Shortest path planning with dominance relation

A method of partitioning a workspace using rectilinear visibility in 3-D or higher space is presented. Unlike the case of 2-D space, where the space of a partition is a rectangle, the shape of a partition in 3-D or higher space is arbitrary. In spite of the arbitrary shape of partitioned regions, it is proved that there exist dominance relations between regions. This relation is then utilized to solve efficiently the shortest path planning problem in 3-D or higher space