SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Mixed finite element methods for elliptic problems
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
Multigrid
Coupling water and smoke to thin deformable and rigid shells
ACM SIGGRAPH 2005 Papers
Robust quasistatic finite elements and flesh simulation
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
Hybrid simulation of deformable solids
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Volume conserving finite element simulations of deformable models
ACM SIGGRAPH 2007 papers
Efficient simulation of inextensible cloth
ACM SIGGRAPH 2007 papers
FastLSM: fast lattice shape matching for robust real-time deformation
ACM SIGGRAPH 2007 papers
A fast variational framework for accurate solid-fluid coupling
ACM SIGGRAPH 2007 papers
Fast viscoelastic behavior with thin features
ACM SIGGRAPH 2008 papers
Animating developable surfaces using nonconforming elements
ACM SIGGRAPH 2008 papers
Numerical coarsening of inhomogeneous elastic materials
ACM SIGGRAPH 2009 papers
Preserving topology and elasticity for embedded deformable models
ACM SIGGRAPH 2009 papers
Comprehensive biomechanical modeling and simulation of the upper body
ACM Transactions on Graphics (TOG)
An efficient multigrid method for the simulation of high-resolution elastic solids
ACM Transactions on Graphics (TOG)
Estimating the Laplace-Beltrami operator by restricting 3D functions
SGP '09 Proceedings of the Symposium on Geometry Processing
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
Fast simulation of skeleton-driven deformable body characters
ACM Transactions on Graphics (TOG)
Journal of Computational Physics
ACM Transactions on Graphics (TOG)
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Lattice deformers are a popular option for modeling the behavior of elastic bodies as they avoid the need for conforming mesh generation, and their regular structure offers significant opportunities for performance optimizations. Our work expands the scope of current lattice-based elastic deformers, adding support for a number of important simulation features. We accommodate complex nonlinear, optionally anisotropic materials while using an economical one-point quadrature scheme. Our formulation fully accommodates near-incompressibility by enforcing accurate nonlinear constraints, supports implicit integration for large time steps, and is not susceptible to locking or poor conditioning of the discrete equations. Additionally, we increase the accuracy of our solver by employing a novel high-order quadrature scheme on lattice cells overlapping with the model boundary, which are treated at sub-cell precision. Finally, we detail how this accurate boundary treatment can be implemented at a minimal computational premium over the cost of a voxel-accurate discretization. We demonstrate our method in the simulation of complex musculoskeletal human models.