logo标签列表

在Unity3d引擎中，欧拉角和四元数之间的转换

c#mathunity-game-enginequaternionseuler-angles
4

我使用了两个例子（也是从这个网站上找的），但结果与Unity所说的不同。

Quaternion.Euler和.eulerAngles是Unity的函数。FromQ函数不执行奇异性检查，而FromQ2函数则会执行。

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 有人能纠正一下这段代码吗？我需要的代码能返回与Unity函数返回值相同的值。
更新：
修复后的代码在这里：http://pastebin.com/riRLRvch。 FromQ和ToQ两个函数都能正常工作。但是我遇到了一个奇异点的问题，无法正确检测到奇异点。
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。对于(90,50,0) - (0.6,0.3,-0.3,0.6)同样如此。

我只看到一种解决方案 - 将“test”计算为xw-yz。但我不确定这是否正确。

如何修复它？

在非单位方法中，您是按照什么顺序应用欧拉旋转的？根据Unity文档：“返回一个旋转，该旋转围绕Z轴旋转z度，围绕X轴旋转x度，并围绕Y轴旋转y度（按照此顺序）。如果您的比较方法不遵循相同的ZXY顺序，那么您的四元数可能不匹配。" - Jerdak
可能吧。我真的不理解我的任务的数学解决方案，所以我无法确定我使用的函数计算角度的顺序。代码没有给我答案。 - Vlad
我是程序员，我不擅长数学，因此我无法自己找到解决方案。 - Vlad
4个回答
11

我已经找到解决方案。

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;
}
1
你测试过这个代码吗？在我的Unity3D（OSX上的3.5.3f3版本）中，它产生了稍微不同的结果。例如：Quaternion q = new Quaternion(-0.4850f, 0.3952f, -0.6186f, -0.4753f);输出（"F4"）： Unity3D: (71.8047, 45.9338, 139.0386) Vlad: (71.8019, 45.9317, 139.0367) - user1323995
@user1323995 我通过将“bruteforced”欧拉角转换为四元数，然后再转回来进行了测试，结果足够精确。 - Vlad
4

这个问题已经三年了，但我需要同样的代码，这里发布的代码似乎都不正确，所以我进行了调整，并找到了这个：

public static Quaternion Euler(float yaw, float pitch, float roll) {
        yaw*=Mathf.Deg2Rad;
        pitch*=Mathf.Deg2Rad;
        roll*=Mathf.Deg2Rad;

        double yawOver2 = yaw * 0.5f;
        float cosYawOver2 = (float)System.Math.Cos(yawOver2);
        float sinYawOver2 = (float)System.Math.Sin(yawOver2);
        double pitchOver2 = pitch * 0.5f;
        float cosPitchOver2 = (float)System.Math.Cos(pitchOver2);
        float sinPitchOver2 = (float)System.Math.Sin(pitchOver2);
        double rollOver2 = roll * 0.5f;
        float cosRollOver2 = (float)System.Math.Cos(rollOver2);
        float sinRollOver2 = (float)System.Math.Sin(rollOver2);            
        Quaternion result;
        result.w = cosYawOver2 * cosPitchOver2 * cosRollOver2 + sinYawOver2 * sinPitchOver2 * sinRollOver2;
        result.x = sinYawOver2 * cosPitchOver2 * cosRollOver2 + cosYawOver2 * sinPitchOver2 * sinRollOver2;
        result.y = cosYawOver2 * sinPitchOver2 * cosRollOver2 - sinYawOver2 * cosPitchOver2 * sinRollOver2;
        result.z = cosYawOver2 * cosPitchOver2 * sinRollOver2 - sinYawOver2 * sinPitchOver2 * cosRollOver2;

        return result;
}

根据一些快速测试，这与Quaternion.Euler完全匹配。
0
这是我的解决方案。它非常接近于Unity的Quaternion.Euler和quaternion.eulerAngles。差异很小，对于任何应用程序都不应该有影响。
public static Vector3 QuaternionToEuler(Quaternion q)
{
    Vector3 euler;

    // if the input quaternion is normalized, this is exactly one. Otherwise, this acts as a correction factor for the quaternion's not-normalizedness
    float unit = (q.x * q.x) + (q.y * q.y) + (q.z * q.z) + (q.w * q.w);

    // this will have a magnitude of 0.5 or greater if and only if this is a singularity case
    float test = q.x * q.w - q.y * q.z;

    if (test > 0.4995f * unit) // singularity at north pole
    {
        euler.x = Mathf.PI / 2;
        euler.y = 2f * Mathf.Atan2(q.y, q.x);
        euler.z = 0;
    }
    else if (test < -0.4995f * unit) // singularity at south pole
    {
        euler.x = -Mathf.PI / 2;
        euler.y = -2f * Mathf.Atan2(q.y, q.x);
        euler.z = 0;
    }
    else // no singularity - this is the majority of cases
    {
        euler.x = Mathf.Asin(2f * (q.w * q.x - q.y * q.z));
        euler.y = Mathf.Atan2(2f * q.w * q.y + 2f * q.z * q.x, 1 - 2f * (q.x * q.x + q.y * q.y));
        euler.z = Mathf.Atan2(2f * q.w * q.z + 2f * q.x * q.y, 1 - 2f * (q.z * q.z + q.x * q.x));
    }

    // all the math so far has been done in radians. Before returning, we convert to degrees...
    euler *= Mathf.Rad2Deg;

    //...and then ensure the degree values are between 0 and 360
    euler.x %= 360;
    euler.y %= 360;
    euler.z %= 360;

    return euler;
}

public static Quaternion EulerToQuaternion(Vector3 euler)
{
    float xOver2 = euler.x * Mathf.Deg2Rad * 0.5f;
    float yOver2 = euler.y * Mathf.Deg2Rad * 0.5f;
    float zOver2 = euler.z * Mathf.Deg2Rad * 0.5f;

    float sinXOver2 = Mathf.Sin(xOver2);
    float cosXOver2 = Mathf.Cos(xOver2);
    float sinYOver2 = Mathf.Sin(yOver2);
    float cosYOver2 = Mathf.Cos(yOver2);
    float sinZOver2 = Mathf.Sin(zOver2);
    float cosZOver2 = Mathf.Cos(zOver2);

    Quaternion result;
    result.x = cosYOver2 * sinXOver2 * cosZOver2 + sinYOver2 * cosXOver2 * sinZOver2;
    result.y = sinYOver2 * cosXOver2 * cosZOver2 - cosYOver2 * sinXOver2 * sinZOver2;
    result.z = cosYOver2 * cosXOver2 * sinZOver2 - sinYOver2 * sinXOver2 * cosZOver2;
    result.w = cosYOver2 * cosXOver2 * cosZOver2 + sinYOver2 * sinXOver2 * sinZOver2;

    return result;
}
...然后确保度数值在-360和360之间。 - Anton Petrov
0
这可能只是一个部分答案，但这里是"ToQ() = Quaternion.Euler()"：
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;
}

你问题中的“FromQ”部分是另一回事。欧拉角比较很麻烦。

我也修复了FromQ。请看开头。 - Vlad
网页内容由stack overflow 提供, 点击上面的
可以查看英文原文，
原文链接