The mathematics of sidewalk illusions - Fumiko Futamura

翻译人员: Cissy Yun 校对人员: yue chen

If you're ever walking down the street

当你走在街上

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

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,

你正见证着一件伟大事件

but only if you stand in exactly the right spot.

但是你一定要站对位置

That happens because these works employ a technique called anamorphosis.

这个发生的原因就是 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

艺术家会造就三维的效果

on two-dimensional surfaces.

在的是二维的平面上

Though it's common today,

虽然，如今这十分常见

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

这种透视画法 在意大利文化复兴时代才开始兴起

Ancient art often showed all figures on the same plane,

古时的画作中的物品多是平面的

varying in size by symbolic importance.

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

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

by drawing them smaller,

以把他们画小些来展示

but many early attempts at perspective were inconsistent or incorrect.

但早起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,

十五世纪的弗洛伦萨

artists realized the illusion of perspective

一些艺术家发觉了透视的假象

could be achieved with higher degrees of sophistication

可以被更好的的方式来达到

by applying mathematical principles.

借助的是数学理论

In 1485, Leonardo da Vinci manipulated the mathematics

在1485年时，达芬奇就是利用这一原理

to create the first known anamorphic drawing.

创作了史上第一幅歪像画

A number of other artists later picked up the technique,

而后，很多位艺术家也学会了这种技巧

including Hans Holbein in "The Ambassadors."

比如说，Hans Holbein的 “大使们”

This painting features a distorted shape that forms into a skull

这幅画作中有一个扭曲的骷髅头

as the viewer approaches from the side.

而从侧面，就可看到正常的头颅

In order to understand how artists achieve that effect,

为了领会艺术家是如何造就歪像

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

我们必须先理解透视绘画的基本原理

Imagine looking out a window.

试想一下，往窗外望去

Light bounces off objects and into your eye,

光线从物体的表面反射

intersecting the window along the way.

透过窗户，射进眼睛中

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

现在想象一下把看到的影像 直接画在窗户上

while standing still and keeping only one eye open.

同时要立正不动，并只睁开一只眼

The result would be nearly indistinguishable from the actual view

结果会和实际景像一模一样

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

你的大脑已经把 加深了这二维图像的维度

but only from that one spot.

然而，这种视觉效果只限于从这一点看去

Standing even just a bit off to the side

当向一旁移动一点点时

would make the drawing lose its 3-D effect.

这种三维效果便会消失

Artists understand that a perspective drawing

艺术家认知到了透视画作

is just a projection onto a 2-D plane.

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

这让他们运用数学来达到透视的基本原理

that allow them to draw without a window.

让他们在没有窗户的情况下 也可以作画

One is that parallel lines, like these,

原理之一是： 这样的平行线

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

需要和画布的表面平行

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

不然的话，从正面看 就要将它们画成在某点相交

known as the vanishing point.

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,"

像“大使们”这幅歪像画作

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

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,

但是往旁边移动到一点

and the skull materializes.

就可以看到正常的骷髅头像

Going back to the window analogy,

用刚刚窗上作画的例子来解释

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

骷髅头就想是从侧面在窗上作画一般

instead of straight on,

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,

用光来照射

a grid,

和网格

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

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

你想引起别人的错觉

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

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

你可以先将一扇窗户直面人行道

and draw what you want to add onto the window.

把图像先画在窗上

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

应该与后来的图像有着相同的视角

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

这将会运用到透视的基本原理

Once the drawing's complete,

当画作完成后

you can use a projector placed where your eye was

你可用一个投影仪放置在你眼睛的位置

to project your drawing down onto the sidewalk,

来将你的画作投影到路上

then chalk over it.

你可以用粉笔将轮廓描下

The sidewalk drawing and the drawing on the window

人行道上的画作和窗上的画作

will be nearly indistinguishable from that point of view,

在某一角度上基本上是不可分辨的

so viewers' brains will again be tricked

所以观看者的大脑会再一次被欺骗

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

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,

还可以投射到多个平面上

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

也可以透过堆凑很多物品来形成错觉

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

世界各地有很多马路

giving way to strange, wonderful, or terrifying visions.

被画上各种奇形怪状，栩栩如生的图像

From your sidewalk to your computer screen,

无论从人行道上 还是在电脑上观看

these are just some of the ways that math and perspective

这些画作都是因为数学原理和透视法则

can open up whole new worlds.

结合后 创造出的无限可能