Fair morse functions for extracting the topological structure of a surface mesh
- 1 August 2004
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 23 (3) , 613-622
- https://doi.org/10.1145/1015706.1015769
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.This publication has 27 references indexed in Scilit:
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