2017/12/21 by Thomas Lewiner, Lewiner, Thomas, Tiago Novello +5
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1712.08136
openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 fields. They model a number of geometric and physical properties, e.g. the principal curvature directions dynamics on surfaces or the stress flux in elasticity. We propose a discretization of a Morse-Smale line field on surfaces, extending Forman's construction for discrete vector fields. More general critical elements and their indices are defined from local matchings, for which Euler theorem and the characterization of homotopy type in terms of critical cells still hold.