Non-orthogonal structures and space tiles for layout, placement, and routing of an integrated circuit

Disclosed is an improved approach for maintaining the structures for objects in a layout. A single type of structure is maintained that can be used to store or track a polygon of any shape, as long as the shape possesses a supported number of sides. The structure is capable of supporting irregular polygons or objects having angled edges. In one approach, the structure maintains information about each polygon as if that polygon is an octagon. Therefore, any polygon having eight or less orthogonal or diagonal sides can be supported using this structure.