  We propose an online planning approach for racing that generates the
time-optimal trajectory for the upcoming track section. The resulting
trajectory takes the current vehicle state, effects caused by \acl{3D} track
geometries, and speed limits dictated by the race rules into account. In each
planning step, an optimal control problem is solved, making a
quasi-steady-state assumption with a point mass model constrained by
gg-diagrams. For its online applicability, we propose an efficient
representation of the gg-diagrams and identify negligible terms to reduce the
computational effort. We demonstrate that the online planning approach can
reproduce the lap times of an offline-generated racing line during single
vehicle racing. Moreover, it finds a new time-optimal solution when a deviation
from the original racing line is necessary, e.g., during an overtaking
maneuver. Motivated by the application in a rule-based race, we also consider
the scenario of a speed limit lower than the current vehicle velocity. We
introduce an initializable slack variable to generate feasible trajectories
despite the constraint violation while reducing the velocity to comply with the
rules.
