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. © 2009 ACM

Making Games to Teach Physics and Mechanics

This survey paper introduces engineering educators to a subfield of computer graphics called physically-based animation (PBA) to advocate for collaboration in creating courses to improve student learning in STEM fields, especially in engineering. Engineering students may not realize the degree to which they can leverage their education to enter the entertainment and simulation industries. The central hypothesis of the paper is that introductory physics can be taught via PBA. The paper provides case studies that demonstrate early promise. The paper gives an overview of how “game engineers” leverage theoretical physics and mathematical concepts merged with design aesthetics to portray realistic and fun experiences, manifesting as game physics. As computing power has increased, the convergence of real and fake physics presents an opportunity to teach physics to non-game students. The field of PBA shows promise for enhancing physics education, but much work remains to determine how it may happen and the place in a college curriculum

Animation of deformable bodies with quadratic bézier finite elements

pre-printIn this article, we investigate the use of quadratic finite elements for graphical animation of deformable bodies.We consider both integrating quadratic elements with conventional linear elements to achieve a computationally efficient adaptive-degree simulation framework as well as wholly quadratic elements for the simulation of nonlinear rest shapes. In both cases, we adopt the B´ezier basis functions and employ a co-rotational linear strain formulation. As with linear elements, the co-rotational formulation allows us to precompute per-element stiffness matrices, resulting in substantial computational savings. We present several examples that demonstrate the advantages of quadratic elements in general and our adaptive-degree system in particular. Furthermore, we demonstrate, for the first time in computer graphics, animations of volumetric deformable bodies with nonlinear rest shapes

Efficient parallelization strategy for real-time FE simulations

This paper introduces an efficient and generic framework for finite-element simulations under an implicit time integration scheme. Being compatible with generic constitutive models, a fast matrix assembly method exploits the fact that system matrices are created in a deterministic way as long as the mesh topology remains constant. Using the sparsity pattern of the assembled system brings about significant optimizations on the assembly stage. As a result, developed techniques of GPU-based parallelization can be directly applied with the assembled system. Moreover, an asynchronous Cholesky precondition scheme is used to improve the convergence of the system solver. On this basis, a GPU-based Cholesky preconditioner is developed, significantly reducing the data transfer between the CPU/GPU during the solving stage. We evaluate the performance of our method with different mesh elements and hyperelastic models and compare it with typical approaches on the CPU and the GPU

Interactive Detailed Cutting of Thin Sheets

International audienceIn this paper we propose a method for the interactive detailed cutting of deformable thin sheets. Our method builds on the ability of frame-based simulation to solve for dynamics using very few control frames while embedding highly detailed geometry - here an adaptive mesh that accurately represents the cut boundaries.Our solution relies on a non-manifold grid to compute shape functions that faithfully adapt to the topological changes occurring while cutting. New frames are dynamically inserted to describe new regions. We provide incremental mechanisms for updating simulation data, enabling us to achieve interactive rates. We illustrate our method with examples inspired by the traditional Kirigami artform

Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young\u27s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

A Smoothed Finite Element-Based Elasticity Model for Soft Bodies

One of the major challenges in mesh-based deformation simulation in computer graphics is to deal with mesh distortion. In this paper, we present a novel mesh-insensitive and softer method for simulating deformable solid bodies under the assumptions of linear elastic mechanics. A face-based strain smoothing method is adopted to alleviate mesh distortion instead of the traditional spatial adaptive smoothing method. Then, we propose a way to combine the strain smoothing method and the corotational method. With this approach, the amplitude and frequency of transient displacements are slightly affected by the distorted mesh. Realistic simulation results are generated under large rotation using a linear elasticity model without adding significant complexity or computational cost to the standard corotational FEM. Meanwhile, softening effect is a by-product of our method

Doctor of Philosophy in Computing

dissertationPhysics-based animation has proven to be a powerful tool for creating compelling animations for film and games. Most techniques in graphics are based on methods developed for predictive simulation for engineering applications; however, the goals for graphics applications are dramatically different than the goals of engineering applications. As a result, most physics-based animation tools are difficult for artists to work with, providing little direct control over simulation results. In this thesis, we describe tools for physics-based animation designed with artist needs and expertise in mind. Most materials can be modeled as elastoplastic: they recover from small deformations, but large deformations permanently alter their rest shape. Unfortunately, large plastic deformations, common in graphical applications, cause simulation instabilities if not addressed. Most elastoplastic simulation techniques in graphics rely on a finite-element approach where objects are discretized into a tetrahedral mesh. Using these approaches, maintaining simulation stability during large plastic flows requires remeshing, a complex and computationally expensive process. We introduce a new point-based approach that does not rely on an explicit mesh and avoids the expense of remeshing. Our approach produces comparable results with much lower implementation complexity. Points are a ubiquitous primitive for many effects, so our approach also integrates well with existing artist pipelines. Next, we introduce a new technique for animating stylized images which we call Dynamic Sprites. Artists can use our tool to create digital assets that interact in a natural, but stylized, way in virtual environments. In order to support the types of nonphysical, exaggerated motions often desired by artists, our approach relies on a heavily modified deformable body simulator, equipped with a set of new intuitive controls and an example-based deformation model. Our approach allows artists to specify how the shape of the object should change as it moves and collides in interactive virtual environments. Finally, we introduce a new technique for animating destructive scenes. Our approach is built on the insight that the most important visual aspects of destruction are plastic deformation and fracture. Like with Dynamic Sprites, we use an example-based model of deformation for intuitive artist control. Our simulator treats objects as rigid when computing dynamics but allows them to deform plastically and fracture in between timesteps based on interactions with the other objects. We demonstrate that our approach can efficiently animate the types of destructive scenes common in film and games. These animation techniques are designed to exploit artist expertise to ease creation of complex animations. By using artist-friendly primitives and allowing artists to provide characteristic deformations as input, our techniques enable artists to create more compelling animations, more easily

Real-time Physics Based Simulation for 3D Computer Graphics

Restoration of realistic animation is a critical part in the area of computer graphics. The goal of this sort of simulation is to imitate the behavior of the transformation in real life to the greatest extent. Physics-based simulation provides a solid background and proficient theories that can be applied in the simulation. In this dissertation, I will present real-time simulations which are physics-based in the area of terrain deformation and ship oscillations. When ground vehicles navigate on soft terrains such as sand, snow and mud, they often leave distinctive tracks. The realistic simulation of such vehicle-terrain interaction is important for ground based visual simulations and many video games. However, the existing research in terrain deformation has not addressed this issue effectively. In this dissertation, I present a new terrain deformation algorithm for simulating vehicle-terrain interaction in real time. The algorithm is based on the classic terramechanics theories, and calculates terrain deformation according to the vehicle load, velocity, tire size, and soil concentration. As a result, this algorithm can simulate different vehicle tracks on different types of terrains with different vehicle properties. I demonstrate my algorithm by vehicle tracks on soft terrain. In the field of ship oscillation simulation, I propose a new method for simulating ship motions in waves. Although there have been plenty of previous work on physics based fluid-solid simulation, most of these methods are not suitable for real-time applications. In particular, few methods are designed specifically for simulating ship motion in waves. My method is based on physics theories of ship motion, but with necessary simplifications to ensure real-time performance. My results show that this method is well suited to simulate sophisticated ship motions in real time applications

Robust interactive simulation of deformable solids with detailed geometry using corotational FEM

This thesis focuses on the interactive simulation of highly detailed deformable solids modelled with the Corotational Finite Element Method. Starting from continuum mechanics we derive the discrete equations of motion and present a simulation scheme with support for user-in-the-loop interaction, geometric constraints and contact treatment. The interplay between accuracy and computational cost is discussed in depth, and practical approximations are analyzed with an emphasis on robustness and efficiency, as required by interactive simulation. The first part of the thesis focuses on deformable material discretization using the Finite Element Method with simplex elements and a corotational linear constitutive model, and presents our contributions to the solution of widely reported robustness problems in case of large stretch deformations and finite element degeneration. First,we introduce a stress differential approximation for quasi-implicit corotational linear FEM that improves its results for large deformations and closely matches the fullyimplicit solution with minor computational overhead. Next, we address the problem ofrobustness and realism in simulations involving element degeneration, and show that existing methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new continuous-time approach, degeneration-aware polar decomposition, that avoids such flaws and yields robust degeneration recovery. In the second part we focus on geometry representation and contact determination for deformable solids with highly detailed surfaces. Given a high resolution closed surface mesh we automatically build a coarse embedding tetrahedralization and a partitioned representation of the collision geometry in a preprocess. During simulation, our proposed contact determination algorithm finds all intersecting pairs of deformed triangles using a memory-efficient barycentric bounding volume hierarchy, connects them into potentially disjoint intersection curves and performs a topological flood process on the exact intersection surfaces to discover a minimal set of contact points. A novel contact normal definition is used to find contact point correspondences suitable for contact treatment.Aquesta tesi tracta sobre la simulació interactiva de sòlids deformables amb superfícies detallades, modelats amb el Mètode dels Elements Finits (FEM) Corotacionals. A partir de la mecànica del continuu derivem les equacions del moviment discretes i presentem un esquema de simulació amb suport per a interacció d'usuari, restriccions geomètriques i tractament de contactes. Aprofundim en la interrelació entre precisió i cost de computació, i analitzem aproximacions pràctiques fent èmfasi en la robustesa i l'eficiència necessàries per a la simulació interactiva. La primera part de la tesi es centra en la discretització del material deformable mitjançant el Mètode dels Elements Finits amb elements de tipus s'implex i un model constituent basat en elasticitat linial corotacional, i presenta les nostres contribucions a la solució de problemes de robustesa àmpliament coneguts que apareixen en cas de sobreelongament i degeneració dels elements finits. Primer introduïm una aproximació dels diferencials d'estress per a FEM linial corotacional amb integració quasi-implícita que en millora els resultats per a deformacions grans i s'apropa a la solució implícita amb un baix cost computacional. A continuació tractem el problema de la robustesa i el realisme en simulacions que inclouen degeneració d'elements finits, i mostrem que els mètodes existents presenten inconvenients que posen en perill la robustesa plausibilitat de la simulació en aplicacions interactives. Proposem un enfocament nou basat en temps continuu, la descomposició polar amb coneixement de degeneració, que evita els inconvenients esmentats i permet corregir la degeneració de forma robusta. A la segona part de la tesi ens centrem en la representació de geometria i la determinació de contactes per a sòlids deformables amb superfícies detallades. A partir d'una malla de superfície tancada construím una tetraedralització englobant de forma automàtica en un preprocés, i particionem la geometria de colisió. Proposem un algorisme de detecció de contactes que troba tots els parells de triangles deformats que intersecten mitjançant una jerarquia de volums englobants en coordenades baricèntriques, els connecta en corbes d'intersecció potencialment disjuntes i realitza un procés d'inundació topològica sobre les superfícies d'intersecció exactes per tal de descobrir un conjunt mínim de punts de contacte. Usem una definició nova de la normal de contacte per tal de calcular correspondències entre punts de contacte útils per al seu tractament.Postprint (published version