Surfaces Cut and Hierarchical Simplicial Complexes

@inproceedings{DazyRM1999,
 abstract = { The Cut algorithm currently used in gOcad to compute surface intersections has several problems occuring at different levels. First, aIl computations (triangle intersection, tine intersection, point colocation) rely mostly on geometrical properties, and numerical errors can sometimes generate slight topological inconsistencies. AIso, the algotihm needs several complex data structures to compute and store ail the necessary information. A new, topology-driven approach for the Cut algorithm is studied. The HESC data structure presented last year (see [7]) will be used ta construct the new algorithm, and eventually to propose a new implementation. The properties of the HESCs allow to make decisions based on topology rather than on geometry, delaying actual computations until they are really needed. Also, an computations can be made in a local basis, thus reducing the risks of numerical problems, and the structure oUers possibilities for the use of exact arithmetic libraries. Finally, the high-level methods provided can be used to write more simple algorithms. },
 author = { Dazy, Matthieu AND Levy, Bruno AND Euler, Nicolas },
 booktitle = { 19th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Surfaces Cut and Hierarchical Simplicial Complexes },
 year = { 1999 }
}