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If you're ever walking down the street and come across an oddly stretched out image, like this,
当你走在街上，突然看见一个奇怪形状的的图案，像这样的，
you'll have an opportunity to see something remarkable, but only if you stand in exactly the right spot.
你正见证着一件伟大事件，但是你一定要站对位置。
That happens because these works employ a technique called anamorphosis.
这个情况发生的原因就是画中运用了歪像原理。
Anamorphosis is a special case of perspective art,
歪像是透视艺术中特殊的一种，
where artists represent realistic three-dimensional views on two-dimensional surfaces.
艺术家会在二维的平面上造就三维的效果。
Though it's common today, this kind of perspective drawing has only been around since the Italian Renaissance.
虽然现如今这种透视画法十分常见，但其实它是在意大利文化复兴时代才开始兴起的。
Ancient art often showed all figures on the same plane, varying in size by symbolic importance.
古时的画作中的物品多是平面的，以大小的不同来使人们认识到其重要与否。
Classical Greek and Roman artists realized they could make objects seem further by drawing them smaller,
古希腊与古罗马的艺术家觉得，他们可以将一样物品的距离感以把他们画小些来展示，
but many early attempts at perspective were inconsistent or incorrect.
但早先对这种透视方法的尝试多数是不连贯和不正确的。
In 15th century Florence, artists realized the illusion of perspective
在十五世纪的佛罗伦萨，一些艺术家发觉了透视的假象
could be achieved with higher degrees of sophistication by applying mathematical principles.
可以借助数学理论以更好的的方式来实现。
In 1485, Leonardo da Vinci manipulated the mathematics to create the first known anamorphic drawing.
在1485年，达芬奇就是利用这一原理创作了史上第一幅歪像画。
A number of other artists later picked up the technique, including Hans Holbein in 'The Ambassadors.'
而后，很多位艺术家也学会了这种技巧，比如说汉斯·荷尔拜因的《大使们》。
This painting features a distorted shape that forms into a skull as the viewer approaches from the side.
这幅画作中有一个扭曲的骷髅头，而从侧面就可看到正常的头颅。
In order to understand how artists achieve that effect, we first have to understand how perspective drawings work in general.
为了领会艺术家是如何造就歪像，我们必须先理解透视绘画的基本原理。
Imagine looking out a window. Light bounces off objects and into your eye, intersecting the window along the way.
试想一下，往窗外望去，光线从物体的表面反射，通过窗户，射进眼睛中。
Now, imagine you could paint the image you see directly onto the window while standing still and keeping only one eye open.
现在想象一下把看到的影像直接画在窗户上，同时要立正不动，并只睁开一只眼。
The result would be nearly indistinguishable from the actual view with your brain adding depth to the 2-D picture, but only from that one spot.
结果会和实际景像一模一样，你的大脑已经把这二维图像的维度加深了，但这种视觉效果只限于从这一点看去。
Standing even just a bit off to the side would make the drawing lose its 3-D effect.
当向一旁移动一点点时，这种三维效果便会消失。
Artists understand that a perspective drawing is just a projection onto a 2-D plane.
艺术家认知到了透视画作就是在二维平面上的投影。
This allows them to use math to come up with basic rules of perspective that allow them to draw without a window.
这使得他们可以用数学来得出基本的透视法则，让他们在没有窗户的情况下也可以作画。
One is that parallel lines, like these, can only be drawn as parallel if they're parallel to the plane of the canvas.
原理之一是，这样的平行线需要和画布的表面平行。
Otherwise, they need to be drawn converging to a common point known as the vanishing point.
不然的话，从正面看就要将它们画成在某点相交，这一点被称为“消失点”。
So that's a standard perspective drawing.
这就是透视画作的标准之一。
With an anamorphic drawing, like 'The Ambassadors,' directly facing the canvas makes the image look stretched and distorted,
像《大使们》这幅歪像画作，正对画作时看到的是扭曲的图像，
but put your eye in exactly the right spot way off to the side, and the skull materializes.
但是往旁边移动到一点就可以看到正常的骷髅头像。
Going back to the window analogy, it's as if the artist painted onto a window positioned at an angle instead of straight on,
用刚刚窗上作画的例子来解释骷髅头，就像是从侧面在窗上作画一般，并不正对着窗户而画上去的，
though that's not how Renaissance artists actually created anamorphic drawings.
但是这并非是文艺复兴时期的艺术家创作歪像画的手法。
Typically, they draw a normal image onto one surface,
他们通常会把一个正常的画像画在一个平面上，
then use a light, a grid, or even strings to project it onto a canvas at an angle.
用光和网格，甚至是线，来将画像在一个角度投影在画布上。
Now let's say you want to make an anamorphic sidewalk drawing.
假设你在人行道上创作一幅歪像图。
In this case, you want to create the illusion that a 3-D image has been added seamlessly into an existing scene.
你想引起别人的错觉，让他们以为一幅三维的画作无缝衔接在了人行道上。
You can first put a window in front of the sidewalk and draw what you want to add onto the window.
你可以先将一扇窗户直面人行道，把图像先画在窗上。
It should be in the same perspective as the rest of the scene, which might require the use of those basic rules of perspective.
这应该与后来的图像有着相同的视角，将会运用到透视的基本原理。
Once the drawing's complete, you can use a projector placed where your eye was
当画作完成后，你可以用一个投影仪放置在你眼睛的位置，
to project your drawing down onto the sidewalk, then chalk over it.
来将你的画作投影到路上，用粉笔将轮廓描下。
The sidewalk drawing and the drawing on the window will be nearly indistinguishable from that point of view,
人行道上的画作和窗上的画作在某一角度上基本上是不可分辨的，
so viewers' brains will again be tricked into believing that the drawing on the ground is three-dimensional.
所以观看者的大脑会再一次被欺骗，他们会认为在地上的画作就是三维的。
And you don't have to project onto a flat surface to create this illusion.
这种错觉不单单可以被投射在单一的平面上。
You can project onto multiple surfaces, or assemble a jumble of objects,
你还可以投射到多个平面上，也可以透过堆凑很多物品来形成错觉，
that from the right point of view, appears to be something else entirely.
从合适的视点还可以看到不同的景象。
All over the planet, you can find solid surfaces giving way to strange, wonderful, or terrifying visions.
世界各地有很多马路被画上各种奇形怪状、栩栩如生的图像。
From your sidewalk to your computer screen, these are just some of the ways that math and perspective can open up whole new worlds.
无论从人行道上还是在电脑上观看，这些画作都是因为数学原理和透视法则结合后创造出的无限可能。
