On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Alpha-shapes and flow shapes are homotopy equivalent
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Extraction of Topologically Simple Isosurfaces from Volume Datasets
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Graphical Models
Identifying flat and tubular regions of a shape by unstable manifolds
Proceedings of the 2006 ACM symposium on Solid and physical modeling
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
Medial axis approximation and unstable flow complex
Proceedings of the twenty-second annual symposium on Computational geometry
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
A flexible framework for surface reconstruction from large point sets
Computers and Graphics
Shape smoothing using double offsets
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Topology Repair of Solid Models Using Skeletons
IEEE Transactions on Visualization and Computer Graphics
A streaming algorithm for surface reconstruction
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Geometric and topological guarantees for the WRAP reconstruction algorithm
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The flow complex: A data structure for geometric modeling
Computational Geometry: Theory and Applications
Recursive geometry of the flow complex and topology of the flow complex filtration
Computational Geometry: Theory and Applications
Multi-component heart reconstruction from volumetric imaging
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Robust construction of the three-dimensional flow complex
Proceedings of the twenty-fourth annual symposium on Computational geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Normal cone approximation and offset shape isotopy
Computational Geometry: Theory and Applications
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Manifold homotopy via the flow complex
SGP '09 Proceedings of the Symposium on Geometry Processing
Stability of curvature measures
SGP '09 Proceedings of the Symposium on Geometry Processing
Technical Section: Fast construction of the Vietoris-Rips complex
Computers and Graphics
The tidy set: a minimal simplicial set for computing homology of clique complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Algorithms and theory of computation handbook
Reconstructing 3D compact sets
Computational Geometry: Theory and Applications
Secondary and tertiary structural fold elucidation from 3d EM maps of macromolecules
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
SMI 2012: Full Consensus meshing
Computers and Graphics
Shape segmentation and matching from noisy point clouds
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
A dynamic surface reconstruction framework for large unstructured point sets
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
A parallel algorithm for computing the flow complex
Proceedings of the twenty-ninth annual symposium on Computational geometry
SMI 2013: Minimizing edge length to connect sparsely sampled unstructured point sets
Computers and Graphics
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Structuring finite sets of points is at the heart of computational geometry. Such point sets arise naturally in many applications. Examples in R3 are point sets sampled from the surface of a solid or the locations of atoms in a molecule. A first step in processing these point sets is to organize them in some data structure. Structuring a point set into a simplicial complex like the Delaunay triangulation has turned out to be appropriate for many modeling tasks. Here we introduce the flow complex which is another simplicial complex that can be computed efficiently from a finite set of points. The flow complex turned out to be well suited for surface reconstruction from a finite sample and for some tasks in structural biology. Here we study mathematical and algorithmic properties of the flow complex and show how to exploit it in applications.