Regular layout shapes are placed in accordance with a virtual grate. A determination is made as to whether an unoccupied layout space adjacent to a regular layout shape to be reinforced, and extending in a direction perpendicular to the regular layout shape, is large enough to support placement of a sub-resolution shape. Upon determining that the unoccupied layout space is large enough to support placement of the sub-resolution shape, the sub-resolution shape is placed so as to be substantially centered upon a virtual line of the virtual grate within the unoccupied layout space. Also, one or more sub-resolution shapes are placed between and parallel with neighboring regular layout shapes when windows of lithographic reinforcement associated with each of the neighboring regular layout shapes permit. The sub-resolution shapes may be placed according to a virtual grate, or may be placed based on proximity to edges of the neighboring regular layout shapes.