Related Experiment Video
Updated: Aug 18, 2026

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
Applications of Forman's discrete Morse theory to topology visualization and mesh compression
Thomas Lewiner1, Hélio Lopes, Geovan Tavares
1Laboratório MatMídia, Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marques de São Vicente 225, Gávea, Rio de Janeiro, RJ, Brasil. tomlew@mat.puc-rio.br
Abstract:
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.
Related Concept Videos
Mesh Analysis
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Real-World Applications of Space Curves
Deformations in a Transverse Cross Section
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
Discrete-Time Fourier Series
For a discrete-time periodic signal x[n]...
Methods of Obtaining Topography
Boundary Conditions: Lossless Lines
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
