A road-model-definition system suitable for an automated-vehicle includes a lidar-unit and a controller. The lidar-unit is suitable to mount on a host-vehicle. The lidar-unit is used to provide a point-cloud descriptive of an area proximate to the host-vehicle. The controller is in communication with the lidar-unit. The controller is configured to: select ground-points from the point-cloud indicative of a travel-surface, tessellate a portion of the area that corresponds to the travel-surface to define a plurality of cells, determine an orientation of each cell based on the ground-points within each cell, define a road-model of the travel-surface based on the orientation of the cells, and operate the host-vehicle in accordance with the road-model.