找到两条给定线2D之间的角度 [英] Find the angle between two given lines 2D

问题描述

我得到的输入是4分.

p1 =(x1，y1)，p2 =(x2，y2)，p3 =(x3，y3)，p4 =(x4，y4).

p1=(x1, y1), p2=(x2, y2), p3=(x3, y3), p4=(x4, y4).

现在我已经计算出p1p2，p2p3，p3p4和p4p1之间的距离.

Now I have calculated the distances between p1p2, p2p3, p3p4 and p4p1.

如何计算p1p2和p2p3之间的角度?这就是角度p2. (显示在下面的图片链接中)；

How do I calculate the angle between p1p2 and p2p3 ? which is the angle p2. (shown in image link below);

我尝试过

 acos((p1p2)^2 + (p2p3)^2 - (p1p3)^2)/(2*p1p2*p2p3))*(180/pi)

但这并不准确，我想对4个角度求和，并检查它们的总和是否为360.因此，我永远不会得到一个无理数.

But this is not accurate, I want to sum 4 angles and check if they sum to 360. And this way I'll never get an irrational number.

请帮忙吗?

推荐答案

要获取两个向量之间的夹角，只需使用它们的内积即可:

To get the angle between two vectors, you simply use their inner product:

v1 = p1-p2;
v2 = p3-p2;

归一化为单位向量并取内积:

Normalize to unit vectors and take inner product:

n1 = v1/norm(v1);
n2 = v2/norm(v2);

cos_p2 = dot(n1,n2);

结果角度为

acos(cos_p2)

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