A system, method, and computer program product for implementing a tree traversal operation for a tree data structure is disclosed. The method includes the steps of receiving at least a portion of a tree data structure that represents a tree having a plurality of nodes and processing, via a tree traversal operation algorithm executed by a processor, one or more nodes of the tree data structure by intersecting the one or more nodes of the tree data structure with a query data structure. A first node of the tree data structure is associated with a first local coordinate system and a second node of the tree data structure is associated with a second local coordinate system, the first node being an ancestor of the second node, and the first local coordinate system and the second local coordinate system are both specified relative to a global coordinate system.