COMPUTATIONAL TOPOLOGY FOR REGULAR CLOSED SETS (WITHIN THE I-TANGO PROJECT)
Thomas Peters, Justin Bisceglio, Christopher M. Hoffmann, Takashi Maekawa, Nicholas M. Patrikalakis, Takis Sakkalis, Nathaniel Stewart · 2004
The Boolean algebra of regular closed sets is prominent in topol- ogy, particularly as a dual for the Stone- Cech compactication. This algebra is also central for the theory of geometric computation, as a representation for combinatorial operations on geometric sets. However, the issue of com- putational approximation introduces unresolved subtleties that do not occur within \pure topology. One major eort towards reconciling this mathe- matical theory with computational practice is our ongoing I-TANGO project. The acronym I-TANGO is an abbreviation for \Intersections|Topology, Ac- curacy and Numerics for Geometric Objects. The long-range goals and initial progress of the I-TANGO team in development of computational topology are presented.