我正在使用 C#，在我的程序中，我在 Quaternions 中收到一个 Ridigbody 的四元数，但轴与我使用的轴的方向不对应，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，切换俯仰、偏航和滚动，使其与我的坐标系相对应，将其转换回四元数，然后生成一个旋转矩阵来变换位置。
但是出了点问题，当我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......所以其中一个函数出错了，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;
}