Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Imaging vector fields using line integral convolution
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Anisotropic nonlinear diffusion in flow visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Collapsing flow topology using area metrics
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
A level-set method for flow visualization
Proceedings of the conference on Visualization '00
A topology simplification method for 2D vector fields
Proceedings of the conference on Visualization '00
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Dynamic real-time deformations using space & time adaptive sampling
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Vortex tracking in scale-space
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Image based flow visualization
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computing singularities of 3D vector fields with Geometric Algebra
Proceedings of the conference on Visualization '02
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces
IEEE Transactions on Visualization and Computer Graphics
A tool for visualizing the topology of three-dimensional vector fields
VIS '91 Proceedings of the 2nd conference on Visualization '91
Discrete exterior calculus
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Flow Field Clustering via Algebraic Multigrid
VIS '04 Proceedings of the conference on Visualization '04
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Efficient Hodge-Helmholtz decomposition of motion fields
Pattern Recognition Letters - Special issue: Advances in pattern recognition
Animating gases with hybrid meshes
ACM SIGGRAPH 2005 Papers
ACM SIGGRAPH 2005 Papers
Modeling and animating gases with simulation features
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
Segmentation of Discrete Vector Fields
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Graphical Models - Special issue on SPM 05
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Stable, circulation-preserving, simplicial fluids
ACM SIGGRAPH 2006 Courses
Interactive Tensor Field Design and Visualization on Surfaces
IEEE Transactions on Visualization and Computer Graphics
Stable, circulation-preserving, simplicial fluids
ACM Transactions on Graphics (TOG)
Discrete differential forms for computational modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Discrete, vorticity-preserving, and stable simplicial fluids
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
IEEE Transactions on Visualization and Computer Graphics
Computation of Localized Flow for Steady and Unsteady Vector Fields and Its Applications
IEEE Transactions on Visualization and Computer Graphics
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discrete quadratic curvature energies
Computer Aided Geometric Design
Journal of Mathematical Imaging and Vision
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Rigid shape interpolation using normal equations
NPAR '08 Proceedings of the 6th international symposium on Non-photorealistic animation and rendering
Collision-free construction of animated feathers using implicit constraint surfaces
ACM Transactions on Graphics (TOG)
Gradient domain mesh deformation: a survey
Journal of Computer Science and Technology
Motion field texture synthesis
ACM SIGGRAPH Asia 2009 papers
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
New Scalar Measures for Diffusion-Weighted MRI Visualization
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Smoothing of partition of unity implicit surfaces for noise robust surface reconstruction
SGP '09 Proceedings of the Symposium on Geometry Processing
Slit map: conformal parameterization for multiply connected surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Flows and Decompositions of Games: Harmonic and Potential Games
Mathematics of Operations Research
Feature detection and tracking in optical flow on non-flat manifolds
Pattern Recognition Letters
Curvature minimization for surface reconstruction with features
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Helmholtz-Hodge decomposition on [0,1]d by divergence-free and curl-free wavelets
Proceedings of the 7th international conference on Curves and Surfaces
Vector field analysis and visualization through variational clustering
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
Localized flow analysis of 2D and 3D vector fields
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
Segmentation of flow fields using pattern matching
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Split Bregman iteration and infinity Laplacian for image decomposition
Journal of Computational and Applied Mathematics
Energy-scale aware feature extraction for flow visualization
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
An operator approach to tangent vector field processing
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finite-difference methods. In this paper, we propose a set of simple and accurate tools for the analysis of 3D discrete vector fields on arbitrary tetrahedral grids. We introduce a variational, multiscale decomposition of vector fields into three intuitive components: a divergence-free part, a curl-free part, and a harmonic part. We show how our discrete approach matches its well-known smooth analog, called the Helmotz-Hodge decomposition, and that the resulting computational tools have very intuitive geometric interpretation. We demonstrate the versatility of these tools in a series of applications, ranging from data visualization to fluid and deformable object simulation.