How one-point linear perspective works

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Dr. Beth Harris: [0:07] This is a video about the elements of linear perspective, with a little bit of history thrown in.

Dr. Steven Zucker: [0:09] I love linear perspective.

Dr. Harris: [0:11] It’s hard not to love linear perspective. It’s like this magic formula.

Dr. Zucker: [0:15] Well, look what even Paolo Uccello was able to do just a few decades after linear perspective was first discovered.

Dr. Harris: [0:22] Linear perspective is a way of recreating the three-dimensional world on a two-dimensional surface, and it’s really accurate.

Dr. Zucker: [0:33] Look at this Paolo Uccello. Look at this study of a chalice. This wasn’t done on a computer. This was done with pen and ink on paper.

Dr. Harris: [0:39] No Photoshop.

Dr. Zucker: [0:40] No Photoshop.

Dr. Harris: [0:44] Let’s give a little bit of historical background, and then we’ll talk about how it’s done.

Dr. Zucker: [0:00] Let’s start first with what the problem was.

Dr. Harris: [0:52] So here we have a painting from the early 1300s by an artist named Duccio who’s painting in Siena, and you can see that Duccio’s interested in creating an earthly space for his figures of the angel Gabriel and Mary, but that the space doesn’t really make sense.

Dr. Zucker: [1:09] What you’re saying is we have kind of a real room here, we can see the beams in the ceiling, we can see the architecture. We can see the doors. He’s really interested in putting these figures in a real place. The problem is, and by the way don’t get me wrong, I love Duccio, but the problem is that Duccio is not constructing that architectural space in a way that looks logical to our eye.

Dr. Harris: [1:32] I think it probably wasn’t a problem for Duccio, but it was a problem for artists about 100 years later who had a different goal, and their goal was a kind of really accurate realism on that flat surface.

Dr. Zucker: [1:44] Before we leave the Duccio, let’s spend just a moment being kind of unfair and finding what’s wrong.

Dr. Harris: [0:00] Okay.

Dr. Zucker: [1:53] For one thing, the beams of the ceiling right up here don’t agree spatially with the seat that the Virgin Mary is on, or with this little stand for the Bible that we see here, or for that matter with the lines that are constructed by the top of the capitals of these pilasters, so none of this is really making sense.

Dr. Harris: [2:10] Right, it’s not a rational space and there’s this increasing interest in the 1400s in rationalism.

Dr. Zucker: [2:17] That’s the period that we really call the Renaissance.

Dr. Harris: [2:20] Right, the early Renaissance, and in Florence in 1420 Brunelleschi — and let’s put up a picture of Brunelleschi.

Dr. Zucker: [0:00] He’s right here, Filippo Brunelleschi.

Dr. Harris: [2:33] He discovers — or some would say rediscovers because some think that maybe the ancient Greeks and Romans had this before — but he discovers linear perspective.

Dr. Zucker: [0:00] He was a genius.

Dr. Harris: [2:41] He was a Renaissance man.

Dr. Zucker: [2:42] He was an architect, he was an engineer, he was a sculptor. And according to tradition, he had gone down to Rome and he was studying ancient Roman buildings, ruins. He wanted to be able to sketch them accurately, and he developed this system, linear perspective, as a way of doing that.

Dr. Harris: [3:03] In 1420 in Florence, he demonstrated this system, and 15 years later, another brilliant Renaissance man, Alberti, codified what Brunelleschi had discovered. He explained the system of linear perspective for artists.

Dr. Zucker: [3:19] He publishes a book called “On Painting” in 1435, and we have a later version of that book right here. Inside that book, he really gives the formula for linear perspective, and that’s what we have here. Let’s just spend a moment talking about how this system works.

Dr. Harris: [3:36] Let’s go down here and let’s actually do a diagram of linear perspective.

Dr. Zucker: [3:42] Now, I cannot do Paolo Uccello’s chalice but I can draw a basic linear perspectival structure.

Dr. Harris: [0:00] Go for it.

Dr. Zucker: [3:48] First of all, we need to understand that one-point linear perspective, sometimes called scientific perspective, is made up of three basic elements. There’s a vanishing point, there is a horizon line, and there are orthogonals. Let’s start off with creating a simple interior. I’m going to draw just a rectangle here.

Dr. Harris: [4:08] This is your painting, this is your flat surface?

Dr. Zucker: [4:09] That’s exactly right. I’m going to decide that the vanishing point needs to be pretty much in the middle. I’m putting the vanishing point right about here. Now, let’s see.

Dr. Harris: [4:22] Why don’t you label that “VP” so we remember it’s vanishing point.

Dr. Zucker: [4:27] Okay, so that’s the vanishing point. Now, what I want to do is I want to create a series of rays that move down to the bottom line. These one could think of as kind of floorboards in a room. Artists had been able to do this. Long before linear perspective, artists had never had a problem with this.

Dr. Harris: [4:51] Well, that’s because they were constructing it intuitively. Intuitively, when you look around at the world, you see walls in a room that look as though if they continued, they would meet, or the floorboards look as though they would meet, so it’s intuitive.

Dr. Zucker: [5:07] I’m actually going to add not only a floor to this room, but I’m going to put in a couple of windows. We’ll just make it very simple here. I’m going to put in a couple of more verticals right here, and then I’m simply going to have all of this meet in the middle at that vanishing point.

[5:20] Now I’m going to use an eraser here to clean this up a little bit so we can get rid of some of the extraneous lines to make things a little more clear. And voilà. You can see a window.

Dr. Harris: [5:34] Okay, a window…

Dr. Zucker: [5:38] Beginning to form. Now here’s the problem. The problem was, if you didn’t want to have floorboards, and instead you wanted to have a tile floor, you had a problem. Because you know intuitively, the horizontal lines have to get closer together as they go back in space.

[5:51] The problem is, it’s hard to exactly figure out what those proportions are as they get denser and denser as they go back in space, so that the floor doesn’t look like it’s popping up.

Dr. Harris: [6:02] Which happened often, actually, in paintings from the Trecento. The idea is that the tiles get smaller and smaller because things generally get smaller and smaller as they move away from us in space.

Dr. Zucker: [6:11] Or appear that way, at least. What Alberti wrote down in “On Painting” was that you need to have a second point in space outside of the picture plane that was at the level of your eye.

[6:23] I’m going to put it here. It’s at the same level as the vanishing point. We would call this, of course, what? This is “H.” This is the horizon line. I missed it, but there it is. [laughs] Then what I would do, and I would of course do this more accurately with a ruler, is I would draw another series of rays from that second point…

Dr. Harris: [6:44] From the exterior point.

Dr. Zucker: [6:46] That’s right, and have it connect to each of those floorboards. As you can see, what’s happening is that that angle becomes more extreme as I move across. I’m doing it freehand, so it’s a little bit hard to see, but you get the point. Now something really interesting just happened, which is I can now create a horizontal line that is at that first intersection. Do you see that right there?

Dr. Harris: [0:00] Mm-hmm.

Dr. Zucker: [7:14] Going straight across.

Dr. Harris: [7:15] I see it.

Dr. Zucker: [7:15] Then I can draw a second one at that second intersection right there, and so forth. They get more and more compressed as I go back in space. The illusion should be, then, a compression in space. I think this will become more clear if I do a little bit of erasing now.

Dr. Harris: [7:37] Okay. While you’re erasing, I want to talk about that word, “illusion.”

Dr. Zucker: [7:40] Okay.

Dr. Harris: [7:41] Because I think it’s key to everything here.

Dr. Zucker: [7:44] Absolutely.

Dr. Harris: [7:45] What artists are looking to do is to create an illusion of reality on this two-dimensional surface. Alberti said a painting should be like a window. In a way, you don’t see the two-dimensional surface. This two-dimensional surface becomes something you look through to a world that is a continuation of our own world.

[8:09] The idea of the illusion being incredibly convincing was so important to the artists of the Renaissance, artists like Masaccio or later Piero della Francesca or Andrea Mantegna.

Dr. Zucker: [8:23] Now I’m going to fill in a few of these tiles alternating, so that you can get a sense of that floor in space. Is that working?

Dr. Harris: [8:33] Even in this rough way here on this tablet, this is working, basically.

Dr. Zucker: [8:34] It actually couldn’t be rougher, could it? [laughter] But I think it still makes the point. If I were then finally to get rid of these lines and in fact get rid of the vanishing point entirely and instead now draw in a back wall, we have something that comes fairly close to looking like an interior space.

Dr. Harris: [9:00] Now, what about putting figures in?

Dr. Zucker: [0:00] Ah. So, now you’re really asking for trouble here.

Dr. Harris: [9:06] I’m sorry. Can you do that?

[0:00] [laughter]

Dr. Zucker: [9:07] I don’t know. Let’s see. If I were to draw a figure, what I would like to do is make sure that the eye level of the figure is approximately at the horizon line. I would put that figure in just about here.

Dr. Harris: [9:26] What if you put a figure more in the foreground or more in the background?

Dr. Zucker: [9:30] If I put a figure that was more in the foreground, I would still want their eye level to be at that imaginary horizon line, but of course, now they would be larger.

Dr. Harris: [9:39] Right, I think this is the part that’s counterintuitive. The heads are on the same level, and it’s the feet that are on different levels.

Dr. Zucker: [9:47] That’s exactly right. Alberti also said that that eye level, that horizon line, would ideally also be the viewer’s eye level, so that the perspective would really work perfectly.

Dr. Harris: [9:59] Okay. We have orthogonals, the diagonal lines that meet at the vanishing point. We know the vanishing point is a point on the horizon line, and we understand how these correspond to the viewer and to creating an illusion of space.

Dr. Zucker: [10:15] Let’s take a look at what somebody who can really draw does with this. Let’s take a look at Leonardo da Vinci’s “The Last Supper.”

Dr. Harris: [10:22] Okay, so not you.

Dr. Zucker: [10:23] Not me at all.

Dr. Harris: [10:24] Someone who can really draw. Okay. Here is Leonardo’s “Last Supper.” Immediately, the interesting thing is that after Brunelleschi discovers linear perspective, artists like Masaccio begin to use it, but they realize that in addition to creating an illusion of space, it has a way of bringing the viewer’s attention to the vanishing point.

[10:46] So artists begin to use it not just to create that illusion, but they begin to use it expressively, and that’s what we really see here with Leonardo.

Dr. Zucker: [10:53] So not only is Leonardo creating this beautiful perspectival space, but he’s also focusing our attention on Jesus Christ at the center, who is the vanishing point.

Dr. Harris: [11:00] Right. It brings our eye, our attention to the divine.

Dr. Zucker: [11:09] Here, we see Leonardo’s “Last Supper.” We can certainly just intuitively make out the orthogonals and the vanishing point, but let’s go down and really look at the diagram.

Dr. Harris: [11:13] Okay. Here we are.

Dr. Zucker: [11:16] It’s interesting. Their eye level all across is basically at the horizon line. Of course, we see the vanishing point, the point where all of the orthogonals intersect, which is right here. We have all of these lines that are moving across the surface of this wall, and they are all bringing our eye right to Jesus Christ in the center.

Dr. Harris: [0:00] And those lines are orthogonal lines. There you have it.

Dr. Zucker: [11:43] That’s how it works.

Dr. Harris: [11:43] Linear perspective.

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