Mathematicians estimated it by inscribing polygons in circles.

数学家通过在圆内接多边形来估算个数值。

The circle, which is effectively a Reuleaux polygon with an infinite number of sides, has the largest.

圆是个有效的鲁洛正多边形有无数条边，有最大的面积。

And over the years, more polygon lines were added, making the players look more and more lifelike.

并且经年累月，增加了更多的多边形线条，让球员们看起来越来越逼。

The tangram is a dissection puzzle consisting of seven flat polygons which are put together to form shapes.

七巧板是个小块拼图游戏，由七个扁平的多边形组成，多边形放在起可以形成其他形状。

Importantly, it also works for some polygons with fewer sides, including heptagons, hexagons, and pentagons.

重要的是， 它也适用边数较少的多边形，包括七边形、六边形和五边形。

If a pixel is entirely inside of a polygon, it gets fully colored.

如果个像素完全在多边形内部，它就会完全着色。

The rate at which a computer fills in polygons is called the fillrate.

计算机填充多边形的速率称为填充率。

Admittedly, this is a pretty ugly filled polygon.

诚然，是个非常丑陋的填充多边形。

So no one was bisecting polygons to find Pi ever again.

所以再也没有人通过二分多边形来寻找圆周率了。

Let's switch colors and switch polygons and put squares around these.

让我们切换颜色、切换多边形并在它们周围放置正方形。

This works with larger polygons too.

也适用更大的多边形。

But if the polygon only grazes a pixel, it’ll get a lighter shade.

但是如果多边形只擦过个像素，它会得到个更浅的阴影。

That’s because this algorithm doesn’t need to sort any polygons, which makes it faster.

是因为该算法不需要对任何多边形进行排序，因此速度更快。

They may be triangles or polygons, or different kinds of shapes that you don't normally expect in a building.

它们可能是三角形或多边形，或者您通常不会在建筑物中看到的各种形状。

In short, Z-buffering keeps track of the closest distance to a polygon for every pixel in the scene.

简而言之，Z 缓冲会跟踪场景中每个像素到多边形的最近距离。

Consider this example scene with three overlapping polygons.

考虑个具有三个重叠多边形的示例场景。

But for more complex shapes, triangles are better -- what are called polygons in 3D graphics.

但对更复杂的形状，三角形更好——在 3D 图形中称为多边形。

Look at this beautiful teapot made out of polygons.

看看个由多边形制成的漂亮茶壶。

Although these models may have some smooth curves or squares and polygons, they're actually all  broken down into small triangles.

虽然模型可能有平滑的曲线或正方形和多边形，但它们实际上都被分解成小三角形。

To make things easier to follow, we’re going to color the polygons differently.

为了让事情更容易理解，我们要给多边形涂上不同的颜色。