Computing the polar decomposition with applications
SIAM Journal on Scientific and Statistical Computing
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
A Fast Finite Element Solution for Cloth Modelling
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Meshless deformations based on shape matching
ACM SIGGRAPH 2005 Papers
Geometric, variational integrators for computer animation
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
PriMo: coupled prisms for intuitive surface modeling
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
As-rigid-as-possible surface modeling
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Inversion handling for stable deformable modeling
The Visual Computer: International Journal of Computer Graphics
ACM Transactions on Graphics (TOG)
Efficient elasticity for character skinning with contact and collisions
ACM SIGGRAPH 2011 papers
Example-based elastic materials
ACM SIGGRAPH 2011 papers
Real-time large-deformation substructuring
ACM SIGGRAPH 2011 papers
Element-wise mixed implicit-explicit integration for stable dynamic simulation of deformable objects
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Interactive surface modeling using modal analysis
ACM Transactions on Graphics (TOG)
Interactive spacetime control of deformable objects
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Fast automatic skinning transformations
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Modeling Polyhedral Meshes with Affine Maps
Computer Graphics Forum
Elasticity-inspired deformers for character articulation
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes
Computer Graphics Forum
Lie bodies: a manifold representation of 3D human shape
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Simulation of deformable solids in interactive virtual reality applications
Proceedings of the 18th ACM symposium on Virtual reality software and technology
Energetically consistent invertible elasticity
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Energetically consistent invertible elasticity
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Injective and bounded distortion mappings in 3D
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
A material point method for snow simulation
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Planar shape interpolation with bounded distortion
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Fast simulation of mass-spring systems
ACM Transactions on Graphics (TOG)
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Consistent volumetric discretizations inside self-intersecting surfaces
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Dirichlet energy for analysis and synthesis of soft maps
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We advocate a simple geometric model for elasticity: distance between the differential of a deformation and the rotation group. It comes with rigorous differential geometric underpinnings, both smooth and discrete, and is computationally almost as simple and efficient as linear elasticity. Owing to its geometric non-linearity, though, it does not suffer from the usual linearization artifacts. A material model with standard elastic moduli (Lamé parameters) falls out naturally, and a minimizer for static problems is easily augmented to construct a fully variational 2nd order time integrator. It has excellent conservation properties even for very coarse simulations, making it very robust. Our analysis was motivated by a number of heuristic, physics-like algorithms from geometry processing (editing, morphing, parameterization, and simulation). Starting with a continuous energy formulation and taking the underlying geometry into account, we simplify and accelerate these algorithms while avoiding common pitfalls. Through the connection with the Biot strain of mechanics, the intuition of previous work that these ideas are "like" elasticity is shown to be spot on.