c# - Unity3d エンジンのような Euler <=> Quaternion 間の変換

Question

私は 2 つの例を使用しました (こちらのサイトからも) が、結果は Unity と言ったものと同じではありません。

Quaternion.Euler と .eulerAngles は Unity 関数です。FromQ は特異点チェックを実行しませんが、FromQ2 は実行します。

結果：

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()

コードはこちら: http://pastebin.ru/eAlTHdYf

誰でもこのコードを修正できますか? Unity 関数が返す値と同じ値を返すコードが必要です。

アップデート

ここに固定コードがあります: http://pastebin.com/riRLRvch . 両方の機能 (FromQ と ToQ) はうまく機能します。しかし、私は特異点に問題があります。特異点を正しく検出できません。

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 は正しい結果を計算できないため、ここに特異点があります。(90, 50, 0) - (0.6, 0.3, -0.3, 0.6) も同様です。

解決策は 1 つだけです。"test" を xw-yz として計算します。しかし、これが正しいかどうかはわかりません。

修正方法は？

Answer 1

私は解決策を見つけました

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;
}

Answer 2

この質問はほぼ3年前のものですが、同じコードが必要で、ここに投稿されたものは間違っているようだったので、微調整してこれを見つけました:

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;
}

いくつかの簡単なテストによると、これは Quaternion.Euler 100% と一致します。

Answer 3

これは部分的な答えに値するだけかもしれませんが、ここに「ToQ（）= Quaternion.Euler（）」があります。

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;
} 

あなたの質問の「FromQ」の部分は別の問題です。オイラー角の比較は背後の痛みです。

Answer 4

これが私の解決策です。これは、Unity の Quaternion.Euler および quaternion.eulerAngles に非常に近いものです。不一致は十分に小さいため、どのアプリケーションでも問題になりません。

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;
}