Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Loops in Reeb Graphs of 2-Manifolds
Discrete & Computational Geometry
Design of data structures for mergeable trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Extreme Elevation on a 2-Manifold
Discrete & Computational Geometry
Stability of Persistence Diagrams
Discrete & Computational Geometry
Generalized Curvatures
Extending Persistence Using Poincaré and Lefschetz Duality
Foundations of Computational Mathematics
Polyhedral gauss maps and curvature characterisation of triangle meshes
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
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The elevation function on a smoothly embedded 2-manifold in ℝ3 reflects the multiscale topography of cavities and protrusions as local maxima. The function has been useful in identifying coarse docking configurations for protein pairs. Transporting the concept from the smooth to the piecewise linear category, this article describes an algorithm for finding all local maxima. While its worst-case running time is the same as of the algorithm used in prior work, its performance in practice is orders of magnitudes superior. We cast light on this improvement by relating the running time to the total absolute Gaussian curvature of the 2-manifold.