In Integrated Circuit (IC) Physical Design, the shapes and other geometric objects that are used to represent the mask data have physical coordinates expressed in a Cartesian plane. When the designs are hierarchical, each level of physical hierarchy has its own coordinate system. When viewed from the top level of a hierarchical design, lower-level shapes must be transformed in order to understand their location from the point of view of the top block. Users and algorithms that manipulate physical data across these hierarchy boundaries must go through the tedious task of transforming data, sometimes multiple times, as it is being changed.