Homology computation during an incremental construction process

Abstract

Controlling the construction of geometric objects is important for several Geometric Modeling applications. Homology (groups and generators) may be useful for this control. For such incremental construction processes, it is interesting to incrementally compute the homology, i.e. to deduce the homological information at step s of the construction from the homological information computed at step s - 1. We here study the application of effective homology results [13] for such incremental computations.