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

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