对向量进行归一化需要什么? [英] What is the need for normalizing a vector?

问题描述

尝试更多地了解向量.

对向量进行归一化需要什么?

What is the need for normalizing a vector?

如果我有一个向量，N = (x, y, z)

If I have a vector, N = (x, y, z)

当你将它归一化时，你实际上得到了什么 - 我知道你必须除以 x/|N|y/|N|&z/|N|.我的问题是，我们为什么要做这件事，我的意思是我们从这个等式中得到了什么?

What do you actually get when you normalize it - I get the idea you have to divide x/|N| y/|N| & z/|N|. My question is, why do we do this thing, I mean what do we get out of this equation?

这样做的意义或内部"目的是什么.

What is the meaning or 'inside' purpose of doing this.

有点数学问题，抱歉，我对这个主题真的不清楚.

A bit of a maths question, I apologize, but I am really not clear in this topic.

推荐答案

这有点像问我们为什么要乘以数字.它总是出现.

That's a bit like asking why we multiply numbers. It comes up all the time.

我们使用的笛卡尔坐标系是正交基(由长度为 1 的向量组成，它们相互正交，基意味着任何向量都可以由这些向量的唯一组合表示)，当你想旋转时您的基础(当您环顾四周时会出现在视频游戏机制中)您使用矩阵，其行和列是正交向量.

The Cartesian coordinate system that we use is an orthonormal basis (consists of vectors of length 1 that are orthogonal to each other, basis means that any vector can be represented by a unique combination of these vectors), when you want to rotate your basis (which occurs in video game mechanics when you look around) you use matrices whose rows and columns are orthonormal vectors.

一旦您开始在线性代数中使用足够多的矩阵，您就会想要正交向量.例子太多了，无法一一列举.

As soon as you start playing around with matrices in linear algebra enough you will want orthonormal vectors. There are too many examples to just name them.

归根结底，我们不需要归一化向量(就像我们不需要需要汉堡包一样，我们可以没有它们，但是谁会去?)，但是 v/|v| 的类似模式经常出现，以至于人们决定给它一个名字和一个特殊的符号(向量上的 ^ 意味着它是一个规范化的向量)作为快捷方式.

At the end of the day we don't need normalized vectors (in the same way as we don't need hamburgers, we could live without them, but who is going to?), but the similar pattern of v / |v| comes up so often that people decided to give it a name and a special notation (a ^ over a vector means it's a normalized vector) as a shortcut.

归一化向量(也称为单位向量)基本上是一个事实.

Normalized vectors (also known as unit vectors) are, basically, a fact of life.

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