0:00:07.653,0:00:09.534
If you're ever walking down the street

0:00:09.534,0:00:13.384
and come across an oddly stretched out[br]image, like this,

0:00:13.384,0:00:17.004
you'll have an opportunity[br]to see something remarkable,

0:00:17.004,0:00:20.494
but only if you stand in exactly[br]the right spot.

0:00:20.494,0:00:25.493
That happens because these works[br]employ a technique called anamorphosis.

0:00:25.493,0:00:28.765
Anamorphosis is a special case[br]of perspective art,

0:00:28.765,0:00:31.794
where artists represent realistic[br]three-dimensional views

0:00:31.794,0:00:34.115
on two-dimensional surfaces.

0:00:34.115,0:00:35.395
Though it's common today,

0:00:35.395,0:00:40.126
this kind of perspective drawing has only[br]been around since the Italian Renaissance.

0:00:40.126,0:00:43.396
Ancient art often showed all figures[br]on the same plane,

0:00:43.396,0:00:47.145
varying in size by symbolic importance.

0:00:47.145,0:00:51.304
Classical Greek and Roman artists realized[br]they could make objects seem further

0:00:51.304,0:00:53.155
by drawing them smaller,

0:00:53.155,0:00:58.535
but many early attempts at perspective[br]were inconsistent or incorrect.

0:00:58.535,0:01:00.536
In 15th century Florence,

0:01:00.536,0:01:02.819
artists realized the illusion [br]of perspective

0:01:02.819,0:01:05.954
could be achieved with higher degrees[br]of sophistication

0:01:05.954,0:01:08.946
by applying mathematical principles.

0:01:08.946,0:01:13.415
In 1485, Leonardo da Vinci [br]manipulated the mathematics

0:01:13.415,0:01:17.576
to create the first known [br]anamorphic drawing.

0:01:17.576,0:01:20.848
A number of other artists later[br]picked up the technique,

0:01:20.848,0:01:25.526
including Hans Holbein [br]in "The Ambassadors."

0:01:25.526,0:01:29.416
This painting features a distorted[br]shape that forms into a skull

0:01:29.416,0:01:32.665
as the viewer approaches from the side.

0:01:32.665,0:01:35.756
In order to understand how artists[br]achieve that effect,

0:01:35.756,0:01:39.836
we first have to understand how [br]perspective drawings work in general.

0:01:39.836,0:01:41.726
Imagine looking out a window.

0:01:41.726,0:01:44.697
Light bounces off objects [br]and into your eye,

0:01:44.697,0:01:47.197
intersecting the window along the way.

0:01:47.197,0:01:51.437
Now, imagine you could paint the image[br]you see directly onto the window

0:01:51.437,0:01:55.734
while standing still and keeping[br]only one eye open.

0:01:55.734,0:01:59.425
The result would be nearly[br]indistinguishable from the actual view

0:01:59.425,0:02:02.457
with your brain adding depth[br]to the 2-D picture,

0:02:02.457,0:02:04.457
but only from that one spot.

0:02:04.457,0:02:06.627
Standing even just a bit off[br]to the side

0:02:06.627,0:02:10.384
would make the drawing [br]lose its 3-D effect.

0:02:10.384,0:02:12.307
Artists understand that [br]a perspective drawing

0:02:12.307,0:02:16.098
is just a projection[br]onto a 2-D plane.

0:02:16.098,0:02:20.529
This allows them to use math to come up[br]with basic rules of perspective

0:02:20.529,0:02:23.971
that allow them to draw without a window.

0:02:23.971,0:02:26.498
One is that parallel lines, like these,

0:02:26.498,0:02:33.118
can only be drawn as parallel if they're[br]parallel to the plane of the canvas.

0:02:33.118,0:02:36.779
Otherwise, they need to be drawn[br]converging to a common point

0:02:36.779,0:02:40.263
known as the vanishing point.

0:02:40.263,0:02:43.009
So that's a standard perspective drawing.

0:02:43.009,0:02:45.891
With an anamorphic drawing,[br]like "The Ambassadors,"

0:02:45.891,0:02:50.498
directly facing the canvas makes the image[br]look stretched and distorted,

0:02:50.498,0:02:54.069
but put your eye in exactly the right spot[br]way off to the side,

0:02:54.069,0:02:56.917
and the skull materializes.

0:02:56.917,0:02:58.530
Going back to the window analogy,

0:02:58.530,0:03:03.079
it's as if the artist painted [br]onto a window positioned at an angle

0:03:03.079,0:03:04.669
instead of straight on,

0:03:04.669,0:03:08.809
though that's not how Renaissance artists[br]actually created anamorphic drawings.

0:03:08.809,0:03:12.209
Typically, they draw a normal image [br]onto one surface,

0:03:12.209,0:03:14.229
then use a light,

0:03:14.229,0:03:15.470
a grid,

0:03:15.470,0:03:20.123
or even strings to project it[br]onto a canvas at an angle.

0:03:20.123,0:03:23.563
Now let's say you want to make[br]an anamorphic sidewalk drawing.

0:03:23.563,0:03:25.999
In this case, you want to create[br]the illusion

0:03:25.999,0:03:30.430
that a 3-D image has been added[br]seamlessly into an existing scene.

0:03:30.430,0:03:33.250
You can first put a window[br]in front of the sidewalk

0:03:33.250,0:03:35.990
and draw what you want to add [br]onto the window.

0:03:35.990,0:03:39.141
It should be in the same perspective[br]as the rest of the scene,

0:03:39.141,0:03:43.132
which might require the use of those[br]basic rules of perspective.

0:03:43.132,0:03:44.541
Once the drawing's complete,

0:03:44.541,0:03:46.979
you can use a projector placed [br]where your eye was

0:03:46.979,0:03:49.581
to project your drawing down [br]onto the sidewalk,

0:03:49.581,0:03:51.560
then chalk over it.

0:03:51.560,0:03:54.010
The sidewalk drawing [br]and the drawing on the window

0:03:54.010,0:03:57.702
will be nearly indistinguishable[br]from that point of view,

0:03:57.702,0:04:00.090
so viewers' brains will again be tricked

0:04:00.090,0:04:04.291
into believing that the drawing[br]on the ground is three-dimensional.

0:04:04.291,0:04:08.061
And you don't have to project onto[br]a flat surface to create this illusion.

0:04:08.061,0:04:10.321
You can project onto multiple surfaces,

0:04:10.321,0:04:14.002
or assemble a jumble of objects,[br]that from the right point of view,

0:04:14.002,0:04:17.901
appears to be something else entirely.

0:04:17.901,0:04:20.363
All over the planet, you can find[br]solid surfaces

0:04:20.363,0:04:23.732
giving way to strange, wonderful,[br]or terrifying visions.

0:04:23.732,0:04:27.372
From your sidewalk [br]to your computer screen,

0:04:27.372,0:04:30.982
these are just some of the ways[br]that math and perspective

0:04:30.982,0:04:33.432
can open up whole new worlds.