The global medial structure of regions in R3

We classify the geometric complexity by giving a structure theorem for the Blum medial axis M . We do so by first giving an algorithm for decomposing M using the local types into “irreducible components” and then representing each medial component as obtained by attaching surfaces with boundaries to 4–valent graphs. The two stages are described by a two level extended graph structure. The top level describes a simplified form of the attaching of the irreducible medial components to each other, and the second level extended graph structure for each irreducible component specifies how to construct the component.