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.
Original language | English (US) |
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Pages (from-to) | 613-622 |
Number of pages | 10 |
Journal | ACM Transactions on Graphics |
Volume | 23 |
Issue number | 3 |
DOIs | |
State | Published - 2004 |
Event | ACM Transactions on Graphics - Proceedings of ACM SIGGRAPH 2004 - Duration: Aug 9 2004 → Aug 12 2004 |
Keywords
- Atlas generation
- Computational topology
- Morse theory
- Surface parameterization
- Texture mapping
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design