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If you're ever walking down the street

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and come across an oddly stretched out
image, like this,

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you'll have an opportunity
to see something remarkable,

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but only if you stand in exactly
the right spot.

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That happens because these works
employ a technique called anamorphosis.

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Anamorphosis is a special case
of perspective art,

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where artists represent realistic
three-dimensional views

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on two-dimensional surfaces.

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Though it's common today,

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this kind of perspective drawing has only
been around since the Italian Renaissance.

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Ancient art often showed all figures
on the same plane,

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varying in size by symbolic importance.

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Classical Greek and Roman artists realized
they could make objects seem further

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by drawing them smaller,

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but many early attempts at perspective
were inconsistent or incorrect.

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In 15th century Florence,

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artists realized the illusion 
of perspective

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could be achieved with higher degrees
of sophistication

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by applying mathematical principles.

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In 1485, Leonardo da Vinci 
manipulated the mathematics

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to create the first known 
anamorphic drawing.

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A number of other artists later
picked up the technique,

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including Hans Holbein 
in "The Ambassadors."

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This painting features a distorted
shape that forms into a skull

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as the viewer approaches from the side.

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In order to understand how artists
achieve that effect,

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we first have to understand how 
perspective drawings work in general.

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Imagine looking out a window.

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Light bounces off objects 
and into your eye,

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intersecting the window along the way.

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Now, imagine you could paint the image
you see directly onto the window

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while standing still and keeping
only one eye open.

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The result would be nearly
indistinguishable from the actual view

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with your brain adding depth
to the 2-D picture,

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but only from that one spot.

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Standing even just a bit off
to the side

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would make the drawing 
lose its 3-D effect.

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Artists understand that 
a perspective drawing

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is just a projection
onto a 2-D plane.

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This allows them to use math to come up
with basic rules of perspective

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that allow them to draw without a window.

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One is that parallel lines, like these,

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can only be drawn as parallel if they're
parallel to the plane of the canvas.

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Otherwise, they need to be drawn
converging to a common point

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known as the vanishing point.

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So that's a standard perspective drawing.

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With an anamorphic drawing,
like "The Ambassadors,"

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directly facing the canvas makes the image
look stretched and distorted,

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but put your eye in exactly the right spot
way off to the side,

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and the skull materializes.

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Going back to the window analogy,

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it's as if the artist painted 
onto a window positioned at an angle

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instead of straight on,

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though that's not how Renaissance artists
actually created anamorphic drawings.

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Typically, they draw a normal image 
onto one surface,

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then use a light,

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a grid,

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or even strings to project it
onto a canvas at an angle.

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Now let's say you want to make
an anamorphic sidewalk drawing.

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In this case, you want to create
the illusion

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that a 3-D image has been added
seamlessly into an existing scene.

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You can first put a window
in front of the sidewalk

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and draw what you want to add 
onto the window.

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It should be in the same perspective
as the rest of the scene,

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which might require the use of those
basic rules of perspective.

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Once the drawing's complete,

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you can use a projector placed 
where your eye was

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to project your drawing down 
onto the sidewalk,

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then chalk over it.

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The sidewalk drawing 
and the drawing on the window

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will be nearly indistinguishable
from that point of view,

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so viewers' brains will again be tricked

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into believing that the drawing
on the ground is three-dimensional.

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And you don't have to project onto
a flat surface to create this illusion.

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You can project onto multiple surfaces,

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or assemble a jumble of objects,
that from the right point of view,

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appears to be something else entirely.

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All over the planet, you can find
solid surfaces

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giving way to strange, wonderful,
or terrifying visions.

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From your sidewalk 
to your computer screen,

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these are just some of the ways
that math and perspective

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can open up whole new worlds.