How to Convert Right-Handed to Left-Handed Coordinates and Quaternions In Unity

Converting Coordinates and Vectors

To convert a right-handed vector (assuming that z is up) to left-handed vector (Unity coordinate system), simply swap y and z coordinates.

The following is a method that performs this conversion:

private Vector3 ConvertRightHandedToLeftHandedVector (Vector3 rightHandedVector)
{      
    return new Vector3(rightHandedVector.x, rightHandedVector.z, rightHandedVector.y);
}

Converting Quaternions

To convert a right-handed quaternion to left-handed quaternion:

1. Negate x
2. Swap y and z and negate both

The following is a method that performs this conversion:

private Quaternion ConvertRightHandedToLeftHandedQuaternion (Quaternion rightHandedQuaternion)
{
    return new Quaternion (- rightHandedQuaternion.x,
                           - rightHandedQuaternion.z,
                           - rightHandedQuaternion.y,
                             rightHandedQuaternion.w);
}