An optimized computational technique for free space localization in 3-D virtual representations of complex environments

Modeling 3D objects as octrees has demonstrated considerable advantages which led to numerous applications in robotics where free space localization is critical. Efficient neighbor finding techniques in tree structures are required for such models to be used properly, especially for path planning and collision avoidance. In this paper, an optimized neighbor finding approach is presented that is based on a recursive addressing scheme which precludes any backtracking into the tree structure while preserving model compactness. Neighboring cell addresses are computed directly given a displacement direction in 3-D space and the address of the starting cell. Neighboring rule sets that have been previously derived for a quadtree representation are now extended to octrees. Given the algebraic rules that are defined, computation of a neighboring cell address in an octree comes down to basic arithmetic operations with carry. The algorithm complexity is kept low in order to provide good performances.