The irregular part of the index space can be represented by a graph
, where N is the set of all nodes in the graph, and
E the set of all edges of the graph connecting various pairs of
nodes. Geometrically,
the nodes correspond to irregular control volumes (cell fragments)
cut out by the intersection of the body with the rectangular mesh, and
the edges correspond to the parts of cell faces that abut a pair of irregular
cell fragments. The remaining parts of space are indexed using elements
of 
, or are covered by the body, and not indexed into at all. However,
it is possible to think of the entire index space (both the regular and
irregular parts) as a graph: in the regular part of the index space, the
nodes are just elements of , and the edges and the cell faces that
separate pair of successive cells along the coordinate directions. If we
used this representation for the entire calculation, the method would
correspond to a unstructured grid method. We will use this
specification of the entire index space as a convenient uniform
interface to both the structured and unstructured parts of the index
space.