Robert Bridson

Robust treatment of collisions, contact and friction for cloth animation

We present an algorithm to efficiently and robustly process collisions, contact and friction in cloth simulation. It works with any technique for simulating the internal dynamics of the cloth, and allows true modeling of cloth thickness. We also show how our simulation data can be post-processed with a collision-aware subdivision scheme to produce smooth and interference free data for rendering.

Animating sand as a fluid

We present a physics-based simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulator with only a few small additions to account for inter-grain and boundary friction.We also propose an alternative method for simulating fluids. Our core representation is a cloud of particles, which allows for accurate and flexible surface tracking and advection, but we use an auxiliary grid to efficiently enforce boundary conditions and incompressibility. We further address the issue of reconstructing a surface from particle data to render each frame.

A fast variational framework for accurate solid-fluid coupling

Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new variational approach which allows robust and accurate solution on relatively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling between fluid and arbitrary solid simulations that always gives a well-posed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the framework with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.

Fast Poisson disk sampling in arbitrary dimensions

In many applications in graphics, particularly rendering, generating samples from a blue noise distribution is important. However, existing efficient techniques do not easily generalize beyond two dimensions. Here I demonstrate a simple modification to dart throwing which permits generation of Poisson disk samples in O(N) time, easily implemented in arbitrary dimension.

Ghost SPH for animating water

We propose a new ghost fluid approach for free surface and solid boundary conditions in Smoothed Particle Hydrodynamics (SPH) liquid simulations. Prior methods either suffer from a spurious numerical surface tension artifact or drift away from the mass conservation constraint, and do not capture realistic cohesion of liquid to solids. Our Ghost SPH scheme resolves this with a new particle sampling algorithm to create a narrow layer of ghost particles in the surrounding air and solid, with careful extrapolation and treatment of fluid variables to reflect the boundary conditions. We also provide a new, simpler form of artificial viscosity based on XSPH. Examples demonstrate how the new approach captures real liquid behaviour previously unattainable by SPH with very little extra cost.

Curl-noise for procedural fluid flow

Procedural methods for animating turbulent fluid are often preferred over simulation, both for speed and for the degree of animator control. We offer an extremely simple approach to efficiently generating turbulent velocity fields based on Perlin noise, with a formula that is exactly incompressible (necessary for the characteristic look of everyday fluids), exactly respects solid boundaries (not allowing fluid to flow through arbitrarily-specified surfaces), and whose amplitude can be modulated in space as desired. In addition, we demonstrate how to combine this with procedural primitives for flow around moving rigid objects, vortices, etc.

Robust Topological Operations for Dynamic Explicit Surfaces

We present a solution to the mesh tangling problem in surface tracking. Using an explicit triangle mesh to track the location of a surface as it moves in three dimensions has many potential advantages for accuracy and efficiency, compared to implicit capturing methods such as level sets. However, particularly when “mesh surgery” is required for topological changes, this approach is prone to tangling: The mesh may self-intersect or otherwise no longer represent a physical interface. Our new approach uses robust collision testing to determine when a mesh operation—such as motion, adaptive refinement, coarsening, or topological change—will lead to an invalid state; we then either roll back noncritical operations or apply robust collision response algorithms, minimally perturbing the mesh to guarantee validity. We present numerical examples demonstrating the robustness and accuracy of the method.

Fluid simulation: SIGGRAPH 2006 course notes Fedkiw and Muller-Fischer presenation videos are available from the citation page

These course notes are designed to give you a practical introduction to fluid simulation for graphics. The field of fluid dynamics, even just in animation, is vast and so not every topic will be covered. The focus of these notes is animating fully three-dimensional incompressible flow, from understanding the math and the algorithms to actual implementation. However, we will include a small amount of material on heightfield simplifications which are important for real-time animation.In general the approach is to make things as simple as possible, but no simpler. Constructing a fluid solver for computer animation is not the easiest thing in the world--there end up being a lot of little details that need attention-- but is perhaps easier than it may appear from surveying the literature. We will also provide pointers to some more advanced topics here and there.

Matching fluid simulation elements to surface geometry and topology

We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples. Constructing the simulation mesh in this way allows us to place samples anywhere in the computational domain; we exploit this by choosing samples that accurately capture the geometry and topology of the liquid surface. When combined with high-resolution explicit surface tracking this allows us to simulate nearly arbitrarily thin features, while eliminating noise and other artifacts that arise when there is a resolution mismatch between the simulation and the surface---and allowing a precise inclusion of surface tension based directly on and at the same resolution as the surface mesh. In addition, we present a simplified Voronoi/Delaunay mesh velocity interpolation scheme, and a direct extension of embedded free surfaces and solid boundaries to Voronoi meshes.

Efficient geometrically exact continuous collision detection

Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.