An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere

@article{Delfinado1995AnIA,
title={An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere},
author={Cecil Jose A. Delfinado and Herbert Edelsbrunner},
journal={Computer Aided Geometric Design},
year={1995},
volume={12},
pages={771-784}
}

A general and direct method for computing the Betti numbers of a finite simplicial complex in ~;J is given. This method is complete for d ~< 3, where versions of this method run in time O(nc~(n) ) and O ( n ) , n the number of simplices. An implementation of the algorithm is applied to alpha shapes, which is a novel geometric modeling tool. Keyword.~: Solid modeling; Geometric algorithms; Graph algorithms; Algebraic topology; Simplicial complexes; Filtrations; Alpha shapes; Homology groups… CONTINUE READING