On the multi-level splitting of finite element spaces
Numerische Mathematik
A fast algorithm for particle simulations
Journal of Computational Physics
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Good vibrations: modal dynamics for graphics and animation
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Updating the inverse of a matrix
SIAM Review
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Dynamic simulation of non-penetrating flexible bodies
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Matrix computations (3rd ed.)
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
ArtDefo: accurate real time deformable objects
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Subdivision schemes for fluid flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Displaced subdivision surfaces
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Interactive animation of structured deformable objects
Proceedings of the 1999 conference on Graphics interface '99
Dynamic real-time deformations using space & time adaptive sampling
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Scanning physical interaction behavior of 3D objects
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
DyRT: dynamic response textures for real time deformation simulation with graphics hardware
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models
IEEE Transactions on Visualization and Computer Graphics
Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation
IEEE Transactions on Visualization and Computer Graphics
Compression of functions defined on surfaces of 3D objects
DCC '97 Proceedings of the Conference on Data Compression
Multiresolution green's function methods for interactive simulation of large-scale elastostatic objects and other physical systems in equilibrium
Deformable model acquisition and validation
Deformable model acquisition and validation
Presence: Teleoperators and Virtual Environments
Virtual Reality-Based Simulation of Endoscopic Surgery
Presence: Teleoperators and Virtual Environments
A new, fast, and efficient image codec based on set partitioning in hierarchical trees
IEEE Transactions on Circuits and Systems for Video Technology
Precomputing interactive dynamic deformable scenes
ACM SIGGRAPH 2003 Papers
GI '04 Proceedings of the 2004 Graphics Interface Conference
Quasi-rigid objects in contact
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Haptics in Minimally Invasive Surgical Simulation and Training
IEEE Computer Graphics and Applications
GelForce: a vision-based traction field computer interface
CHI '05 Extended Abstracts on Human Factors in Computing Systems
Clustering method for fast deformation with constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Distributed training system with high-resolution deformable virtual models
Proceedings of the 43rd annual Southeast regional conference - Volume 1
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Adaptive deformations with fast tight bounds
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Haptic Feedback Based on Physically Based Modeling for Cellular Manipulation Systems
EuroHaptics '08 Proceedings of the 6th international conference on Haptics: Perception, Devices and Scenarios
Preserving topology and elasticity for embedded deformable models
ACM SIGGRAPH 2009 papers
The point collocation-based method of finite spheres (PCMFS) for real time surgery simulation
Computers and Structures
International Journal of Robotics Research
Sparse meshless models of complex deformable solids
ACM SIGGRAPH 2011 papers
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Subspace integration with local deformations
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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We present a framework for low-latency interactive simulation of linear elastostatic models, and other systems arising from linear elliptic partial differential equations, which makes it feasible to interactively simulate large-scale physical models. The deformation of the models is described using precomputed Green's functions (GFs), and runtime boundary value problems (BVPs) are solved using existing Capacitance Matrix Algorithms (CMAs). Multiresolution techniques are introduced to control the amount of information input and output from the solver thus making it practical to simulate and store very large models. A key component is the efficient compressed representation of the precomputed GFs using second-generation wavelets on surfaces. This aids in reducing the large memory requirement of storing the dense GF matrix, and the fast inverse wavelet transform allows for fast summation methods to be used at run-time for response synthesis. Resulting GF compression factors are directly related to interactive simulation speedup, and examples are provided with hundredfold improvements at modest error levels. We also introduce a multiresolution constraint satisfaction technique formulated as a hierarchical CMA, so named because of its use of hierarchical GFs describing the response due to hierarchical basis constraints. This direct solution approach is suitable for hard real-time simulation since it provides a mechanism for gracefully degrading to coarser resolution constraint approximations. The GFs' multiresolution displacement fields also allow for run-time adaptive multiresolution rendering.