For each grid point we need to define the set of nearby grid
points for which an edge may be constructed. Special care must be
given to defining the neighborhood of a boundary grid point to ensure
that identifications and the C-space boundary (if it exists) are
respected. If is not a boundary grid point, then the
*1-neighborhood* is defined as

For an -dimensional C-space there at most -neighbors. In two dimensions, this yields at most four -neighbors, which can be thought of as ``up,'' ``down,'' ``left,'' and ``right.'' There are

A *2-neighborhood* is defined as

Similarly, a

Steven M LaValle 2012-04-20