Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds
type: Item
instance of: scholarly article
title: Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds
zbMATH Open document ID: 1029.57023
author: Herbert Edelsbrunner
author: Afra Zomorodian
author: J. L. Harer
published in: Discrete \& Computational Geometry
publication date: 2003-08-21T00:00:00Z
review text: The authors define the Morse-Smale complex decomposing a piecewise linear 2-manifold and present algorithms for constructing and simplifying this complex. In many physical problems in which some measurements over a space are considered, one obtains the corresponding height function over the space. Then one can do a topological study of the geographic landscape modelled as a height function \(h: D\to\mathbb{R}\) over a two-dimensional domain \(D\). Inspired by some problems arising in this study, the authors present a solution in the piecewise linear domain. They present: (i) an algorithm for constructing a complex whose combinatorial form matches that of the Morse-Smale complex, (ii) an algorithm for deriving the Morse-Smale complex from the complex in (i) via local transformations, (iii) an algorithm for constructing a hierarchy of Morse-Smale complexes, again via local transformations, (iv) the application of the algorithms to concrete problems.
Mathematics Subject Classification ID: 57Q05
Mathematics Subject Classification ID: 57Q25
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 1969113
zbMATH Keywords: Morse-Smale complex
zbMATH Keywords: piecewise linear 2-manifold
zbMATH Keywords: hierarchy
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
full work available at URL: s00454-003-2926-5
OpenAlex ID: W2068014716
DOI: 10.1007/S00454-003-2926-5
description: scientific article; zbMATH DE number 1969113