欧拉 <=> 之间的转换Unity3d引擎中的四元数 [英] Conversion between Euler <=> Quaternion like in Unity3d engine
问题描述
我已经使用了两个示例(也来自该站点),但结果与那些说 Unity 的不一样.
I've used two examples (from this site too), but results are not the same as those that said Unity.
Quaternion.Euler 和 .eulerAngles 是 Unity 函数.FromQ 不执行奇点检查,FromQ2 执行.
Quaternion.Euler and .eulerAngles are Unity functions. FromQ doesn't perform singularity check, FromQ2 does.
结果:
eulers = (100,55,-11):
Quaternion.Euler(eulers) == (0.6, 0.4, -0.4, 0.5)
ToQ(eulers)); == (0.5, -0.4, 0.2, 0.7) // 0.5, -0.4 right but in wrong order
FromQ(ToQ(eulers)) == (55.0, 100.0, -11.0)
FromQ2(ToQ(eulers)) == (-55.5, -6.3, 71.0) // something right
Quaternion.Euler(eulers).eulerAngles == (80.0, 235.0, 169.0)
FromQ2(Quaternion.Euler(eulers)) == (65.8, 1.9, 99.8)
ToQ(eulers).eulerAngles == (70.0, 286.9, 341.4)
FromQ(Quaternion.Euler(eulers)) == (-65.8, 76.0, 4.6)
It must be:
FromQ() = FromQ2() = .eulerAngles,
ToQ() = Quaternion.Euler()
代码在这里:http://pastebin.ru/eAlTHdYf
谁能更正这个代码?我需要能够返回与 Unity 函数返回的值相同的值的代码.
Can anyone correct this code? I need code that will return the values that are identical to the values that Unity functions returns.
这是固定代码:http://pastebin.com/riRLRvch.这两个函数(FromQ 和 ToQ)运行良好.但我有一个奇点的问题.无法正确检测奇点.
Here is fixed code: http://pastebin.com/riRLRvch. Both functions (FromQ and ToQ) work well. But I have a problem with a singularity. It can't detect the singularity properly.
For example (90, 0, 50) in quaternion is (0.6, -0.3, 0.3, 0.6).
test = x * y + z * w = 0 (must be close to 0.5 or -0.5)
FromQ 无法计算出正确的结果,所以我们在这里有奇点.(90, 50, 0) - (0.6, 0.3, -0.3, 0.6) 相同.
FromQ can't calculate correct result so we have the singularity here. The same for (90, 50, 0) - (0.6, 0.3, -0.3, 0.6).
我只看到一种解决方案 - 将测试"计算为 xw-yz.但我不确定这是否正确.
I see only one solution - calculate "test" as xw-yz. But I'm not sure this is right.
如何解决?
推荐答案
我找到了解决方案
public static Quaternion ToQ (Vector3 v)
{
return ToQ (v.y, v.x, v.z);
}
public static Quaternion ToQ (float yaw, float pitch, float roll)
{
yaw *= Mathf.Deg2Rad;
pitch *= Mathf.Deg2Rad;
roll *= Mathf.Deg2Rad;
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;
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;
}
public static Vector3 FromQ2 (Quaternion q1)
{
float sqw = q1.w * q1.w;
float sqx = q1.x * q1.x;
float sqy = q1.y * q1.y;
float sqz = q1.z * q1.z;
float unit = sqx + sqy + sqz + sqw; // if normalised is one, otherwise is correction factor
float test = q1.x * q1.w - q1.y * q1.z;
Vector3 v;
if (test>0.4995f*unit) { // singularity at north pole
v.y = 2f * Mathf.Atan2 (q1.y, q1.x);
v.x = Mathf.PI / 2;
v.z = 0;
return NormalizeAngles (v * Mathf.Rad2Deg);
}
if (test<-0.4995f*unit) { // singularity at south pole
v.y = -2f * Mathf.Atan2 (q1.y, q1.x);
v.x = -Mathf.PI / 2;
v.z = 0;
return NormalizeAngles (v * Mathf.Rad2Deg);
}
Quaternion q = new Quaternion (q1.w, q1.z, q1.x, q1.y);
v.y = (float)Math.Atan2 (2f * q.x * q.w + 2f * q.y * q.z, 1 - 2f * (q.z * q.z + q.w * q.w)); // Yaw
v.x = (float)Math.Asin (2f * (q.x * q.z - q.w * q.y)); // Pitch
v.z = (float)Math.Atan2 (2f * q.x * q.y + 2f * q.z * q.w, 1 - 2f * (q.y * q.y + q.z * q.z)); // Roll
return NormalizeAngles (v * Mathf.Rad2Deg);
}
static Vector3 NormalizeAngles (Vector3 angles)
{
angles.x = NormalizeAngle (angles.x);
angles.y = NormalizeAngle (angles.y);
angles.z = NormalizeAngle (angles.z);
return angles;
}
static float NormalizeAngle (float angle)
{
while (angle>360)
angle -= 360;
while (angle<0)
angle += 360;
return angle;
}
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