Real-Time Deformation and Fracture in a Game Environment

This paper describes a simulation system that has been developed to model the deformation and fracture of solid objects in a real-time gaming context. Based around a corotational tetrahedral finite element method, this system has been constructed from components published in the graphics and computational physics literatures. The goal of this paper is to describe how these components can be combined to produce an engine that is robust to unpredictable user interactions, fast enough to model reasonable scenarios at real-time speeds, suitable for use in the design of a game level, and with appropriate controls allowing content creators to match artistic direction. Details concerning parallel implementation, solver design, rendering method, and other aspects of the simulation are elucidated with the intent of providing a guide to others wishing to implement similar systems. Examples from in-game scenes captured on the Xbox 360, PS3, and PC platforms are included.

Real-Time Deformation and Fracture in a Game Environment


A Point-based Method for Animating Elastoplastic Solids

In this paper we describe a point-based approach for animating elastoplastic materials. Our primary contribution is a simple method for computing the deformation gradient for each particle in the simulation. The deformation gradient is computed for each particle by finding the affine transformation that best approximates the motion of neighboring particles over a single timestep. These transformations are then composed to compute the total deformation gradient that describes the deformation around a particle over the course of the simulation. Given the deformation gradient we can apply arbitrary constitutive models and compute the resulting elastic forces. Our method has two primary advantages: we do not store or compare to an initial rest configuration and we work directly with the deformation gradient. The first advantage avoids poor numerical conditioning and the second naturally leads to a multiplicative model of deformation appropriate for finite deformations. We demonstrate our approach on a number of examples that exhibit a wide range of material behaviors.

A Point-based Method for Animating Elastoplastic Solids

A Point-based Method for Animating Incompressible Flow

In this paper, we present a point-based method for animating incompressible flow. The advection term is handled by moving the sample points through the flow in a Lagrangian fashion. However, unlike most previous approaches, the pressure term is handled by performing a projection onto a divergence-free field. To perform the pressure projection, we compute a Voronoi diagram with the sample points as input. Borrowing from Finite Volume Methods, we then invoke the divergence theorem and ensure that each Voronoi cell is divergence free. To handle complex boundary conditions, Voronoi cells are clipped against obstacle boundaries and free surfaces. The method is stable, flexible and combines many of the desirable features of point-based and grid-based methods. We demonstrate our approach on several examples of splashing and streaming liquid and swirling smoke.

A Point-based method for Animating Incompressible Flow

Simple, yet accurate tensile stiffness

Recent Particle System models have evolved toward accurate representation of elastic stiffness based on continuum mechanics, converging to formulations that make them quite analogous to fast Finite Element methods. These formulations usually involve the linearization of tensors that help their formulation in the context of linear elasticity. Toward our objective of simulating the nonlinear properties of cloth accurately, we show through this work that this linearization can indeed be suppressed and replaced by adapted strain-stress laws relating precisely the nonlinear behavior of the material. This leads to very streamlined computations that are particularly efficient for simulating the nonlinear anisotropic tensile elasticity of deformable surfaces. Through a simple and efficient implementation using the Particle System formalism, we demonstrate the efficiency of this method with examples related to garment simulation.

Simple, yet accurate tensile stiffness

Interleaving Delaunay Refinement and Optimization for Practical Isotropic Tetrahedron Mesh Generation

We present a practical approach to isotropic tetrahedral meshing of 3D domains bounded by piecewise smooth surfaces. Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh optimization to generate quality meshes that satisfy a set of user-defined criteria. This interleaving is shown to be more conservative in number of Steiner point insertions than refinement alone, and to produce higher quality meshes than optimization alone. A careful treatment of boundaries and their features is presented, offering a versatile framework for designing smoothly graded tetrahedral meshes.

Interleaving Delaunay Refinement and Optimization for Practical Isotropic Tetrahedron Mesh Generation

Asynchronous Contact Mechanics

We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of well-posed problems (a) have no interpenetrations, (b) obey causality, momentum- and energy-conservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two- and three-dimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact.

Asynchronous Contact Mechanics

Capture and Modeling of Non-Linear Heterogeneous Soft Tissue

This paper introduces a data-driven representation and modeling technique for simulating non-linear heterogeneous soft tissue. It simplifies the construction of convincing deformable models by avoiding complex selection and tuning of physical material parameters, yet retaining the richness of non-linear heterogeneous behavior. We acquire a set of example deformations of a real object, and represent each of them as a spatially varying stress-strain relationship in a finite-element model. We then model the material by non-linear interpolation of these stress-strain relationships in strain-space. Our method relies on a simple-to-build capture system and an efficient run-time simulation algorithm based on incremental loading, making it suitable for interactive computer graphics applications. We present the results of our approach for several nonlinear materials and biological soft tissue, with accurate agreement of our model to the measured data.

Capture and Modeling of Non-Linear Heterogeneous Soft Tissue

SIGGRAPH 2009 Papers

It’s that time of year again… Here’s the link to Ke-Sen’s more complete list.

Physics-related papers:

Enrichment Textures for Detailed Cutting of Shells

We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by custom designed basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in enrichment textures, which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose harmonic enrichment functions to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of C1 continuous basis functions and thus allows for simpler, C0 continuous XFEM enrichment functions.

Enrichment Textures for Detailed Cutting of Shells

Predictive-Corrective Incompressible SPH

We present a novel, incompressible fluid simulation method based on the Lagrangian Smoothed Particle Hydrodynamics (SPH) model. In our method, incompressibility is enforced by using a prediction-correction scheme to determine the particle pressures. For this, the information about density fluctuations is actively propagated through the fluid and pressure values are updated until the targeted density is satisfied. With this approach, we avoid the computational expenses of solving a pressure Poisson equation, while still being able to use large time steps in the simulation. The achieved results show that our predictive-corrective incompressible SPH (PCISPH) method clearly outperforms the commonly used weakly compressible SPH (WCSPH) model by more than an order of magnitude while the computations are in good agreement with the WCSPH results.

Predictive-Corrective Incompressible SPH