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 …

Morse theory offers a natural and mathematically‐sound tool for shape analysis and
understanding. It allows studying the behavior of a scalar function defined on a manifold …

Geological structures, both at the surface and subsurface levels, are typically represented by
means of voxel data. This model presents a major drawback: its large storage requirements …

Unstructured meshes are characterized by data points irregularly distributed in the Euclidian
space. Due to the irregular nature of these data, computing connectivity information between …

This article presents a geometric algebra-based model for topological relation computation.
This computational model is composed of three major components: the Grassmann structure …

We consider the problem of computing discrete Morse and Morse‐Smale complexes on an
unstructured tetrahedral mesh discretizing the domain of a 3D scalar field. We use a duality …

We consider the problem of efficient computing and simplifying Morse complexes on a
Triangulated Irregular Network (TIN) based on discrete Morse theory. We develop a compact …

We introduce the Stellar decomposition, a model for efficient topological data structures over
a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a …

Unstructured data are collections of points with irregular topology, often represented through
simplicial meshes, such as triangle and tetrahedral meshes. Whenever possible such …

We address the problem of performing efficient spatial and topological queries on large
tetrahedral meshes with arbitrary topology and complex boundaries. Such meshes arise in …