Geoffrey Irving

Invertible finite elements for robust simulation of large deformation

We present an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, our model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells such as cloth. We also provide a mechanism for controlling plastic deformation, which allows a deformable object to be guided towards a desired final shape without sacrificing realistic behavior. Finally, we present an improved method for rigid body collision handling in the context of mixed explicit/implicit time-stepping.

Efficient simulation of large bodies of water by coupling two and three dimensional techniques

We present a new method for the efficient simulation of large bodies of water, especially effective when three-dimensional surface effects are important. Similar to a traditional two-dimensional height field approach, most of the water volume is represented by tall cells which are assumed to have linear pressure profiles. In order to avoid the limitations typically associated with a height field approach, we simulate the entire top surface of the water volume with a state of the art, fully three-dimensional Navier-Stokes free surface solver. Our philosophy is to use the best available method near the interface (in the three-dimensional region) and to coarsen the mesh away from the interface for efficiency. We coarsen with tall, thin cells (as opposed to octrees or AMR), because they maintain good resolution horizontally allowing for accurate representation of bottom topography.

Robust quasistatic finite elements and flesh simulation

Quasistatic and implicit time integration schemes are typically employed to alleviate the stringent time step restrictions imposed by their explicit counterparts. However, both quasistatic and implicit methods are subject to hidden time step restrictions associated with both the prevention of element inversion and the effects of discontinuous contact forces. Furthermore, although fast iterative solvers typically require a symmetric positive definite global stiffness matrix, a number of factors can lead to indefiniteness such as large jumps in boundary conditions, heavy compression, etc. We present a novel quasistatic algorithm that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration. Additionally, we robustly compute smooth elastic forces in the presence of highly deformed, inverted elements alleviating artificial time step restrictions typically required to prevent such states. Finally, we propose a novel strategy for treating both collision and self-collision in this context.

Volume conserving finite element simulations of deformable models

We propose a numerical method for modeling highly deformable nonlinear incompressible solids that conserves the volume locally near each node in a finite element mesh. Our method works with arbitrary constitutive models, is applicable to both passive and active materials (e.g. muscles), and works with simple tetrahedra without the need for multiple quadrature points or stabilization techniques. Although simple linear tetrahedra typically suffer from locking when modeling incompressible materials, our method enforces incompressibility per node (in a one-ring), and we demonstrate that it is free from locking. We correct errors in volume without introducing oscillations by treating position and velocity in separate implicit solves. Finally, we propose a novel method for treating both object contact and self-contact as linear constraints during the incompressible solve, alleviating issues in enforcing multiple possibly conflicting constraints.

Hybrid simulation of deformable solids

Although mesh-based methods are efficient for simulating simple hyperelasticity, maintaining and adapting a mesh-based representation is less appealing in more complex scenarios, e.g. collision, plasticity and fracture. Thus, meshless or point-based methods have enjoyed recent popularity due to their added flexibility in dealing with these situations. Our approach begins with an initial mesh that is either conforming (as generated by ones favorite meshing algorithm) or non-conforming (e.g. a BCC background lattice). We then propose a framework for embedding arbitrary sample points into this initial mesh allowing for the straightforward handling of collisions, plasticity and fracture without the need for complex remeshing. A straightforward consequence of this new framework is the ability to naturally handle T-junctions alleviating the requirement for a manifold initial mesh. The arbitrarily added embedded points are endowed with full simulation capability allowing them to collide, interact with each other, and interact with the parent geometry in the fashion of a particle-centric simulation system. We demonstrate how this formulation facilitates tasks such as arbitrary refinement or resampling for collision processing, the handling of multiple and possibly conflicting constraints (e.g. when cloth is nonphysically pinched between two objects), the straightforward treatment of fracture, and sub-element resolution of elasticity and plasticity.

Melting and burning solids into liquids and gases

We propose a novel technique for melting and burning solid materials, including the simulation of the resulting liquid and gas. The solid is simulated with traditional mesh-based techniques (triangles or tetrahedra) which enable robust handling of both deformable and rigid objects, collision and self-collision, rolling, friction, stacking, etc. The subsequently created liquid or gas is simulated with modern grid-based techniques, including vorticity confinement and the particle level set method. The main advantage of our method is that state-of-the-art techniques are used for both the solid and the fluid without compromising simulation quality when coupling them together or converting one into the other. For example, we avoid modeling solids as Eulerian grid-based fluids with high viscosity or viscoelasticity, which would preclude the handling of thin shells, self-collision, rolling, etc. Thus, our method allows one to achieve new effects while still using their favorite algorithms (and implementations) for simulating both solids and fluids, whereas other coupling algorithms require major algorithm and implementation overhauls and still fail to produce rich coupling effects (e.g., melting and burning solids).

Robust High-Resolution Cloth Using Parallelism, History-Based Collisions, and Accurate Friction

In this paper we simulate high resolution cloth consisting of up to 2 million triangles which allows us to achieve highly detailed folds and wrinkles. Since the level of detail is also influenced by object collision and self collision, we propose a more accurate model for cloth-object friction. We also propose a robust history-based repulsion/collision framework where repulsions are treated accurately and efficiently on a per time step basis. Distributed memory parallelism is used for both time evolution and collisions and we specifically address Gauss-Seidel ordering of repulsion/collision response. This algorithm is demonstrated by several high resolution and high-fidelity simulations.

A quantized-diffusion model for rendering translucent materials

We present a new BSSRDF for rendering images of translucent materials. Previous diffusion BSSRDFs are limited by the accuracy of classical diffusion theory. We introduce a modified diffusion theory that is more accurate for highly absorbing materials and near the point of illumination. The new diffusion solution accurately decouples single and multiple scattering. We then derive a novel, analytic, extended-source solution to the multilayer search-light problem by quantizing the diffusion Greens function. This allows the application of the diffusion multipole model to material layers several orders of magnitude thinner than previously possible and creates accurate results under high-frequency illumination. Quantized diffusion provides both a new physical foundation and a variable-accuracy construction method for sum-of-Gaussians BSSRDFs, which have many useful properties for efficient rendering and appearance capture. Our BSSRDF maps directly to previous real-time rendering algorithms. For film production rendering, we propose several improvements to previous hierarchical point cloud algorithms by introducing a new radial-binning data structure and a doubly-adaptive traversal strategy.

Tetrahedral and hexahedral invertible finite elements

We review an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, the model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells such as cloth. We also discuss a mechanism for controlling plastic deformation, which allows a deformable object to be guided towards a desired final shape without sacrificing realistic behavior, and an improved method for rigid body collision handling in the context of mixed explicit/implicit time-stepping. Finally, we present a novel extension of our method to arbitrary element types including specific details for hexahedral elements.

Compression and direct manipulation of complex blendshape models

We present a method to compress complex blendshape models and thereby enable interactive, hardware-accelerated animation of these models. Facial blendshape models in production are typically large in terms of both the resolution of the model and the number of target shapes. They are represented by a single huge blendshape matrix, whose size presents a storage burden and prevents real-time processing. To address this problem, we present a new matrix compression scheme based on a hierarchically semi-separable (HSS) representation with matrix block reordering. The compressed data are also suitable for parallel processing. An efficient GPU implementation provides very fast feedback of the resulting animation. Compared with the original data, our technique leads to a huge improvement in both storage and processing efficiency without incurring any visual artifacts. As an application, we introduce an extended version of the direct manipulation method to control a large number of facial blendshapes efficiently and intuitively.