21 citations · 23 across the 6 of their papers we have counts for
7 papers
Discrete Line Fields on Surfaces
Tiago Novello, João Paixão, Carlos Tomei +1
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their…
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…
Parameterized Complexity of Discrete Morse Theory
Benjamin A. Burton, Thomas Lewiner, João Paixão +1
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. Howeve…
Schnyder woods for higher genus triangulated surfaces, with applications to encoding
Luca Castelli Aleardi, Eric Fusy, Thomas Lewiner
Schnyder woods are a well-known combinatorial structure for plane triangulations, which yields a decomposition into 3 spanning trees. We extend here definitions and algorithms for…
Discrete Affine Surfaces based on Quadrangular Meshes
Marcos Craizer, Henri Anciaux, Thomas Lewiner
In this paper we are interested in defining affine structures on discrete quadrangular surfaces of the affine three-space. We introduce, in a constructive way, two classes of such…
Discrete Affine Minimal Surfaces with Indefinite Metric
Marcos Craizer, Henri Anciaux, Thomas Lewiner
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces…