The Topology ToolKit

@article{Tierny2018TheTT,
  title={The Topology ToolKit},
  author={Julien Tierny and Guillaume Favelier and Joshua A. Levine and Charles Gueunet and Michael Michaux},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  year={2018},
  volume={24},
  pages={832-842}
}
This system paper presents the Topology ToolKit (TTK), a software platform designed for the topological analysis of scalar data in scientific visualization. While topological data analysis has gained in popularity over the last two decades, it has not yet been widely adopted as a standard data analysis tool for end users or developers. TTK aims at addressing this problem by providing a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of… 

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References

SHOWING 1-10 OF 116 REFERENCES
Efficient Software for Programmable Visual Analysis Using Morse-Smale Complexes
TLDR
Two open source software modules for the computation, analysis, and visualization of scientific data using the Morse-Smale complex are presented and the ability to couple the visual analysis and the computation with ParaView, a popular general purpose visualization tool is highlighted.
Robust on-line computation of Reeb graphs: simplicity and speed
TLDR
An on-line algorithm is introduced that reads a stream of elements and continuously maintains the Reeb graph of all elements already reed and is robust in handling non-manifold meshes and general in its applicability to input models of any dimension.
Interactive Exploration and Analysis of Large-Scale Simulations Using Topology-Based Data Segmentation
TLDR
A new topological framework that in a single-pass extracts and encodes entire families of possible features definitions as well as their statistical properties is presented, demonstrated by extracting and analyzing burning cells from a large-scale turbulent combustion simulation.
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
TLDR
A new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closure-finite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes is described.
Conforming Morse-Smale Complexes
TLDR
A new combinatorial technique to compute an MS complex that conforms to both an input scalar field and an additional, prior segmentation of the domain, effectively resulting in anMS complex that is as geometrically accurate as the employed numerical integration.
Computing Morse-Smale Complexes with Accurate Geometry
TLDR
Two new algorithms are introduced: a randomized algorithm to compute the discrete gradient of a scalar field that converges under refinement; and a deterministic variant which directly computes accurate geometry and thus correct connectivity of the MS complex.
Introduction to the R package TDA
We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given
Fast and Exact Fiber Surfaces for Tetrahedral Meshes
TLDR
This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes, which assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends.
Topology-Controlled Volume Rendering
TLDR
A framework for direct volume rendering based on segmenting a volume into regions of equivalent contour topology and applying separate transfer functions to each region and a unique transfer function can be assigned to each subvolume corresponding to a branch of the contour tree.
The PR-star octree: a spatio-topological data structure for tetrahedral meshes
TLDR
The PR-star octree representation is proposed as a combined spatial data structure for performing efficient topological queries on tetrahedral meshes and demonstrated in several typical GIS applications, including detection of the domain boundaries, computation of local curvature estimates and mesh simplification.
...
...