Conversion between Quaternions & Angular (Axis-Angle) Vectors

quaternion-axis-angle-vector.cs

public static Vector3 GetAxis(Quaternion q)
{
  Vector3 v = new Vector3(q.x, q.y, q.z);
  float len = v.magnitude;
  if (len < MathUtil.Epsilon)
    return Vector3.left;

  return v / len;
}

public static float GetAngle(Quaternion q)
{
  return 2.0f * Mathf.Acos(Mathf.Clamp(q.w, -1.0f, 1.0f));
}

public static Quaternion FromAngularVector(Vector3 v)
{
  float len = v.magnitude;
  if (len < MathUtil.Epsilon)
    return Quaternion.identity;

  v /= len;

  float h = 0.5f * len;
  float s = Mathf.Sin(h);
  float c = Mathf.Cos(h);

  return new Quaternion(s * v.x, s * v.y, s * v.z, c);
}

public static Vector3 ToAngularVector(Quaternion q)
{
  Vector3 axis = GetAxis(q);
  float angle = GetAngle(q);

  return angle * axis;
}