如何从三个点计算角度? [英] How to calculate an angle from three points?

问题描述

假设你有这个:

P1 = (x=2, y=50)
P2 = (x=9, y=40)
P3 = (x=5, y=20)

假设 P1 是圆的中心点.它总是一样的.我想要由 P2 和 P3 组成的角度，或者换句话说，是 P1 旁边的角度.准确地说是内角.它始终是锐角，因此小于 -90 度.

Assume that P1 is the center point of a circle. It is always the same. I want the angle that is made up by P2 and P3, or in other words the angle that is next to P1. The inner angle to be precise. It will always be an acute angle, so less than -90 degrees.

我想:伙计，那是简单的几何数学.但是我现在已经寻找了大约 6 个小时的公式，只发现人们在谈论复杂的 NASA 东西，比如 arccos 和矢量标量产品的东西.我的头感觉就像在冰箱里.

I thought: Man, that's simple geometry math. But I have looked for a formula for around 6 hours now, and only find people talking about complicated NASA stuff like arccos and vector scalar product stuff. My head feels like it's in a fridge.

这里有一些数学大师认为这是一个简单的问题?我认为编程语言在这里并不重要，但对于那些认为重要的人来说:java 和objective-c.我两个都需要它，但还没有为这些标记它.

Some math gurus here that think this is a simple problem? I don't think the programming language matters here, but for those who think it does: java and objective-c. I need it for both, but haven't tagged it for these.

推荐答案

如果你的意思是P1是顶点的角度那么使用余弦定律 应该起作用:

If you mean the angle that P1 is the vertex of then using the Law of Cosines should work:

arccos((P₁₂²+ P₁₃² - P₂₃²)/(2 *P₁₂ * P₁₃))

arccos((P₁₂² + P₁₃² - P₂₃²) / (2 * P₁₂ * P₁₃))

其中 P₁₂ 是从 P1 到 P2 的段的长度，计算公式为

where P₁₂ is the length of the segment from P1 to P2, calculated by

sqrt((P1_x -P2_x)² +(P1_y -P2_y)²)

sqrt((P1_x - P2_x)² + (P1_y - P2_y)²)

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