SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
Good vibrations: modal dynamics for graphics and animation
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Dynamic simulation of non-penetrating flexible bodies
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
NeuroAnimator: fast neural network emulation and control of physics-based models
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
ArtDefo: accurate real time deformable objects
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation
Proceedings of the 27th 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
Synthesizing sounds from physically based motion
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
EigenSkin: real time large deformation character skinning in hardware
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Scientific Computing: An Introductory Survey
Scientific Computing: An Introductory Survey
Fast animation and control of nonrigid structures
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
DyRT: dynamic response textures for real time deformation simulation with graphics hardware
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation
IEEE Transactions on Visualization and Computer Graphics
Physically Based Models with Rigid and Deformable Components
IEEE Computer Graphics and Applications
Precomputing interactive dynamic deformable scenes
ACM SIGGRAPH 2003 Papers
Modal Warping: Real-Time Simulation of Large Rotational Deformation and Manipulation
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2005 Papers
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
ACM SIGGRAPH 2005 Papers
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Key Point Subspace Acceleration and soft caching
ACM SIGGRAPH 2007 papers
Real-time reduced large-deformation models and distributed contact for computer graphics and haptics
Real-time reduced large-deformation models and distributed contact for computer graphics and haptics
Flexible simulation of deformable models using discontinuous Galerkin FEM
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Numerical coarsening of inhomogeneous elastic materials
ACM SIGGRAPH 2009 papers
Harmonic shells: a practical nonlinear sound model for near-rigid thin shells
ACM SIGGRAPH Asia 2009 papers
Skipping steps in deformable simulation with online model reduction
ACM SIGGRAPH Asia 2009 papers
Semi-automated soft-tissue acquisition and modeling forsurgical simulation
CASE'09 Proceedings of the fifth annual IEEE international conference on Automation science and engineering
Unified simulation of elastic rods, shells, and solids
ACM SIGGRAPH 2010 papers
Efficient yarn-based cloth with adaptive contact linearization
ACM SIGGRAPH 2010 papers
Stable spaces for real-time clothing
ACM SIGGRAPH 2010 papers
ACM Transactions on Graphics (TOG)
Sparse meshless models of complex deformable solids
ACM SIGGRAPH 2011 papers
Real-time large-deformation substructuring
ACM SIGGRAPH 2011 papers
Physics-based character skinning using multi-domain subspace deformations
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Interactive surface modeling using modal analysis
ACM Transactions on Graphics (TOG)
Fast automatic skinning transformations
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Subspace integration with local deformations
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Non-polynomial Galerkin projection on deforming meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Near-exhaustive precomputation of secondary cloth effects
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
An efficient construction of reduced deformable objects
ACM Transactions on Graphics (TOG)
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We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate sub-space forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multi-modal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration.