Data structures and network algorithms
Data structures and network algorithms
Measurement of protein surface shape by solid angles
Journal of Molecular Graphics
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Designing a data structure for polyhedral surfaces
Proceedings of the fourteenth annual symposium on Computational geometry
On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Two- and three-dimensional patterns of the face
Two- and three-dimensional patterns of the face
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Optimal discrete Morse functions for 2-manifolds
Computational Geometry: Theory and Applications
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Extreme elevation on a 2-manifold
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Clustering techniques for protein surfaces
Pattern Recognition
Principal curvatures from the integral invariant viewpoint
Computer Aided Geometric Design
Topologically Clean Distance Fields
IEEE Transactions on Visualization and Computer Graphics
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)
Integral invariants for robust geometry processing
Computer Aided Geometric Design
Analysis of scalar fields over point cloud data
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Ascending and descending regions of a discrete Morse function
Computational Geometry: Theory and Applications
Computing Elevation Maxima by Searching the Gauss Sphere
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Recognition of Occluded Shapes Using Size Functions
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Discrete Distortion for Surface Meshes
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Identifying the nature of the interface in protein-protein complexes
ISB '10 Proceedings of the International Symposium on Biocomputing
Separatrix persistence: extraction of salient edges on surfaces using topological methods
SGP '09 Proceedings of the Symposium on Geometry Processing
Patch layout from feature graphs
Computer-Aided Design
Multiresolution morse triangulations
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Computing elevation maxima by searching the gauss sphere
Journal of Experimental Algorithmics (JEA)
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
Short Communication to SMI 2011: CAD mesh model segmentation by clustering
Computers and Graphics
Baby morse theory in data analysis
Proceedings of the 2011 workshop on Knowledge discovery, modeling and simulation
Computing morse decompositions for triangulated terrains: an analysis and an experimental evaluation
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Computing the volume of a union of balls: A certified algorithm
ACM Transactions on Mathematical Software (TOMS)
Implicit flow routing on terrains with applications to surface networks and drainage structures
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Certified computation of planar morse-smale complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Parallel Computation of 3D Morse-Smale Complexes
Computer Graphics Forum
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Extraction of feature lines on surface meshes based on discrete morse theory
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Topology-based smoothing of 2D scalar fields with C1-continuity
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Technical Section: Topological saliency
Computers and Graphics
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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Docking is the process by which two or several molecules form a complex. Docking involves the geometry of the molecular surfaces, as well as chemical and energetical considerations. In the mid-eighties, Connolly proposed a docking algorithm matching surface knobs with surface depressions. Knobs and depressions refer to the extrema of the Connolly function, which is defined as follows. Given a surface M bounding a three-dimensional domain X, and a sphere S centered at a point p of M, the Connolly function is equal to the solid angle of the portion of S containing within X.We recast the notions of knobs and depressions in the framework of Morse theory for functions defined over two-dimensional manifolds. First, we study the critical points of the Connolly function for smooth surfaces. Second, we provide an efficient algorithm for computing the Connolly function over a triangulated surface. Third, we introduce a Morse-Smale decomposition based on Forman's discrete Morse theory, and provide an O(n log n) algorithm to construct it. This decomposition induces a partition of the surface into regions of homogeneous flow, and provides an elegant way to relate local quantities to global ones--from critical points to Euler's characteristic of the surface. Fourth, we apply this Morse-Smale decomposition to the discrete gradient vector field induced by Connolly's function, and present experimental results for several mesh models.