Fig. 1. An example of a combinatorial stratification of a 2-cell complex.

Fig. 2. A second example of combinatorial stratification.

Fig. 3. HC-Rep data structure.

Fig. 4. The Surface node.

Fig. 5. Surface-Edge representation: (a) interior edge and (b) boundary edge.

Fig. 6. Boundary vertex representation.

Fig. 7. The Curve node.

Fig. 8. The Point node.

Fig. 9. Handlebody decomposition of a closed curve.

Fig. 10. Handlebody decomposition of a torus.

Fig. 11. Point creator.

Fig. 12. Curve creator.

Fig. 13. Surface creator.

Fig. 14. Split boundary edge operator.

Fig. 15. Curve building operators: (a) type 1 and (b) type 2.

Fig. 16. Surface building operator of type 1.

Fig. 17. Surface building operator of type 2.

Fig. 18. Surface building operator of type 3.

Fig. 19. Surface building operator of type 4.

Fig. 20. Surface building operator of type 5.

Fig. 21. Unbuild surface operator of type 2.

Fig. 22. Global operator K{V}.

Fig. 23. Global operator K{E}.

Fig. 24. Global operator K{F}.

Fig. 25. Harp and contact vertices: (a) the modeled harp and (b) contact vertices of the harp.

Fig. 26. Example of a non-manifold object: (a) a non-manifold HC-Rep object and (b) the contact cells.