An Iterative, Octree-Based Algorithm for Distance Computation Between Polyhedra with Complex Surfaces

In a current research project, our group is developing a 3D Spatial Query Language for Building Information Models. Among other features, the spatial language includes metric operators, i.e. operators that depend on the distance between 3D spatial objects. To implement these operators, a fast and well-scaling algorithm based on the octree-encoded discretized geometry for computing the distance between two polyhedra was developed. The proposed algorithm implements a divide-and-conquer strategy: It uses comparably cheap polygon-octant intersection tests to build up the octree, and subsequently performs very simple distance calculations between two octants, that can be realized as fast integer operations. The paper describes the algorithm in detail, discusses its scaling behavior and the advantages of using an octree encoding.