When two lines meet at a point, or vertex, an angle is formed.

当两条线相交在点，即顶点时，就形成了个角。

Here’s a closer look at what happens when we make the folds at this vertex.

下仔细看看我们在这个顶点做折叠时会发生什么。

Now I want you to focus on the vertices of  that triangle, these white dots.

现在我希望你把注意力集中在那个三角形的顶点上，这些白点。

Let's begin with the first step called vertex shading.

让我们从“顶点着色”开始。

V stands for vertices, E for edges, F for faces.

V 代表顶点，E 代表边，F 代表。

Here's a closer look at what happens when we make the falls at this vertex.

下仔细看看我们在这个顶点坠落时会发生什么。

So to our question, can you make it so that every vertex has a red, green and blue neighbor?

那么对于我们的问题，你能让每个顶点都有个红色、绿色和蓝色的邻居吗？

If we add a mountain fold at this vertex, there are three valleys and two mountains.

如果我们在这个顶点加上个山折，就是三个山谷和两个山峰。

So, let's focus on a single vertex.

因此，让我们关注个顶点。

Rearranging a little, you  would take the number of edges minus the number of vertices plus two.

稍微重新排列下，你可以用边的数量减去顶点的数量再加上二。

So we can see here it says, " Consider reducing the number of triangles and consider reducing the work in the vertex shader."

“考虑减少三角形的数量，并考虑减少顶点着色点的工作。”

So the total number of vertices here  would not be N but N plus N choose four total intersection points.

因此，这里的顶点总数不是 N，而是 N 加 N 选择四个交点。

But the key is to treat this as a new graph  where those intersection points are them vertices.

但关键是将其为个新图，其中这些交点是顶点。

Whose corners have vertices (1, 1, 1), (1, 1, -1), on and on and on.

其角有顶点 (1, 1, 1), (1, 1, -1)，等等。

Though in that case, colors were given to pairs of vertices instead of individual ones.

但在这种情况下，颜色被赋予给成对的顶点而不是单个的顶点。

These two stars, which form the vertices of the Summer Triangle along with Deneb, are clearly visible during summer from places in the mid-northern latitudes.

这两颗恒星和天津四起构成了夏季大三角，在夏季从中纬度地区可以清晰地看到。

If I hover over the vertices row, here I can get an idea of, OK, what's the summary for that draw call for the vertices submitted to the scenes?

如果我在顶点行上悬停，我就能够了解那个顶点的绘制调用提交到场景的总数是多少？

To start, take a 2x2 box centered at the origin Its corners around the vertices (1, 1), (1, -1), (-1, 1) and (-1, -1).

首先，取个以原点为中心的 2x2 盒子， 其角围绕顶点 (1, 1)、(1, -1)、(-1, 1) 和 (-1, -1)。

So each step here we're looking at the three neighbors of a given vertex, counting up the red ones, and adding that to a total tally.

因此，这里的每我们都会查看给定顶点的三个邻居，计算红色顶点的数量， 并将其添加到总计数中。

Visually it's like mixing 3 different colors across a triangle, but instead  we're using the three vertex normal directions.

从觉上看， 这就像在三角形上混合 3 种不同的颜色，但我们使用的是三个顶点法线方向。