Journal
ACM TRANSACTIONS ON GRAPHICS
Volume 23, Issue 3, Pages 613-622Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/1015706.1015769
Keywords
atlas generation; computational topology; Morse theory; surface parameterization; texture mapping
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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.
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