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## AP®︎/College Art History

### Course: AP®︎/College Art History > Unit 1

Lesson 6: The language of art history# How one-point linear perspective works

Speakers: Dr. Steven Zucker & Dr. Beth Harris. Created by Beth Harris and Steven Zucker.

## Want to join the conversation?

- At2:34Dr. Harris mentions that some may argue the ancient Greeks and Romans utilized some elements of linear perspective. My questions are:

1) Can someone please provide links to these ancient Greek or Roman instances of linear perspective?

2) More importantly, are there reasons why these techniques were "lost" or "under-utilized" after the ancient Greek and Roman cultures until the Renaissance?(23 votes)- 1) I'd like to point out Elucid's Elements book as a source to ancient Greek/Roman instances of linear-perspective. Linear-perspective is a mathematical process that's fairly akin to orthogonal or orthonormal projections of a 3D object onto a 2D axis. The basic mathematical principles of Linear Perspective as later described in the book 'On Painting' were all developed by Greek and Roman society. Particularly, Elucid's element's Book 5: Ratios and Magnitudes as well as Books 2-4 and 6.

http://aleph0.clarku.edu/~djoyce/java/elements/bookV/bookV.html#defs(18 votes)

- We often talk about linear perspective (as is the case in the video) as a "discovery", but is this really correct? Can we call it a discovery in traditional terms, or is it more of an innovation, as other artistic techniques, such as shading, are used to make paintings more realistic?(13 votes)
- I think you have to examine the debate between mathematics being a discovery or an invention. The traditional view of 'copyright' as it pertains to mathematics. The general notion is that facts cannot be copyrighted.

For example, the location of the white house or it's address cannot be copyrighted; nor can my phone number. Math is considered to be a 'fact' and that new mathematical discoveries are just 'uncovering' pre-existing facts. Like for example, a right-angle triangle having at least one degree with 45 degrees is considered a fact that was discovered and could have been found in 'nature' with careful enough observation.

If you look at the book of 'steps' or 'rules' by which to create a linear perspective 'on painting' which is probably akin to a 3D to 2D translation section in a linear algebra textbook, I would describe that book as a publishing of a mathematic discovery of a fact. Infact, linear-perspective in mathematical terms would be an orthogonal projection.

I don't believe there is a significant degree of interpretation or creativity of the linear-perspective process is applied, but rather, a degree of accuracy. The end-result of the linear-perspective painting if the rules/steps are followed I think is more dependent upon the skill of the artist in terms of artistic techniques.(22 votes)

- Is it possible to create an illusion of a four-dimensional reality using our 3-d space (the fourth dimension not being time, but another spatial dimension)?(7 votes)
- Picasso's abstract works is often said to be based of this idea. It shows as example a portrait of a woman face, but like not ordinary single viewpoint but many viewpoints as once that can be looked like a object like in a many sides.(11 votes)

- Does mathematics have something to do with this Linear Perspective?(6 votes)
- When selecting a Horizon Point (HP) outside of the picture, how do you know where to place this on your horizon? Surely, where you place the HP will affect the angle of the rays (~6:55) and thus the height of the intersections therafter.(5 votes)
- From what I understand from the video the Horizon Point (HP) is actually what will determine the Horizon Line (HL). Now again, the way I understand it, the HL is meant to be eye level with the viewer. Take a world for example, using the Equator as the HL. Now if you put the HP Northwest instead of due West, you haven't changed it you have merely rotated it. . . If I really wanted to screw with the intersections, I'd move the vanishing point.(1 vote)

- I am very sorry to bother, But what are Orthogonals? (not Orthographic)(4 votes)
- In this context an orthogonal is a line that seems to recede into the depicted space of a painting but is in fact a diagonal line on the surface of the canvas.(3 votes)

- Does the figures eyes always have to be on the same level as the horizon line? What if in the composition, for example, there is one standing, one sitting, and one laying down? How do I know where to put them acording to the horizon line?(3 votes)
- You would make sure that the eyes of each figure would line up with rays drawn through the external point drawn on the horizon line, so that their perspective would be maintained no matter how big or how close they were.

The reason they put the eyes on the horizon line is for aesthetic reasons.(3 votes)

- Did Alberti base his knowledge of art off the Greeks and the Romans, other painters in his time, or his own works when he wrote "On Painting"?(3 votes)
- Alberti credits the concept of Linear Perspective to Filippo Brunelleschi. He even dedicated the 1436 edition of "On Painting" to Brunelleschi. Although, as an interesting side note... the first real depiction of linear perspective can be found in Ambrogio Lorenzetti's "Annunciation" from 1344 which precedes Alberti's work by nearly a century.

http://en.wikipedia.org/wiki/File:Lorenzetti_Ambrogio_annunciation-_1344..jpg(3 votes)

- Hi....I was sitting in my kitchen looking at a 4 shelf metal stand and trying to draw it...had a hard time in drawing the angles...can I use one-point linear perspective to draw this ?(4 votes)
- Yes, just make the shelves lean towards the vanishing point.(0 votes)

- At6:47, could the point on the horizon be put anywhere?(2 votes)
- Yes, it can go anywhere from the left edge to the right edge, but when you move away from the center it produces the impression of looking in an oblique direction rather than drectly ahead of you. An example is the late Renaissance painting by Tintoretto, "The Finding of the Body of Saint Mark," which has the vanishing point off to the left. Here is the link: http://upload.wikimedia.org/wikipedia/commons/7/71/Jacopo_Tintoretto_001.jpg(2 votes)

## Video transcript

[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. [MUSIC PLAYING]