寻找矢量之间的符号角 [英] Finding Signed Angle Between Vectors

问题描述

你如何找到从向量a到b的有符号角度theta？

How would you find the signed angle theta from vector a to b?

是的，我知道theta = arccos（（ab）/（| a | | b |））。

And yes, I know that theta = arccos((a.b)/(|a||b|)).

但是，这不包含符号（即它不区分顺时针或逆时针旋转）。

However, this does not contain a sign (i.e. it doesn't distinguish between a clockwise or counterclockwise rotation).

我需要能告诉我从a到b旋转的最小角度。正号表示从+ x轴向+ y轴的旋转。相反，负号表示从+ x轴向-y轴的旋转。

I need something that can tell me the minimum angle to rotate from a to b. A positive sign indicates a rotation from +x-axis towards +y-axis. Conversely, a negative sign indicates a rotation from +x-axis towards -y-axis.

assert angle((1,0),(0,1)) == pi/2.
assert angle((0,1),(1,0)) == -pi/2.

推荐答案

如果您的数学中有atan2（）函数选择的库：

If you have an atan2() function in your math library of choice:

signed_angle = atan2(b.y,b.x) - atan2(a.y,a.x)

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