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
Matrix computations (3rd ed.)
Modeling the motion of a hot, turbulent gas
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Precomputing interactive dynamic deformable scenes
ACM SIGGRAPH 2003 Papers
TensorTextures: multilinear image-based rendering
ACM SIGGRAPH 2004 Papers
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Algorithm Design
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
ACM SIGGRAPH 2005 Papers
Error Estimation for Reduced-Order Models of Dynamical Systems
SIAM Journal on Numerical Analysis
Fluid animation with dynamic meshes
ACM SIGGRAPH 2006 Papers
Model reduction for real-time fluids
ACM SIGGRAPH 2006 Papers
Key Point Subspace Acceleration and soft caching
ACM SIGGRAPH 2007 papers
ACM SIGGRAPH 2007 courses
Wavelet turbulence for fluid simulation
ACM SIGGRAPH 2008 papers
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
Optimizing cubature for efficient integration of subspace deformations
ACM SIGGRAPH Asia 2008 papers
Fast animation of turbulence using energy transport and procedural synthesis
ACM SIGGRAPH Asia 2008 papers
Energy-preserving integrators for fluid animation
ACM SIGGRAPH 2009 papers
Modular bases for fluid dynamics
ACM SIGGRAPH 2009 papers
Journal of Computational Physics
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
Evolving sub-grid turbulence for smoke animation
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Low viscosity flow simulations for animation
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A novel algorithm for incompressible flow using only a coarse grid projection
ACM SIGGRAPH 2010 papers
Physically Based Rendering, Second Edition: From Theory To Implementation
Physically Based Rendering, Second Edition: From Theory To Implementation
Reduced-order modeling of transonic flows around an airfoil submitted to small deformations
Journal of Computational Physics
Physics-based character skinning using multi-domain subspace deformations
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Compression and direct manipulation of complex blendshape models
Proceedings of the 2011 SIGGRAPH Asia Conference
Fluid simulation using Laplacian eigenfunctions
ACM Transactions on Graphics (TOG)
Efficient Parallel Nonnegative Least Squares on Multicore Architectures
SIAM Journal on Scientific Computing
Lagrangian vortex sheets for animating fluids
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Reliable reduced-order models for time-dependent linearized Euler equations
Journal of Computational Physics
POD-Based reduced-order models with deforming grids
Mathematical and Computer Modelling: An International Journal
Scalable fluid simulation in linear time on shared memory multiprocessors
Proceedings of the Digital Production Symposium
Linear-time smoke animation with vortex sheet meshes
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Non-polynomial Galerkin projection on deforming meshes
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
An efficient construction of reduced deformable objects
ACM Transactions on Graphics (TOG)
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We present a new subspace integration method that is capable of efficiently adding and subtracting dynamics from an existing high-resolution fluid simulation. We show how to analyze the results of an existing high-resolution simulation, discover an efficient reduced approximation, and use it to quickly "re-simulate" novel variations of the original dynamics. Prior subspace methods have had difficulty re-simulating the original input dynamics because they lack efficient means of handling semi-Lagrangian advection methods. We show that multi-dimensional cubature schemes can be applied to this and other advection methods, such as MacCormack advection. The remaining pressure and diffusion stages can be written as a single matrix-vector multiply, so as with previous subspace methods, no matrix inversion is needed at runtime. We additionally propose a novel importance sampling-based fitting algorithm that asymptotically accelerates the precomputation stage, and show that the Iterated Orthogonal Projection method can be used to elegantly incorporate moving internal boundaries into a subspace simulation. In addition to efficiently producing variations of the original input, our method can produce novel, abstract fluid motions that we have not seen from any other solver.