A computationally cheap method for computing collision-free trajectories with multiple moving obstacles is proposed here while meeting comfort and safety criteria. By avoiding search in the trajectory calculation and instead using a geometrical set to calculate the trajectory, the calculation time is significantly reduced. The geometrical set is calculated by solving a support vector machine problem and solving the SVM problem characterizes maximum separating surfaces between obstacles and the ego vehicle in the time-space domain. The trajectory on the separating surface might not be kinematically feasible. Therefore, a vehicle model and a Newton-Raphson based procedure is proposed to obtain a safe, kinematically feasible trajectory on the separating surface. A roundabout scenario and two take-over scenarios with different configurations are used to investigate the properties of the proposed algorithm. Robustness properties of the proposed algorithm is investigated by a large number of randomly initiated simulation scenarios.