Nested refinement domains for tetrahedral and diamond hierarchies

Three nested refinement domains for hierarchies of tetrahedra and diamonds. The descendant domain (left) is the limit shape of thedomain covered by all descendants of a given diamond (colored). Due to the fractal nature of these shapes, we introduce the more conservative
convex descendant domain (middle) and bounding box descendant domain (right) to simplify the computation while still tightly covering the
descendant domain. In each case, the refinement domain of one of the diamond’s parents, grandparents and great-grandparents is shown.