1 Direction: Reflecting Line
The construction is equivalent to the purely minkowskian case we have seen earlier, the only change consists in the reflecting direction (dashed line) which can be arbitrarily chosen.
As expected, the result is a common point which is the center of a circumscribed equilateral hyperbola. It is no more straight, but its assymptotes follow the reflecting direction and its perpendicular .
2 Directions: Reflecting Line and Guide
We introduced a guiding direction for the reflections, which are no more perpendicular to the reflecting direction.
In this case, there is sttill a circumbscribed hyperbola, but it is not equilateral. The assymptotes, now, follow both reflecting and guiding directions, whcih can be interchanged.