a LookAt helper method

QuaternionLookAt.cs

// assumes that the input vectors are normalized and orthogonal
public static Quaternion LookAt(in Vector3 forward, in Vector3 up)
{
  var right = Vector3.Cross(up, forward);

  Quaternion quaternion;
  quaternion.W = (float)Math.Sqrt(1.0f + right.X + up.Y + forward.Z) * 0.5f;
  var w4_recip = 1.0f / (4.0f * quaternion.W);
  quaternion.X = (forward.Y - up.Z) * w4_recip;
  quaternion.Y = (right.Z - forward.X) * w4_recip;
  quaternion.Z = (up.X - right.Y) * w4_recip;
  return quaternion;
}