Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Volumetric Data Analysis using Morse-Smale Complexes
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
IEEE Transactions on Visualization and Computer Graphics
Data structures for simplicial complexes: an analysis and a comparison
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Technical Section: Computing smooth approximations of scalar functions with constraints
Computers and Graphics
On converting sets of tetrahedra to combinatorial and PL manifolds
Computer Aided Geometric Design
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
A lightweight approach to repairing digitized polygon meshes
The Visual Computer: International Journal of Computer Graphics
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This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PL-manifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminating at a local minimum. Existing approaches for two and three dimensions define few ad hoc procedures to calculate these segments within simplices of dimensions one, two and three. Unfortunately, in a dimension-independent setting this case-by-case approach is no longer applicable, and a generalized theory and a corresponding algorithm must be designed. In this paper, the calculation is based on the derivation of the analytical form of the hyperplane containing the simplex, independent of its dimension. Our prototype implementation demonstrates that the algorithm is efficient even for significantly complex domains.