C# 四元数到欧拉角算法-如何转换为'；Y=向上'；在惯用手之间呢？

我有一个在四元数和欧拉角之间转换的算法

    public static Vector3 ToEulerAngles(this Quaternion q)
    {
        // Store the Euler angles in radians
        Vector3 pitchYawRoll = new Vector3();

        double sqw = q.W * q.W;
        double sqx = q.X * q.X;
        double sqy = q.Y * q.Y;
        double sqz = q.Z * q.Z;

        // If quaternion is normalised the unit is one, otherwise it is the correction factor
        double unit = sqx + sqy + sqz + sqw;
        double test = q.X * q.Y + q.Z * q.W;

        if (test > 0.4999f * unit)                              // 0.4999f OR 0.5f - EPSILON
        {
            // Singularity at north pole
            pitchYawRoll.Y = 2f * (float)Math.Atan2(q.X, q.W);  // Yaw
            pitchYawRoll.X = PI * 0.5f;                         // Pitch
            pitchYawRoll.Z = 0f;                                // Roll
            return pitchYawRoll;
        }
        else if (test < -0.4999f * unit)                        // -0.4999f OR -0.5f + EPSILON
        {
            // Singularity at south pole
            pitchYawRoll.Y = -2f * (float)Math.Atan2(q.X, q.W); // Yaw
            pitchYawRoll.X = -PI * 0.5f;                        // Pitch
            pitchYawRoll.Z = 0f;                                // Roll
            return pitchYawRoll;
        }
        else
        {
            pitchYawRoll.Y = (float)Math.Atan2(2f * q.Y * q.W - 2f * q.X * q.Z, sqx - sqy - sqz + sqw);       // Yaw
            pitchYawRoll.X = (float)Math.Asin(2f * test / unit);                                             // Pitch
            pitchYawRoll.Z = (float)Math.Atan2(2f * q.X * q.W - 2f * q.Y * q.Z, -sqx + sqy - sqz + sqw);      // Roll
        }

        return pitchYawRoll;
    }

---

以下是使用相同偏航、俯仰、横摇定义的更改方法：

public static Quaternion CreateFromYawPitchRoll(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;
    result.X = cosYawOver2 * cosPitchOver2 * cosRollOver2 + sinYawOver2 * sinPitchOver2 * sinRollOver2;
    result.Y = cosYawOver2 * cosPitchOver2 * sinRollOver2 - sinYawOver2 * sinPitchOver2 * cosRollOver2;
    result.Z = cosYawOver2 * sinPitchOver2 * cosRollOver2 + sinYawOver2 * cosPitchOver2 * sinRollOver2;
    result.W = sinYawOver2 * cosPitchOver2 * cosRollOver2 - cosYawOver2 * sinPitchOver2 * sinRollOver2;
    return result;
} 

对于

ToEulerAngles

（未注明奇点）：

我进行了以下测试：

var q = CreateFromYawPitchRoll(0.2f, 0.3f, 0.7f);
var e = ToEulerAngles(q);
var q2 = CreateFromYawPitchRoll(e.Y, e.X, e.Z);

结果如下：

e = (0.3, 0.2, 0.7) //pitch, yaw, roll
q2 = q

---

来源：

四元数和欧拉角与坐标系对齐和头部无关。偏航、俯仰和滚转分别定义围绕z、y和x轴的旋转。轴的方向无关紧要。如果我将其与XNA的Quaternion.CreateFromYawPitchRoll结合使用，则不会得到原始的四元数。然后，这些功能可能使用不同的轴偏航/俯仰/滚动关联。交换euler角度，以便定义匹配。您可以根据我所做的编辑发布一个示例，其中现在包括四元数。CreateFromYawPitchRoll？回答很好，谢谢。奇点是否与最初编写的一样正确？

if（test>0.4999f*单位）//0.4999f或0.5f-ε{//北极俯仰角奇点yawroll.Y=2f*（float）Math.Atan2（q.Y，q.W）；//偏航pitchYawRoll.X=PI*0.5f；//俯仰pitchYawRoll.Z=0f；//滚转返回pitchYawRoll；}

刚刚选中，PI不会产生正确的结果。例如，来自YawPitchRoll（（float）Math.PI，0f，0f）

测试的
必须是
=q.X*q.Z-q.W*q.Y
。然而，关于奇点值，我不是绝对肯定。你最好试一试。那个“测试”的方程式不可能是正确的。它为（0，0，0）和（PI，0，0）生成一个值0。
var q = CreateFromYawPitchRoll(0.2f, 0.3f, 0.7f);
var e = ToEulerAngles(q);
var q2 = CreateFromYawPitchRoll(e.Y, e.X, e.Z);

e = (0.3, 0.2, 0.7) //pitch, yaw, roll
q2 = q