#### Discretization

Assume that is discretized by using the resolutions , ,, and , in which each is a positive integer. This allows the resolution to be different for each C-space coordinate. Either a standard grid or a Sukharev grid can be used. Let

 (5.35)

in which the first components and the last components are 0. A grid point is a configuration that can be expressed in the form5.10

 (5.36)

in which each . The integers , , can be imagined as array indices for the grid. Let the term boundary grid point refer to a grid point for which or for some . Due to identifications, boundary grid points might have more than one representation using (5.36).

Steven M LaValle 2012-04-20