从四元数中提取偏航 [英] Extracting Yaw from a Quaternion

问题描述

我有一个旋转四元数，并且想要提取绕Up轴(偏航角)的旋转角度.我正在使用XNA，据我所知，没有内置功能.最好的方法是什么?

I have a rotation quaternion and want to extract the angle of rotation about the Up axis (the yaw). I am using XNA and as far as I can tell there is no inbuilt function for this. What is the best way to do this?

感谢您的帮助， 韦纳图

Thanks for any help, Venatu

推荐答案

旋转的四元数表示形式是轴线和角度的变化.因此，如果绕轴 x ， y ， z 旋转 r 弧度，则四元数 q 是:

The quaternion representation of rotation is a variation on axis and angle. So if you rotate by r radians around axis x, y, z, then your quaternion q is:

q[0] = cos(r/2);
q[1] = sin(r/2)*x;
q[2] = sin(r/2)*y;
q[3] = sin(r/2)*z;

如果要创建仅绕 y 轴旋转的四元数，可以将 x 和 z 轴归零，然后重新-对四元数进行归一化:

If you want to create a quaternion that only rotates around the y axis, you zero out the x and z axes and then re-normalize the quaternion:

q[1] = 0;
q[3] = 0;
double mag = sqrt(q[0]*q[0] + q[2]*q[2]);
q[0] /= mag;
q[2] /= mag;

如果想要得到的角度:

double ang = 2*acos(q[0]);

这假设四元数表示形式已存储:w，x，y，z.如果q [0]和q [2]都为零或接近零，则四元数应为{1,0,0,0}.

This assumes that the quaternion representation is stored: w,x,y,z. If both q[0] and q[2] are zero, or close to it, the resulting quaternion should just be {1,0,0,0}.

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