BlitzBasic.com论坛的Kryzon（死链接）在这里帮助了我：
我正在用SharpDX编写一个相机，并在四元数的帮助下旋转它。
- 相机旋转设置为俯仰（X旋转）、偏航（Y旋转）和滚转（Z旋转），即所谓的"Tiat-Bryan"角度（这些是而不是欧拉角度，它将具有XYX旋转，而不是XYZ）
- 我使用的是左手坐标系：X+是向右的，Y+是向上的，Z+是向下的屏幕
- 如果我绕X旋转（"俯仰"），正值会使相机向下看。如果我绕Y旋转（"偏航"），正值会使相机看起来向左。如果我绕Z轴旋转（"滚动"），相机将顺时针滚动
我已经能够从四元数s中获得俯仰、偏航和滚转。下面的C#代码：
public static class QuaternionExtensions
{
public static Vector3 GetPitchYawRoll(this Quaternion q)
{
return new Vector3(q.GetPitch(), q.GetYaw(), q.GetRoll());
}
public static float GetPitch(this Quaternion q)
{
return q.GetK().GetPitch();
}
public static float GetYaw(this Quaternion q)
{
return q.GetK().GetYaw();
}
public static float GetRoll(this Quaternion q)
{
// This is M12 * M22 of rotation matrix
float xx = q.X * q.X;
float xy = q.X * q.Y;
float zz = q.Z * q.Z;
float wz = q.W * q.Z;
return (float)Math.Atan2(2f * (xy - wz), 1f - 2f * (xx + zz));
}
public static Vector3 GetK(this Quaternion q)
{
float xz = q.X * q.Z;
float wy = q.W * q.Y;
float yz = q.Y * q.Z;
float wx = q.W * q.X;
float xx = q.X * q.X;
float yy = q.Y * q.Y;
return new Vector3(
2f * (xz - wy),
2f * (yz + wx),
1f - 2f * (xx + yy));
}
}
public static class Vector3Extensions
{
public static float GetPitch(this Vector3 v)
{
return (float)-Math.Atan2(v.Y, Math.Sqrt(v.X * v.X + v.Z * v.Z));
}
public static float GetYaw(this Vector3 v)
{
return (float)-Math.Atan2(v.X, v.Z);
}
}
我不知道怎么回事。如何通过指定俯仰、偏航和滚转来获得四元数（例如，从GetPitchYawRoll返回的Vector3中的内容）？
internal static class QuaternionExtensions
{
internal static Vector3 GetYawPitchRollVector(this Quaternion q)
{
return new Vector3(q.GetYaw(), q.GetPitch(), q.GetRoll());
}
private static float GetYaw(this Quaternion q)
{
float x2 = q.X * q.X;
float y2 = q.Y * q.Y;
return (float)Math.Atan2(2f * q.Y * q.W - 2f * q.Z * q.X, 1f - 2f * y2 - 2f * x2);
}
private static float GetPitch(this Quaternion q)
{
return (float)-Math.Asin(2f * q.Z * q.Y + 2f * q.X * q.W);
}
private static float GetRoll(this Quaternion q)
{
float x2 = q.X * q.X;
float z2 = q.Z * q.Z;
return (float)-Math.Atan2(2f * q.Z * q.W - 2f * q.Y * q.X, 1f - 2f * z2 - 2f * x2);
}
}
internal static class Vector3Extensions
{
internal static Quaternion GetYawPitchRollQuaternion(this Vector3 v)
{
float c1 = (float)Math.Cos(-v.Z / 2.0);
float c2 = (float)Math.Cos(-v.Y / 2.0);
float c3 = (float)Math.Cos( v.X / 2.0);
float c1c2 = c1 * c2;
float s1 = (float)Math.Sin(-v.Z / 2.0);
float s2 = (float)Math.Sin(-v.Y / 2.0);
float s3 = (float)Math.Sin( v.X / 2.0);
float s1s2 = s1 * s2;
return new Quaternion(
c1 * s2 * c3 - s1 * c2 * s3,
c1c2 * s3 + s1s2 * c3,
s1 * c2 * c3 + c1 * s2 * s3,
c1c2 * c3 - s1s2 * s3);
}
}
这通常被称为欧拉角，
http://en.wikipedia.org/wiki/Euler_angles
转换的所有变体都可以在https://github.com/erich666/GraphicsGems/blob/master/gemsiv/euler_angle/EulerAngles.c
最初由Ken Shoemake撰写，1993