Hierarchical Morse Complexes for Piecewise Linear 2-Manifolds

Hierarchical Morse Complexes for Piecewise Linear 2-Manifolds (2001)

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by Herbert Edelsbrunner , John Harer , Afra Zomorodian

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Datum	Value	Source
TITLE	Hierarchical Morse Complexes for Piecewise Linear 2-Manifolds	user correction - Legacy Corrections
AUTHOR NAME	Herbert Edelsbrunner	SVM HeaderParse 0.1
AUTHOR AFFIL	Dept. of Computer Science; Duke University, Durham	SVM HeaderParse 0.2
AUTHOR NAME	John Harer	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Mathematics; Duke University	SVM HeaderParse 0.2
AUTHOR ADDR	Durham, North Carolina	SVM HeaderParse 0.1
AUTHOR NAME	Afra Zomorodian	SVM HeaderParse 0.1
AUTHOR AFFIL	Dept. of Computer Science; University of Illinois	SVM HeaderParse 0.2
AUTHOR ADDR	Urbana, Illinois	SVM HeaderParse 0.1
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 ...	user correction - Legacy Corrections
YEAR	2001	user correction - Legacy Corrections
CITATIONS	15 found	ParsCit 1.0