确定平均角度 [英] Determining the average angle

问题描述

我正在开发一个涉及在游戏中获取摄影机角度的应用程序.角度可以是0-359之间的任何值. 0是北，90是东，180是南，等等.我使用的是API，该类在Camera类中具有getAngle()方法.

I'm developing an application that involves getting the camera angle in a game. The angle can be anywhere from 0-359. 0 is North, 90 is East, 180 is South, etc. I'm using an API, which has a getAngle() method in Camera class.

我如何找到不同相机角度之间的平均值. 0和359的真实平均值是179.5.作为摄影机角度，应该是南，但是显然0和359都非常接近北.

How would I find the average between different camera angles. The real average of 0 and 359 is 179.5. As a camera angle, that would be South, but obviously 0 and 359 are both very close to North.

推荐答案

您可以从向量的角度来考虑它.假设θ1和θ2是您用弧度表示的两个角度.然后我们可以确定在这些角度的单位矢量的x和y分量:

You can think of it in terms of vectors. Let θ1 and θ2 be your two angles expressed in radians. Then we can determine the x and y components of the unit vectors that are at these angles:

x1 = sin(θ1)
y1 = cos(θ1)

x2 = sin(θ2)
y2 = cos(θ2)

然后可以将这两个向量相加，并确定结果的x和y分量:

You can then add these two vectors, and determine the x and y components of the result:

x* = x1 + x2
y* = y1 + y2

最后，您可以确定此结果矢量的角度:

Finally, you can determine the angle of this resulting vector:

θavg = tan-1(y*/x*)

，或者甚至更好，请使用atan2(许多语言支持的功能):

or, even better, use atan2 (a function supported by many languages):

θavg = atan2(y*, x*)

您可能必须分别处理y* = 0 和 x* = 0的情况，因为这意味着两个向量指向的方向完全相反(所以平均值"应该是多少? ).

You will probably have to separately handle the cases where y* = 0 and x* = 0, since this means the two vectors are pointing in exactly opposite directions (so what should the 'average' be?).

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