Caillebotte for now) is seen walking a couple of steps ahead of a woman dressed in black. Women dressed in this manner, and hanging out by the railway station in nineteenth century France, were assumed to be prostitutes. If we assume that this woman is walking alone, and that old Gus has simply passed her by on the street, then we can be pretty sure in this assumption as to her trade. Women rarely, if ever, would walk unaccompanied in so rough a neighborhood. 

And if he is walking with her, why is he acting cagey and walking so far ahead? No well bred man would precede his companion. Either way, and despite the fact that she is looking at him, Caillebotte seems oblivious to her presence and is instead gazing at the man on the bridge. 

Dressed in the blue and bowler hat of a laborer, perhaps he is simply lost in thoughts of work and life. Caillebotte the engineer and lifelong bachelor, might naturally have an affinity for this. But perhaps this man in blue - idle during what is after all the middle of the work day, judging by the shadows - is on the prowl for someone just like Caillebotte. The painting has been interpreted as two men cruising each other.

I like how Caillebotte changed the architecture of the bridge between paintings

As if to prove my point, Caillebotte created this second painting around the same time. It's a wonderful cinematic moment that seems to capture the scene a few seconds after the first painting. Caillebotte has ditched his female companion (for it was never her that he was interested in), and has stopped by the man in blue. Is this just the engineer in him that's been distracted by the marvels of steel and industry on the horizon, or is he up for a little what-not in the hoo-ha with our man in blue? 

Well, "who cares," is the obvious answer. But it's fun to speculate, and the air of mystery around the painting is much of its enduring charm. What's especially interesting is how he has used linear perspective to help construct his narrative. 

He tampered with the reality of the actual scene, straightening buildings on the background that are in actuality oblique to the bridge, and widened the left of the bridge so that "the universe faithfully transcribed proves an illusion, and accuracy covers a lie." [Kirk Varnedoe]

"The superfluity of lines, which all seem to converge on the profile of the man, raises the question of what exactly Caillebotte was seeking to achieve through such unusual emphasis. Everything would seem to suggest that it identifies this man as the protagonist of a narrative encompassing the entire work." [Hirmer]

Various interpretations exist. Some say that this rigidly constructed scene "depicts a city that would have interested the Futurists, a place of dynamic intersections and personal anonymity, where human relationships count for nothing." [source]

"They seem to be quite alone," says Nicolas Sainte Fare Garnot, curator of the Jacquemart-Andre Museum. "Every person is lost in a very wide world."

In an earlier painted sketch (above), the architecture of the bridge dominates and overwhelms the scene. Though we see the same man, it's hard for our attention not to be sucked to the back of the painting, towards Place de l'Europe.

This sketch seems to back up the "critique of modernization" interpretation, with its overbearing architecture dwarfing a faceless man.

In another sketch, he's introduced a couple to stop our gaze from being distracted by the roaring perspective, and to draw our attention back to the guy on the right. Caillebotte paints the couple's heads at the same level, suggesting a whispered conversation regarding the other man's intentions. Perhaps this is the moment before a robbery. 

He's instantly created narrative, and established that human interaction (or the lack of it) is precisely what the painting's about.

Comparison between sketch (left) and final painting (right)

Comparing the compositions of the sketch and the final painting (above), the woman in the sketch (left) looks like a basketball player. She's massive. With her long dress, she appears to be even taller than him. This clearly wouldn't do for a gentleman to be dating a giraffe in 19th Century Paris.

But Caillebotte obviously wanted to keep those two heads close together and aligned with the horizon line in the final painting. Why? Maybe it's simply a compositional choice he made about the connection between their heads being more important than the distance between their steps.

In order to do that, and to remain true to linear perspective, he had to position the woman a few steps behind our protagonist so that she didn't appear to be as tall as him. 

Maybe the painting is simply about a shared moment of intimacy between them. In the close up, he appears to be leaning back as if to hear what she's saying. She seems to look at him adoringly. We're also aware that there are other figures on the bridge. The tight bunching of heads along the horizon line emphasizes the isolation of the figure in the shadows.

Suddenly, we've got it all wrong. Caillebotte is not the man walking with the woman; he's the man standing by the bridge. Isolated by the shadows and alone with head in hands, it's Caillebotte the sad loner.

"Modern life doesn't create close relations between human beings," Garnot says. "You are [in] complete loneliness in these new buildings, new avenues, new boulevards. There's something quite sad about that."

We'll never know the intended meaning of the painting. Caillebotte was known in his time as a collector of paintings and not as a painter, his work only becoming popular as late as 1950. He started painting relatively late, at age 27, and only lived to 45. A catalog from his Musée d'Orsay show states that "since the artist is dead, no amount of documentation will ever recapture a complete reckoning of his view of the world, or understanding of him as an individual."