Fast analytical medial-axis localization in convex polyhedra

The topography (not the field of radius values) of the medial axis of a convex d-dimensional polyhedron can be represented by: (1) The (2- to (d+1)-fold) intersections of internal Voronoi cell polyhedron hyperfaces. (2) The locus of first derivation discontinuities on the distance transform (DT). (3) A cross-linked tree of intersections, with the DT maximum as root, the polyhedron hyperfaces and edges as leaves. (4) The medial framework, the sub-tree of 1D intersections, with the edges of the DT maximum as root, the polyhedron edges as leaves. Based on representation 1 the method proposed locates (“constructs”)-starting from the polyhedron edges, guided by representation 3, in order of increasing DT value-the intersections of representation 4. The 2D complexity is O(n_e log n_e), with n_e the number of polygon edges. The 3D complexity is O(n_c log n_c)<O(n_v log n_v), where n_c equals the number of Voronoi faces and n_v is the number of Voronoi elements