Structural operators for modeling 3-manifolds
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Geometric compression through topological surgery
ACM Transactions on Graphics (TOG)
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Algorithm 447: efficient algorithms for graph manipulation
Communications of the ACM
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Optimal discrete Morse functions for 2-manifolds
Computational Geometry: Theory and Applications
Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Ascending and descending regions of a discrete Morse function
Computational Geometry: Theory and Applications
Smale-like decomposition and forman theory for discrete scalar fields
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Parallel Computation of 3D Morse-Smale Complexes
Computer Graphics Forum
Nearly Recurrent Components in 3D Piecewise Constant Vector Fields
Computer Graphics Forum
A spatial approach to morphological feature extraction from irregularly sampled scalar fields
Proceedings of the Third ACM SIGSPATIAL International Workshop on GeoStreaming
Parameterized complexity of discrete morse theory
Proceedings of the twenty-ninth annual symposium on Computational geometry
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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Morse theory is a powerful tool for investigating the topology of smooth manifolds. It has been widely used by the computational topology, computer graphics, and geometric modeling communities to devise topology-based algorithms and data structures. Forman introduced a discrete version of this theory which is purely combinatorial. This work aims to build, visualize, and apply the basic elements of Forman's discrete Morse theory. It intends to use some of those concepts to visually study the topology of an object. As a basis, an algorithmic construction of optimal Forman's discrete gradient vector fields is provided. This construction is then used to topologically analyze mesh compression schemes, such as Edgebreaker and Grow&Fold. In particular, this paper proves that the complexity class of the strategy optimization of Grow&Fold is MAX-SNP hard.