>欧拉
我正在使用C#,在我的程序中,我收到四元数中的一个四元体,但该轴不对应于我使用的轴的方向,所以我想旋转四元数。 为了做到这一点,我将四元数转换为欧拉角,切换音高,偏航和滚动,使其与我的坐标系相关,将其转换回四元数,然后生成一个旋转矩阵来转换位置。
然而,事情出错了,当我只是将相同的输入从四元数转换为欧拉,并返回时,我得到另一个四元数...所以其中一个函数做错了,我不知道在哪里...
Quaternion q = new Quaternion(-0.4, -0.7, -0.8, 0.5);
double yaw = 0, pitch = 0, roll = 0;
toEuler(q, ref yaw, ref pitch, ref roll);
Quaternion quat = ToQ((float)(yaw), (float)(pitch), (float)(roll));
private void toEuler(Quaternion q, ref double x, ref double y, ref double z)
{
double test = q.X * q.Y + q.Z * q.W;
if (test > 0.499) // singularity at north pole
{
y = 2.0F * System.Math.Atan2(q.X, q.W);
z = Math.PI / 2.0F;
x = 0.0F;
return;
}
if (test < -0.499) // singularity at south pole
{
y = -2.0F * System.Math.Atan2(q.X, q.W);
z = -Math.PI / 2.0F;
x = 0.0F;
return;
}
double sqx = q.X * q.X;
double sqy = q.Y * q.Y;
double sqz = q.Z * q.Z;
y = System.Math.Atan2(2.0F * q.Y * q.W - 2.0 * q.X * q.Z, 1.0F - 2.0 * sqy - 2.0 * sqz);
z = System.Math.Asin(2.0F * test);
x = System.Math.Atan2(2.0 * q.X * q.W - 2.0 * q.Y * q.Z, 1.0F - 2.0 * sqx - 2.0 * sqz);
}
public Quaternion ToQ(float yaw, float pitch, float roll)
{
float rollOver2 = roll * 0.5f;
float sinRollOver2 = (float)Math.Sin((double)rollOver2);
float cosRollOver2 = (float)Math.Cos((double)rollOver2);
float pitchOver2 = pitch * 0.5f;
float sinPitchOver2 = (float)Math.Sin((double)pitchOver2);
float cosPitchOver2 = (float)Math.Cos((double)pitchOver2);
float yawOver2 = yaw * 0.5f;
float sinYawOver2 = (float)Math.Sin((double)yawOver2);
float cosYawOver2 = (float)Math.Cos((double)yawOver2);
Quaternion result = new Quaternion();
result.W = cosYawOver2 * cosPitchOver2 * cosRollOver2 + sinYawOver2 * sinPitchOver2 * sinRollOver2;
result.X = cosYawOver2 * sinPitchOver2 * cosRollOver2 + sinYawOver2 * cosPitchOver2 * sinRollOver2;
result.Y = sinYawOver2 * cosPitchOver2 * cosRollOver2 - cosYawOver2 * sinPitchOver2 * sinRollOver2;
result.Z = cosYawOver2 * cosPitchOver2 * sinRollOver2 - sinYawOver2 * sinPitchOver2 * cosRollOver2;
return result;
}
你的四元数似乎没有标准化。 代表轮换的四元数应该有标准1。
确保你在转换“to”和“from”时使用相同的欧拉天使。
你可以从Ken Shoemake找到很好的参考代码http://tog.acm.org/resources/GraphicsGems/gemsiv/euler_angle/
和“欧拉角转换”Ken Humamake出自“Graphics Gems”系列
为了扩大Ben的答案,通过除以平方和的平方根来归一化四元数。
如果您需要旋转四元数并保持其长度,我建议使用四元数进行旋转。 维基百科有一个很好的网页:https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
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