[MUSIC PLAYING]
SPEAKER 1: So this is a video about the elements
of linear perspective with a little bit of history
thrown in.
SPEAKER 2: I love linear perspective.
SPEAKER 1: It's hard not to love linear perspective.
It's like this magic formula.
SPEAKER 2: Well, look what even Paolo Uccello
was able to do just a few decades
after linear perspective was first discovered.
SPEAKER 1: So linear perspective is
a way of recreating the three-dimensional world
on a two-dimensional surface.
And it's really accurate.
SPEAKER 2: Well, 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.
SPEAKER 1: No Photoshop.
SPEAKER 2: No Photoshop.
SPEAKER 1: So let's give a little bit
of historical background, and then we'll
talk about how it's done.
SPEAKER 2: OK.
So let's start first with what the problem was.
SPEAKER 1: OK.
So here we have a painting from the early 1300s
by an artist named Duccio, who's painting at Siena.
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.
SPEAKER 2: OK.
So what you're saying is that 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.
And so 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 is that Duccio is not
constructing that architectural space
in a way that looks logical to our eye.
SPEAKER 1: And 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.
SPEAKER 2: OK.
But before we leave the Duccio, let's
spend just a moment being kind of unfair
and finding what's wrong.
SPEAKER 1: OK.
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.
So none of this is really making sense.
SPEAKER 1: Right.
It's not a rational space.
And there's this increasing interest
in the 1400s in rationalism.
SPEAKER 2: That's the period that we really
call the Renaissance.
SPEAKER 1: Right.
The early Renaissance.
And so in Florence in 1420, Brunelleschi-- and let's
put up a picture of Brunelleschi.
SPEAKER 2: OK.
So he's right here, Filippo Brunelleschi.
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.
SPEAKER 2: So he was a genius.
SPEAKER 1: He was a Renaissance man.
SPEAKER 2: 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,
and he wanted to be able to sketch them accurately.
And he developed this system, linear perspective,
as a way of doing that.
SPEAKER 1: And 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.
SPEAKER 2: So he publishes a book called On Painting
in 1435, and we have a later version
of that book right here.
And inside that book, he really gives the formula
for linear perspective, and that's what we have here.
So let's just spend a moment talking
about how this system works.
SPEAKER 1: OK.
So let's go down here, and let's actually
do a diagram of linear perspective.
SPEAKER 2: OK.
Now I cannot do Paolo Uccello's chalice,
but I can draw a basic linear perspectival structure.
SPEAKER 1: OK, go for it.
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.
There's a vanishing point, there is a horizon line,
and there are orthogonals.
So let's start off with just creating a simple interior.
I'm going to draw just a rectangle here.
SPEAKER 1: So this is your painting.
This is your flat surface.
SPEAKER 2: That's exactly right.
And I'm going to decide that the vanishing point needs
to be pretty much in the middle.
SPEAKER 1: OK.
SPEAKER 2: So I'm putting the vanishing point right
about here.
SPEAKER 1: OK.
SPEAKER 2: OK?
Now let's see.
SPEAKER 1: Why don't you label that VP
so we remember it's vanishing point.
SPEAKER 2: OK.
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.
And these, one could think of as kind of floorboards in a room,
right?
And artists had been able to do this long
before linear perspective.
Artists had never had a problem with this.
SPEAKER 1: Right.
Well, that's because they were constructing it intuitively.
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.
Or the floorboards look as though they would meet.
So it's kind of intuitive.
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.
We'll just make it very simple here.
So I'll put in a couple more verticals right here.
And then I'm simply going to have all of this
meet in the middle at that vanishing point.
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.
And voila.
You can sort of see a window--
SPEAKER 1: OK.
I've got a window.
SPEAKER 2: --beginning to form.
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.
Because you know intuitively the horizontal lines
have to get closer together as they go back in space.
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.
SPEAKER 1: Which happened often, actually,
in paintings from the Trecento.
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.
SPEAKER 2: Or appear that way, at least.
SPEAKER 1: Right.
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.
So I'm just going to put it here.
It's at the same level as the vanishing point, right?
And so we would call this, of course, what?
This is H. This is the horizon line.
And I missed it, but there it is.
SPEAKER 1: OK.
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.
SPEAKER 2: That's right.
And have it connect to each of those floorboards, right?
And so as you can see, what's happening
is that that angle becomes more extreme as I move across.
Right?
And 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?--
going straight across.
SPEAKER 1: I see it.
SPEAKER 2: Then I can draw a second one
at that second intersection right there, and so forth.
And they get more and more compressed
as I go back in space.
And the illusion should be, then,
a kind of compression in space.
So I think this will become more clear if I just
do a little bit of erasing now.
SPEAKER 1: OK.
While you're erasing, I want to talk about that word illusion.
SPEAKER 2: OK.
SPEAKER 1: Because I think it's key to everything here.
SPEAKER 2: Absolutely.
SPEAKER 1: 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.
So in a way, you don't see the two-dimensional surface.
A two-dimensional surface becomes
something you look through to a world that
is a continuation of our own world.
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.
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?
SPEAKER 1: So even in this rough way here on this tablet,
this is working, basically.
SPEAKER 2: It actually couldn't be rougher, could it?
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.
SPEAKER 1: Now what about putting figures in?
SPEAKER 2: Ah.
So now you're really asking for trouble here.
SPEAKER 1: I'm sorry.
Can you do that?
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.
So I would put that figure in just about here.
SPEAKER 1: And what if you put a figure more in the foreground
or more in the background?
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.
But of course, now they would be larger.
SPEAKER 1: Right.
So I think this is the part that's counter-intuitive.
The heads are on the same level, and it's
the feet that are on different levels.
SPEAKER 2: That's exactly right.
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.
SPEAKER 1: OK.
So 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.
SPEAKER 2: Let's take a look at what
somebody who can really draw does with this.
SPEAKER 1: OK.
SPEAKER 2: Let's take a look at Leonardo da Vinci's
The Last Supper.
SPEAKER 1: OK.
So not you.
SPEAKER 2: Not me at all.
SPEAKER 1: Someone who can really draw.
OK.
So 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.
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.
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.
SPEAKER 1: Right.
It brings our eye, our attention to the divine.
SPEAKER 2: So here we see Leonardo's Last Supper,
and we can certainly just intuitively make out
the orthogonals and the vanishing point.
But let's go down and really look at the diagram.
SPEAKER 1: OK.
Here we are.
SPEAKER 2: So it's interesting.
Their eye level all across is basically at the horizon line.
And of course, we see the vanishing point,
the point where all of the orthogonals intersect,
which is right here.
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.
SPEAKER 1: And those lines are orthogonal lines.
And there you have it.
SPEAKER 2: That's how it works.
SPEAKER 1: Linear perspective.
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