Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Introduction to algorithms
On the complexity of computing the homology type of a triangulation
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Compatible tetrahedralizations
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Weighted alpha shapes
The union of balls and its dual shape
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Compatible tetrahedralizations
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Computing Betti numbers via combinatorial Laplacians
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Algorithms for manifolds and simplicial complexes in Euclidean 3-space (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Introducing alpha shapes for the analysis of path integral Monte Carlo results
VIS '94 Proceedings of the conference on Visualization '94
Cycle bases of graphs and sampled manifolds
Computer Aided Geometric Design
Zigzag persistent homology in matrix multiplication time
Proceedings of the twenty-seventh annual symposium on Computational geometry
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
Alpha, betti and the megaparsec universe: on the topology of the cosmic web
Transactions on Computational Science XIV
Compatible Tetrahedralizations
Fundamenta Informaticae
| Hi-index | 0.00 |
A general and direct method for computing the betti numbers of thehomology groups of a finite simplicial complex is given. Forsubcomplexes of a triangulation of S3 this method has implementations that run in timeO(n&dgr;(n))and O(n), wheren is the number of simplices in thetriangulation. If applied to the family of &dgr;-shapes of a finitepoint set in R3 it takes timeO(n&dgr;(n))to compute the betti numbers of all &dgr;-shapes.