The fast adaptive composite grid (FAC) method for elliptic equation
Mathematics of Computation
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Multigrid
Dynamic real-time deformations using space & time adaptive sampling
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
A multiresolution framework for dynamic deformations
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Subdivision-based multilevel methods for large scale engineering simulation of thin shells
Proceedings of the seventh ACM symposium on Solid modeling and applications
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Graphical modeling and animation of ductile fracture
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Robust treatment of collisions, contact and friction for cloth animation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Efficient collision detection of complex deformable models using AABB trees
Journal of Graphics Tools
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Evaluating the visual fidelity of physically based animations
ACM SIGGRAPH 2003 Papers
Sensation preserving simplification for haptic rendering
ACM SIGGRAPH 2003 Papers
GI '04 Proceedings of the 2004 Graphics Interface Conference
BD-tree: output-sensitive collision detection for reduced deformable models
ACM SIGGRAPH 2004 Papers
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Multilevel Solvers for Unstructured Surface Meshes
SIAM Journal on Scientific Computing
Meshless deformations based on shape matching
ACM SIGGRAPH 2005 Papers
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
ACM SIGGRAPH 2005 Papers
A fast multigrid algorithm for mesh deformation
ACM SIGGRAPH 2006 Papers
Fast proximity computation among deformable models using discrete Voronoi diagrams
ACM SIGGRAPH 2006 Papers
Resolving surface collisions through intersection contour minimization
ACM SIGGRAPH 2006 Papers
Staggered projections for frictional contact in multibody systems
ACM SIGGRAPH Asia 2008 papers
Bounded normal trees for reduced deformations of triangulated surfaces
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Fast adaptive shape matching deformations
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Flexible simulation of deformable models using discontinuous Galerkin FEM
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
An efficient multigrid method for the simulation of high-resolution elastic solids
ACM Transactions on Graphics (TOG)
Polyhedral finite elements using harmonic basis functions
SGP '08 Proceedings of the Symposium on Geometry Processing
Subspace self-collision culling
ACM SIGGRAPH 2010 papers
Volume contact constraints at arbitrary resolution
ACM SIGGRAPH 2010 papers
Multi-resolution isotropic strain limiting
ACM SIGGRAPH Asia 2010 papers
A parallel multigrid Poisson solver for fluids simulation on large grids
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Efficient elasticity for character skinning with contact and collisions
ACM SIGGRAPH 2011 papers
Simulating liquids and solid-liquid interactions with lagrangian meshes
ACM Transactions on Graphics (TOG)
Numerical methods for linear complementarity problems in physics-based animation
ACM SIGGRAPH 2013 Courses
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Simulation of deformations and collision detection are two highly intertwined problems that are often treated separately. This is especially true in existing elegant adaptive simulation techniques, where standard collision detection algorithms cannot leverage the adaptively selected degrees of freedom. We propose a seamless integration of multigrid algorithms and collision detection that identifies boundary conditions while inherently exploiting adaptivity. We realize this integration through multiscale bounding hierarchies, a novel unified hierarchical representation, together with an adaptive multigrid algorithm for irregular meshes and an adaptivity-aware hierarchical collision detection algorithm. Our solution produces detailed deformations with adapted computational cost, but it also enables robust interactive simulation of self-colliding deformable objects with high-resolution surfaces.