Abstract: Methods and apparatuses are described for generating three-dimensional representations of sets of objects automatically from point cloud data of those sets of objects. The methods and apparatuses partition the space occupied by the objects into a plurality of volumes. If points within a volume approximately coexist on a surface, such a volume is designated a surface volume. Surface volumes with approximately coplanar surfaces are combined to form larger surface volumes. If points within a volume approximately coexist on a line, such a volume is designated a line volume. Line volumes with approximately collinear lines are combined to form larger line volumes.