  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.
