DMCA
Hierarchical Morse Complexes for Piecewise Linear 2-Manifolds (2001)
Cached
Download Links
| Citations: | 66 - 2 self |
BibTeX
@MISC{Edelsbrunner01hierarchicalmorse,
author = {Herbert Edelsbrunner and John Harer and Afra Zomorodian},
title = {Hierarchical Morse Complexes for Piecewise Linear 2-Manifolds},
year = {2001}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We present algorithms for constructing a hierarchy of increasingly coarse Morse complexes that decompose a piecewise linear 2-manifold. While Morse complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse complexes by cancelling pairs of critical points in order of increasing persistence. Keywords Computational topology, PL manifolds, Morse theory, topological persistence, hierarchy, algorithms, implementation, terrains 1. INTRODUCTION In this paper, we define the Morse complex decomposing a piecewise linear 2-manifold and present algorithms for constructing and simplifying this complex. 1.1 Motivation Physical simulation problems often start with a space and measurements over this space. If the measurements are scalar values, we talk about a height function of that space. We use this name throughout the paper, although the functions can ...
Keyphrases
hierarchical morse complex piecewise linear morse complex coarse morse complex critical point structural integrity smooth category pl manifold present algorithm piecewise linear category scalar value morse theory height function topological persistence keywords computational topology motivation physical simulation problem
