Querying and interacting with models of massive material micro-structure requires localized on-demand generation of the micro-structure since the full-scale storing and retrieving is cost prohibitive. When the micro-structure is efficiently represented as the image of a canonical structure under a non-linear space deformation to allow it to conform to curved shape, the additional challenge is to relate the query of the mapped micro-structure back to its canonical structure. This paper presents an efficient algorithm to pull back a mapped micro-structure to a partition of the canonical domain structure into boxes and only activates boxes whose image is likely intersected by a plane. The active boxes are organized into a forest whose trees are traversed depth first to generate mapped micro-structure only of the active boxes. The traversal supports, for example, 3D print slice generation in additive manufacturing.