/// <summary>
/// Return the FRotator orientation corresponding to the direction in which the vector points.
/// Sets Yaw and Pitch to the proper numbers, and sets roll to zero because the roll can't be determined from a vector.
/// </summary>
/// <returns>FRotator from the Vector's direction.</returns>
public FRotator ToOrientationRotator()
{
FRotator r;
// Find yaw.
r.Yaw = FMath.Atan2(Y, X) * (180.0f / FMath.PI);
// Find pitch.
r.Pitch = FMath.Atan2(Z, FMath.Sqrt(X * X + Y * Y)) * (180.0f / FMath.PI);
// Find roll.
r.Roll = 0;
r.DiagnosticCheckNaN("FVector4::Rotation(): Rotator result " + r + " contains NaN! Input FVector4 = " + this);
return(r);
}
/// <summary>
/// Get the FRotator representation of this Quaternion.
/// </summary>
public FRotator Rotator()
{
DiagnosticCheckNaN();
float singularityTest = Z * X - W * Y;
float yawY = 2.0f * (W * Z + X * Y);
float yawX = (1.0f - 2.0f * (FMath.Square(Y) + FMath.Square(Z)));
// reference
// http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/
// this value was found from experience, the above websites recommend different values
// but that isn't the case for us, so I went through different testing, and finally found the case
// where both of world lives happily.
const float singularityThreshold = 0.4999995f;
const float radToDeg = (180.0f) / FMath.PI;
FRotator rotatorFromQuat;
if (singularityTest < -singularityThreshold)
{
rotatorFromQuat.Pitch = -90.0f;
rotatorFromQuat.Yaw = FMath.Atan2(yawY, yawX) * radToDeg;
rotatorFromQuat.Roll = FRotator.NormalizeAxis(-rotatorFromQuat.Yaw - (2.0f * FMath.Atan2(X, W) * radToDeg));
}
else if (singularityTest > singularityThreshold)
{
rotatorFromQuat.Pitch = 90.0f;
rotatorFromQuat.Yaw = FMath.Atan2(yawY, yawX) * radToDeg;
rotatorFromQuat.Roll = FRotator.NormalizeAxis(rotatorFromQuat.Yaw - (2.0f * FMath.Atan2(X, W) * radToDeg));
}
else
{
rotatorFromQuat.Pitch = FMath.FastAsin(2.0f * (singularityTest)) * radToDeg;
rotatorFromQuat.Yaw = FMath.Atan2(yawY, yawX) * radToDeg;
rotatorFromQuat.Roll = FMath.Atan2(-2.0f * (W * X + Y * Z), (1.0f - 2.0f * (FMath.Square(X) + FMath.Square(Y)))) * radToDeg;
}
rotatorFromQuat.DiagnosticCheckNaN("FQuat::Rotator(): Rotator result " + rotatorFromQuat + " contains NaN! Quat = " + this.ToString() +
", YawY = " + yawY + ", YawX = " + yawX);
return(rotatorFromQuat);
}
/// <summary>
/// Return the Quaternion orientation corresponding to the direction in which the vector points.
/// </summary>
/// <returns>Quaternion from the Vector's direction.</returns>
public FQuat ToOrientationQuat()
{
// Essentially an optimized Vector->Rotator->Quat made possible by knowing Roll == 0, and avoiding radians->degrees->radians.
// This is done to avoid adding any roll (which our API states as a constraint).
float yawRad = FMath.Atan2(Y, X);
float pitchRad = FMath.Atan2(Z, FMath.Sqrt(X * X + Y * Y));
float divideByTwo = 0.5f;
float sp, sy;
float cp, cy;
FMath.SinCos(out sp, out cp, pitchRad * divideByTwo);
FMath.SinCos(out sy, out cy, yawRad * divideByTwo);
FQuat rotationQuat;
rotationQuat.X = sp * sy;
rotationQuat.Y = -sp * cy;
rotationQuat.Z = cp * sy;
rotationQuat.W = cp * cy;
return(rotationQuat);
}
