How one-point linear perspective works

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How one-point linear perspective works발음듣기

[MUSIC PLAYING] SPEAKER 1: So this is a video about the elements of linear perspective with a little bit of history thrown in.발음듣기

SPEAKER 2: I love linear perspective.발음듣기

SPEAKER 1: It's hard not to love linear perspective. It's like this magic formula. 발음듣기

SPEAKER 2: Well, look what even Paolo Uccello was able to do just a few decades after linear perspective was first discovered.발음듣기

SPEAKER 1: So linear perspective is a way of recreating the three-dimensional world on a two-dimensional surface. And it's really accurate. 발음듣기

SPEAKER 2: Well, look at this Paolo Uccello. Look at this Study of a Chalice.발음듣기

This wasn't done on a computer.발음듣기

This was done with pen and ink on paper.발음듣기

SPEAKER 1: No Photoshop.발음듣기

SPEAKER 2: No Photoshop.발음듣기

SPEAKER 1: So let's give a little bit of historical background, and then we'll talk about how it's done.발음듣기

SPEAKER 2: OK. So let's start first with what the problem was.발음듣기

SPEAKER 1: OK. So here we have a painting from the early 1300s by an artist named Duccio, who's painting at Siena.발음듣기

And you can see that Duccio's interested in creating an earthly space for his figure of the Angel Gabriel and Mary, but that the space doesn't really make sense.발음듣기

SPEAKER 2: OK. So what you're saying is that we have kind of a real room here.발음듣기

We can see the beams in the ceiling.발음듣기

We can see the architecture. We can see the doors.발음듣기

And so he's really interested in putting these figures in a real place.발음듣기

The problem is-- and by the way, don't get me wrong. I love Duccio.발음듣기

But the problem is that Duccio is not constructing that architectural space in a way that looks logical to our eye.발음듣기

SPEAKER 1: And I think it probably wasn't a problem for Duccio.발음듣기

But it was a problem for artists about 100 years later who had a different goal.발음듣기

And their goal was a kind of really accurate realism on that flat surface.발음듣기

SPEAKER 2: OK. But before we leave the Duccio, let's spend just a moment being kind of unfair and finding what's wrong.발음듣기

SPEAKER 1: OK.발음듣기

SPEAKER 2: OK. So 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 balusters.발음듣기

So none of this is really making sense.발음듣기

SPEAKER 1: Right. It's not a rational space.발음듣기

And there's this increasing interest in the 1400s in rationalism.발음듣기

SPEAKER 2: That's the period that we really call the Renaissance.발음듣기

SPEAKER 1: Right. The early Renaissance.발음듣기

And so in Florence in 1420, Brunelleschi-- and let's put up a picture of Brunelleschi.발음듣기

SPEAKER 2: OK. So he's right here, Filippo Brunelleschi.발음듣기

SPEAKER 1: And 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.발음듣기

SPEAKER 2: So he was a genius.발음듣기

SPEAKER 1: He was a Renaissance man.발음듣기

SPEAKER 2: He was an architect.발음듣기

He was an engineer. He was a sculptor.발음듣기

And according to tradition, he had gone down to Rome, and he was studying ancient Roman buildings, ruins, and he wanted to be able to sketch them accurately.발음듣기

And he developed this system, linear perspective, as a way of doing that.발음듣기

SPEAKER 1: And in 1420 in Florence, he demonstrated this system.발음듣기

And 15 years later, another brilliant Renaissance man, Alberti, codified what Brunelleschi had discovered.발음듣기

He explained the system of linear perspective for artists.발음듣기

SPEAKER 2: So he publishes a book called On Painting in 1435, and we have a later version of that book right here.발음듣기

And inside that book, he really gives the formula for linear perspective, and that's what we have here.발음듣기

So let's just spend a moment talking about how this system works.발음듣기

SPEAKER 1: OK. So let's go down here, and let's actually do a diagram of linear perspective.발음듣기

SPEAKER 2: OK. Now I cannot do Paolo Uccello's chalice, but I can draw a basic linear perspectival structure.발음듣기

SPEAKER 1: OK, go for it.발음듣기

SPEAKER 2: OK. So first of all, we need to understand that one-point linear perspective, sometimes called scientific perspective, is made up of three basic elements.발음듣기

There's a vanishing point, there is a horizon line, and there are orthogonals.발음듣기

So let's start off with just creating a simple interior.발음듣기

I'm going to draw just a rectangle here.발음듣기

SPEAKER 1: So this is your painting. This is your flat surface. 발음듣기

SPEAKER 2: That's exactly right.발음듣기

And I'm going to decide that the vanishing point needs to be pretty much in the middle.발음듣기

SPEAKER 1: OK.발음듣기

SPEAKER 2: So I'm putting the vanishing point right about here.발음듣기

SPEAKER 1: OK.발음듣기

SPEAKER 2: OK? Now let's see.발음듣기

SPEAKER 1: Why don't you label that VP so we remember it's vanishing point.발음듣기

SPEAKER 2: OK. So that's the vanishing point.발음듣기

Now what I want to do is I want to create a series of rays that move down to the bottom line.발음듣기

And these, one could think of as kind of floorboards in a room, right?발음듣기

And artists had been able to do this long before linear perspective.발음듣기

Artists had never had a problem with this.발음듣기

SPEAKER 1: Right. Well, that's because they were constructing it intuitively.발음듣기

And intuitively, when you look around at the world, you see walls in a room that look as though if they continued they would meet.발음듣기

Or the floorboards look as though they would meet. So it's kind of intuitive.발음듣기

SPEAKER 2: So I'm actually going to add not only a floor to this room, but I'm going to put in a couple of windows.발음듣기

We'll just make it very simple here.발음듣기

So I'll put in a couple more verticals right here.발음듣기

And then I'm simply going to have all of this meet in the middle at that vanishing point.발음듣기

Now I'm going to use an eraser here just to clean this up just a little bit so we can get rid of some of the extraneous lines just to make things a little more clear.발음듣기

And voila. You can sort of see a window-- 발음듣기

SPEAKER 1: OK. I've got a window.발음듣기

SPEAKER 2: --beginning to form.발음듣기

But 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.발음듣기

Because you know intuitively the horizontal lines have to get closer together as they go back in space.발음듣기

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.발음듣기

SPEAKER 1: Which happened often, actually, in paintings from the Trecento.발음듣기

So 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.발음듣기

SPEAKER 2: Or appear that way, at least.발음듣기

SPEAKER 1: Right.발음듣기

SPEAKER 2: So 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.발음듣기

So I'm just going to put it here.발음듣기

It's at the same level as the vanishing point, right?발음듣기

And so we would call this, of course, what?발음듣기

This is H. This is the horizon line.발음듣기

And I missed it, but there it is.발음듣기

SPEAKER 1: OK.발음듣기

SPEAKER 2: OK. And 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-- SPEAKER 1: From the exterior point.발음듣기

SPEAKER 2: That's right. And have it connect to each of those floorboards, right?발음듣기

And so as you can see, what's happening is that that angle becomes more extreme as I move across.발음듣기

Right? And I'm doing it freehand, so it's a little bit hard to see, but you get the point.발음듣기

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?--going straight across.발음듣기

SPEAKER 1: I see it.발음듣기

SPEAKER 2: Then I can draw a second one at that second intersection right there, and so forth.발음듣기

And they get more and more compressed as I go back in space.발음듣기

And the illusion should be, then, a kind of compression in space.발음듣기

So I think this will become more clear if I just do a little bit of erasing now.발음듣기

SPEAKER 1: OK. While you're erasing, I want to talk about that word illusion.발음듣기

SPEAKER 2: OK.발음듣기

SPEAKER 1: Because I think it's key to everything here.발음듣기

SPEAKER 2: Absolutely.발음듣기

SPEAKER 1: What artists are looking to do is to create an illusion of reality on this two-dimensional surface.발음듣기

Alberti said a painting should be like a window.발음듣기

So in a way, you don't see the two-dimensional surface.발음듣기

A two-dimensional surface becomes something you look through to a world that is a continuation of our own world.발음듣기

So 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.발음듣기

SPEAKER 2: And so now I'm just going to fill in a few of these tiles alternating so that you really can get a sense of that floor in space. Whoops. So is that working? 발음듣기

SPEAKER 1: So even in this rough way here on this tablet, this is working, basically.발음듣기

SPEAKER 2: It actually couldn't be rougher, could it? But I think it still makes the point.발음듣기

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.발음듣기

SPEAKER 1: Now what about putting figures in?발음듣기

SPEAKER 2: Ah. So now you're really asking for trouble here.발음듣기

SPEAKER 1: I'm sorry. Can you do that? 발음듣기

SPEAKER 2: I don't know. Let's see. So 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.발음듣기

So I would put that figure in just about here.발음듣기

SPEAKER 1: And what if you put a figure more in the foreground or more in the background?발음듣기

SPEAKER 2: So 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.발음듣기

But of course, now they would be larger.발음듣기

SPEAKER 1: Right. So I think this is the part that's counter-intuitive.발음듣기

The heads are on the same level, and it's the feet that are on different levels.발음듣기

SPEAKER 2: That's exactly right.발음듣기

And 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.발음듣기

SPEAKER 1: OK. So we have orthogonals, the diagonal lines that meet at the vanishing point.발음듣기

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.발음듣기

SPEAKER 2: Let's take a look at what somebody who can really draw does with this.발음듣기

SPEAKER 1: OK.발음듣기

SPEAKER 2: Let's take a look at Leonardo da Vinci's The Last Supper.발음듣기

SPEAKER 1: OK. So not you.발음듣기

SPEAKER 2: Not me at all.발음듣기

SPEAKER 1: Someone who can really draw. OK. So here is Leonardo's Last Supper.발음듣기

Immediately, the interesting thing is that after Brunelleschi discovers linear perspective, artists like Masaccio begin to use it.발음듣기

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.발음듣기

So artists begin to use it not just to create that illusion, but they begin to use it expressively.발음듣기

And that's what we really see here with Leonardo.발음듣기

SPEAKER 2: 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.발음듣기

SPEAKER 1: Right. It brings our eye, our attention to the divine.발음듣기

SPEAKER 2: So here we see Leonardo's Last Supper, and we can certainly just intuitively make out the orthogonals and the vanishing point.발음듣기

But let's go down and really look at the diagram.발음듣기

SPEAKER 1: OK. Here we are.발음듣기

SPEAKER 2: So it's interesting.발음듣기

Their eye level all across is basically at the horizon line.발음듣기

And of course, we see the vanishing point, the point where all of the orthogonals intersect, which is right here.발음듣기

And so 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.발음듣기

SPEAKER 1: And those lines are orthogonal lines. And there you have it. 발음듣기

SPEAKER 2: That's how it works.발음듣기

SPEAKER 1: Linear perspective. [MUSIC PLAYING]발음듣기

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