How one-point linear perspective works Speakers: Dr. Steven Zucker & Dr. Beth Harris
How one-point linear perspective works
- Dr. Harris: So this is a video about the elements of linear perspective with a little bit
- of history thrown in. Dr. Zucker: I love linear perspective. Dr. Harris: It's hard not to
- love linear perspective. It's like this magic formula.
- Dr. Zucker: Well, look what even Paolo Uccello was able to do just a few decades
- after linear perspective was first discovered. Dr. Harris: So, linear perspective
- is a way of recreating the 3-dimensional world
- on a 2-dimensional surface and it's really accurate.
- Dr. Zucker: 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.
- Dr. Harris: No PhotoShop. Dr. Zucker: No PhotoShop. Dr. Harris: So, let's give a little bit of
- historical background and then we'll talk about how it's done. Dr. Zucker: Ok, so let's start
- first with what the problem was. Dr. Harris: Ok, so here we have a painting
- from the early 1300s, by an artist named Duccio who is painting in Siena
- and you can see that Duccio is interested in creating
- an earthly space for his figure of the angel Gabriel and Mary
- but that the space doesn't really make sense. Dr. Zucker: Ok, so what you're saying
- is that we have a kind of a real room here if we can see the beams and the ceiling,
- we can see the architecture, we can see the doors, and so he is really
- interested in putting his 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: And I think, you know, it probably
- wasn't a problem for Duccio but it was a problem for artists about a
- hundred years later who had a different goal, and their goal was a
- kind of really accurate realism on that flat surface.
- Dr. Zucker: Ok, but before we leave the Duccio, let's spend just a moment being
- kind of unfair and finding what's wrong. Dr. Harris: Ok. Dr. Zucker: 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 cup of the capitals of these pilasters, so none of this is really
- making any sense. Dr. Harris: Right, it's not a rational space, and there's this
- increasing interest in the 1400s in rationalism.
- Dr. Zucker: That's the period that we really call the Renaissance. Dr. Harris, Right, the early Renaissance.
- And so, in Florence in 1420, Brunelleschi
- - and let's put up a picture of Brunelleschi - Dr. Zucker: Ok, so he is right
- here, Filippo Brunelleschi. Dr. Harris: And he discovers, or somewhat say
- rediscovers - because some think that maybe the Ancient Greeks and Romans had this before -
- but he discovers linear perspective. Dr. Zucker: So, he was
- a genius. Dr. Harris: He was a Renaissance man. Dr. Zucker: 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. Dr. Zucker: And, in
- 1420 in Florence he demonstrated this system and fifteen years
- later, another brilliant Renaissance man, Alberti,
- codified what Brunelleschi had discovered.
- He explained the system of linear perspective for artists. Dr. Zucker: 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 is what we have here. So, let's just spend a moment talking
- about how this system works. Dr. Harris: Ok, so let's go down here
- and let's actually do a diagram of linear perspective. Dr. Zucker: Ok, now I cannot
- do Paolo Uccello's chalice but I can draw a basic
- linear perspectival structure. Dr. Harris: Ok, go for it. Dr. Zucker: 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 is 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.
- Dr. Harris: So this is your painting, this is your flat surface. Dr. Zucker: That is exactly right. And
- I'm going to decide that the vanishing point
- needs to be pretty much in the middle. Dr. Harris: Ok. Dr. Zucker: So, I'm putting the vanishing point
- right about here. Dr. Harris: Ok. Dr. Zucker: Ok. Now, let's see... Dr. Harris: Why don't you label
- that 'VP', so we remember it is vanishing point. Dr. Zucker: Ok, so that is 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
- floor boards in a room, right? And artists have been
- able to do this. Long before linear perspective, artists have never
- had a problem with this. Dr. Harris: Right. Well, that is 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 continue they would meet or the floor boards look
- as though they would meet, so it's kind of intuitive. Dr. Zucker: So, I'm actually going to add not only
- a floor to this room but I am going to put in a couple of windows. We' ll just make it very simple.
- OK, so I'm putting in a couple of more verticles 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. So we see
- a window. Dr. Harris: OK, we've got a window... Dr. Zucker: ... beginning to form. But, now here's the problem.
- The problem was that if you didn't want to have floor boards and instead you wanted to have
- a tiled 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 is 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: Which happened often actually in paintings from the Trecento.
- The idea is that the tiles get smaller and smaller as things generally gets smaller
- and smaller as they move away from us in space. Dr. Zucker: Or appear that way, at least.
- What Alberti wrote down in 'On painting' was is that you need to have a second point in space
- outside the picture plane, that was at the level of your eye. I'm just going to put it here
- at the same level as the vanishing point, we would call this of course, what? This is 'H', this is the
- horizon line, and I missed it but there it is
- 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. Dr. Harris: From the exteriour point.
- Dr.Zucker: That's right, and have it connect to each of those floorboards.
- So as you can see, what's happening is that, that angle is becoming more extreme
- as they move across, and I'm doing it free hand 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 horizontal lines that is at that first intersection, you see that right there, going
- straight across? 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.
- Dr. Harris: While you're erasing I want to talk about that word 'illusion'.
- Because I think it's key to everything here. What artists are looking
- to do, is to create an illusion of reality on this 2-dimensional surface.
- Alberti said a painting should be like a window, so in a way you don't see, the
- 2-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 increadably
- convincing was so important to the artists of the Renaissance, like Masaccio or later
- Piero della Francesca, or Andrea Mantegna. Dr. Zucker: And so, now I'm going to fill in
- a few of these tiles alternating, so you really can get a sense of that floor in space.
- So is that working? Dr. Harris: Even in this rough way here on this tablet, it's working
- basically. Dr. Zucker: 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. Dr. Harris: Now what about putting
- figures in? Dr. Zucker: Ah, so now you're really asking for trouble. Dr. Harris: Sorry, can you
- do that? Dr. Zucker: 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
- so I would put that figure in just about here. Dr. Harris: And what about if you put a figure more
- in the foreground or more in the background? Dr. Zucker: 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 now be larger. Dr. Harris: Right, so I think this is the part that is
- counter intuitive, the heads are on the same level and it's the feet that are on
- different levels. Dr. Zucker: That's exactly right. And Alberti also said that; that eye level,
- that horizon line would ideally also be the viewers eye level so that the perspective
- would really work perfectly. Dr. Harris: Ok, so we have the orthoganals, the diagonal lines
- that meet at the vanishing point, we know that the vanishing point is a point on the
- horizon line and we understand how these correspond to the viewer and to creating
- an illusional space. Dr. Zucker: Let's take a look at what somebody who can really
- draw does with this; Leonardo da Vinci's 'The last supper'. Dr. Harris: Ok, so not you.
- Dr. Zucker: Not me at all. Dr. Harris: Someone who can really draw.
- So here is Leonardo's last supper. Immediately the interesting thing is that after
- Brunelleschi discovers linear perspectiv, artists like Masaccio begin to use it,
- but they realize that in addition to create an illusional space it has a way of
- bringing the viewers attention to the vanishing point, so artists begin to use it,
- not just to create illusion, but they begin to use it expressively and that is what we
- really see here with Leonardo. Dr. Zucker: So not only is Leonardo creating this
- beautiful perspectile space, but he is also focusing our attention on Jesus Christ
- at the center, who is the vanishing point. Dr. Harris: It brings our eye, our attention to the divine.
- Dr. Zucker: 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.
- Dr. Harris: Ok, here we are. Dr. Zucker: 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 were all the orthogonals intersect which is right here and so we have all these
- lines, that are moving across this surface of this wall, and they are all bringing our eyes
- right to Jesus Christ in the center. Dr. Harris: And those lines are orthogonal lines.
- Dr. Harris: And there you have it. Dr. Zucker: That's how it works. Dr. Harris: Linear perspective.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
Have something that's not a question about this content?
This discussion area is not meant for answering homework questions.
Share a tip
When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
Thank the author
This is great, I finally understand quadratic functions!
Have something that's not a tip or thanks about this content?
This discussion area is not meant for answering homework questions.
At 2:33, Sal said "single bonds" but meant "covalent bonds."
For general discussions about Khan Academy, visit our Reddit discussion page.
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
- disrespectful or offensive
- an advertisement
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
- a tip or thanks in Questions
- a question in Tips & Thanks
- an answer that should be its own question