This paper describes an algorithm for performing arbitrary translations and rotations of objects represented by octrees. Given an octree in a standard position and a transformation, the algorithm builds a new tree in a top down fashion, visiting each node in the new tree only once, and constructing only those nodes that appear in the final tree. It works by projecting the transformed space over the original tree, and labeling the new nodes according to the labels of the nodes in the underlying untransformed tree.