This paper presents a novel path planning algorithm for on-road autonomous driving. The algorithm targets long and wide vehicles, in which the overhangs (i.e., the vehicle chassis extending beyond the front and rear wheelbase) can endanger other vehicles, pedestrians, or even the vehicle itself. The vehicle motion is described in a road-aligned coordinate frame. A novel method for computing the vehicle limits is proposed guaranteeing feasibility of the planned path when converted back into the original coordinate frame. The algorithm is posed as a convex optimization that takes into account the exact dimensions of the vehicle and the road, while minimizing the amount of overhang outside of the drivable surface. The results of the proposed algorithm are compared in a simulation of a real road scenario against a centerline tracking scheme. The results show a significant decrease on the amount of overhang area outside of the drivable surface, leading to an increased safety in driving maneuvers. The real-time applicability of the method is shown, by using it in a receding-horizon framework.