Proceedings of the 2006 ACM symposium on Solid and physical modeling
Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
I/O-efficient batched union-find and its applications to terrain analysis
Proceedings of the twenty-second annual symposium on Computational geometry
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities
IEEE Transactions on Visualization and Computer Graphics
Salient critical points for meshes
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Computer-Aided Design
Topologically Clean Distance Fields
IEEE Transactions on Visualization and Computer Graphics
Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Multi-scale dual morse complexes for representing terrain morphology
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
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
Technical Section: Computing smooth approximations of scalar functions with constraints
Computers and Graphics
Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree
Computational Geometry: Theory and Applications
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Topology- and error-driven extension of scalar functions from surfaces to volumes
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Tree-Based Encoding for Cancellations on Morse Complexes
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
A wave-based anisotropic quadrangulation method
ACM SIGGRAPH 2010 papers
Cancellation of critical points in 2D and 3D Morse and Morse-Smale complexes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
International Journal of Computer Vision
Multiresolution morse triangulations
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
I/O-efficient batched union-find and its applications to terrain analysis
ACM Transactions on Algorithms (TALG)
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
Simplifying morphological representations of 2D and 3D scalar fields
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
A multi-resolution representation for terrain morphology
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
SMI 2012: Short Dimension-independent multi-resolution Morse complexes
Computers and Graphics
Parallel Computation of 3D Morse-Smale Complexes
Computer Graphics Forum
Automating Transfer Function Design with Valley Cell-Based Clustering of 2D Density Plots
Computer Graphics Forum
Smooth Shape-Aware Functions with Controlled Extrema
Computer Graphics Forum
Combining in-situ and in-transit processing to enable extreme-scale scientific analysis
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Visualization for the Physical Sciences
Computer Graphics Forum
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
Technical note: Kinematic skeleton extraction from 3D articulated models
Computer-Aided Design
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We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.