Fig. 1. Illustration of the MAT dual structure and MAT.

Fig. 2. Illustration of convex and concave edges.

Fig. 3. An example Boundary Representation data structure.

Fig. 4. Original object and MAT (from [25]).

Fig. 5. (a) Annotated MAT and (b) Delaunay nodes (from [25]).

Fig. 6. Accretive construction of the Delaunay nodes (from [25]).

Fig. 7. Regular shapes.

Fig. 8. MAT calculation using the divide and conquer process (from [25]).

Fig. 9. MAT calculation process steps (from [21]).

Fig. 10. Corner block and MAT.

Fig. 11. Divide and conquer dual structures and Delaunay nodes from subdivision.

Fig. 12. Vertex with two concave edges.

(a) Original pocket.

(b) Normal dual of v.

(c) Concave edges split.

(d) modified dual of v.

Fig. 13. Modified dual around concave vertex.

Fig. 14. Subdividing faces with one concave edge node.

Fig. 15. Square torus, MAT and Delaunay nodes (from [25]).

Fig. 16. Separation at necks.

Fig. 17. Arrangement of nodes in topological dual.

Fig. 18. Adjacent Delaunay node faces to be extracted.

Fig. 19. Extracted faces.

Fig. 20. U-shaped block, MAT and node structure.

Fig. 21. Node structure.

Fig. 22. Offset 0.5, all nodes joined.

Fig. 23. Offset 1, nodes 4, 5, 6 and 7 disappear.

Fig. 24. Offset 1.5, same topology as Fig. 23.

Fig. 25. Offset 2, only nodes 10, 11, 12 and 13 remain.

Fig. 26. All offset objects.

Fig. 27. Joined node substructures.

Fig. A.1. Cube structure elements.

Fig. A.2. Original edge and dualled edge.

Fig. A.3. Corner block.

Fig. A.4. Vertices of the dual.

Fig. A.5. Winged-edge structure pointers.

Fig. A.6. Addition of first edge in dual structure.

Fig. A.7. Addition of second edge in dual structure.

Fig. A.8. Addition of third edge in dual structure.

Fig. A.9. Final dual structure.

Fig. A.10. Concave edges in dual structure split.

Fig. A.11. Concave edge adjacent faces in dual structure split.

Fig. A.12. Concave vertex face in dual structure split.

Original and dualled body elements

Structure lists for corner block