21 citations · 47 across the 9 of their papers we have counts for
4 papers · 1 filter
Greedy Morse matchings and discrete smoothness
Joao Paixao, Joao Lagoas, Thomas Lewiner +1
Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a comp…
Discrete Gradient Line Fields on Surfaces
Thomas Lewiner, Tiago Novello, Joao Paixao +1
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector…
Random collapsibility and 3-sphere recognition
João Paixão, Jonathan Spreer
A triangulation of a -manifold can be shown to be homeomorphic to the -sphere by describing a discrete Morse function on it with only two critical faces, that is, a sequence…
Computational topology and normal surfaces: Theoretical and experimental complexity bounds
Benjamin A. Burton, João Paixão, Jonathan Spreer
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to expone…