An algorithm is described that efficiently updates an object's octree representation as the object is linearly translated through space. The algorithm performs in-place updating of the octree, by performing simple arithmetic on the path representations of the nodes to be translated. The locations of the ends of the nodes after translation are computed, and the intervening space is filled by a simple traversal. Among others, one advantage of such algorithms is in devising collision free and efficient trajectories of moving objects in robotics.