NDLI: Fair morse functions for extracting the topological structure of a surface mesh

Content Provider	ACM Digital Library
Author	Garland, Michael Ni, Xinlai Hart, John C.
Copyright Year	2004
Abstract	Morse theory reveals the topological structure of a shape based on the critical points of a real function over the shape. A poor choice of this real function can lead to a complex configuration of an unnecessarily high number of critical points. This paper solves a relaxed form of Laplace's equation to find a "fair" Morse function with a user-controlled number and configuration of critical points. When the number is minimal, the resulting Morse complex cuts the shape into a disk. Specifying additional critical points at surface features yields a base domain that better represents the geometry and shares the same topology as the original mesh, and can also cluster a mesh into approximately developable patches. We make Morse theory on meshes more robust with teflon saddles and flat edge collapses, and devise a new "intermediate value propagation" multigrid solver for finding fair Morse functions that runs in provably linear time.
Starting Page	613
Ending Page	622
Page Count	10
File Format	PDF
ISSN	07300301
e-ISSN	15577368
DOI	10.1145/1015706.1015769
Volume Number	23
Issue Number	3
Journal	ACM Transactions on Graphics (TOG)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2004-08-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Morse theory Atlas generation Computational topology Surface parameterization Texture mapping
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design

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