It's not too hard to see that all those possible normal vectors trace out the surface of a sphere.

不难看出，所有这些能的 法线向量都在球体表面上。

The  square could be rotated about that normal vector.

正方形以绕该法线向量旋转。

So, the force normal  is to the right.

，的法线是向右的。

It’s just that the normal line, which is the imaginary line that the angles are relative to, changes.

只是法线，也就是角度相对的假想线，发生了变化。

It's just that the normal line, which is the imaginary line that the angles are relative to, changes.

只是法线，即zoya所附着的假想线，发生了变化。

Because everything about  its shadow comes down to that normal vector.

为它的阴影的一切都归结为法线向量。

It's  only dependent on the cosine of the angle between that normal vector and the vertical, which is  kind of neat.

它仅取决于法线向量与垂直方向之间角度的余弦，这很简洁。

You  could say we only ever want to consider the normal vector that is pointing up, that has a  positive z component.

以说我们只想考虑指向上方、具有正 z 分量的法线向量。

The subject is placed at the rule-of-thirds lines, and there's more space in the direction the subject's facing, allowing what's called lead room.

主体被放置在三分法线上，并且主体面对的方向有更多空间，允许所谓的引导空间。

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

从视觉上看， 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。

Next, we  use a method called barycentric coordinates to produce a smooth gradient of normals across the  surface of a triangle.

接下来，我们使用一种称为重心坐标的方法来在三角形的表面上产生平滑的法线梯度。

Just like mixing the three colors across a triangle  this pixel's normal will be a proportional mix of the three vertex normals of the triangle.

就像在三角形中混合三种颜色一样，这个像素的法线将是三角形的三个顶点法线按比例混合。

Furthermore, when it comes to video game graphics, there are advanced topics such as Shadows, Reflections, UVs, Normal Maps and more.

外，当谈到视频游戏图形时，还有诸如阴影、反射、UV、法线贴图等高级主题。

The direction they face is called the Surface Normal, and we can visualize that direction with a little 3D arrow that’s perpendicular to the polygon’s surface.

它们面对的方向称为表面法线，我们以用一个垂直于多边形表面的小 3D 箭头来视化该方向。

If we just look at one  of those slices, who has a normal vector an angle theta away from the vertical, its shadow  might look something like this.

如果我们只看其中一个切片，其法线向量与垂直方向成 θ 角，它的阴影能看起来像这样。

What seems relevant is the angle  that that normal vector makes with the vertical, with the direction where the light is  coming from, which we might call theta.

看起来相关的是法线向量与垂直方向以及光线来自的方向（我们以称之为 theta）所成的角度。

For a given fragment we take the center of each  pixel and use the vertex normals and coordinates of the pre-rasterized triangle to calculate the  barycentric normal of that particular pixel.

对于给定的片段，我们取每个像素的中心，并使用预光栅化三角形的顶点法线和坐标来计算该特定像素的重心法线。

To figure it out, we use ray tracing with this simplified screen space 3D representation and  bounce the rays off of the lake's pixels using the normal map.

为了解决这个问题，我们使用光线追踪和这个简化的屏幕空间 3D 表示，并使用法线贴图将光线从湖面像素上反射回来。

So, in order to produce smooth shading, instead of using surface normals, we use one normal for  each vertex calculated using the average of the normals of the adjacent triangles.

， 为了产生平滑着色，我们不使用表面法线， 而是使用相邻三角形的法线平均值计算的每个顶点使用一条法线。

One key problem with it is that the triangles  within an object each have only a single normal, and thus each triangle will share the  same color throughout the triangle's surface.

一个关键问题是，一个物体内的每个三角形都只有一个法线，每个三角形的整个表面都会共享相同的颜色。