Breaking Good: Fracture Modes for Realtime Destruction

Drawing a direct analogy with the well-studied vibration or elastic modes, we introduce an object's fracture modes, which constitute its preferred or most natural ways of breaking. We formulate a sparsified eigenvalue problem, which we solve iteratively to obtain the n lowest-energy modes. These can be precomputed for a given shape to obtain a prefracture pattern that can substitute the state of the art for realtime applications at no runtime cost but significantly greater realism. Furthermore, any realtime impact can be projected onto our modes to obtain impact-dependent fracture patterns without the need for any online crack propagation simulation. We not only introduce this theoretically novel concept, but also show its fundamental and practical superiority in a diverse set of examples and contexts

ACM Transactions on Graphics

We present a boundary element based method for fast simulation of brittle fracture. By introducing simplifying assumptions that allow us to quickly estimate stress intensities and opening displacements during crack propagation, we build a fracture algorithm where the cost of each time step scales linearly with the length of the crackfront. The transition from a full boundary element method to our faster variant is possible at the beginning of any time step. This allows us to build a hybrid method, which uses the expensive but more accurate BEM while the number of degrees of freedom is low, and uses the fast method once that number exceeds a given threshold as the crack geometry becomes more complicated. Furthermore, we integrate this fracture simulation with a standard rigid-body solver. Our rigid-body coupling solves a Neumann boundary value problem by carefully separating translational, rotational and deformational components of the collision forces and then applying a Tikhonov regularizer to the resulting linear system. We show that our method produces physically reasonable results in standard test cases and is capable of dealing with complex scenes faster than previous finite- or boundary element approaches

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

A GROWTH-BASED APPROACH TO THE AUTOMATIC GENERATION OF NAVIGATION MESHES

Providing an understanding of space in game and simulation environments is one of the major challenges associated with moving artificially intelligent characters through these environments. The usage of some form of navigation mesh has become the standard method to provide a representation of the walkable space in game environments to characters moving around in that environment. There is currently no standardized best method of producing a navigation mesh. In fact, producing an optimal navigation mesh has been shown to be an NP-Hard problem. Current approaches are a patchwork of divergent methods all of which have issues either in the time to create the navigation meshes (e.g., the best looking navigation meshes have traditionally been produced by hand which is time consuming), generate substandard quality navigation meshes (e.g., many of the automatic mesh production algorithms result in highly triangulated meshes that pose problems for character navigation), or yield meshes that contain gaps of areas that should be included in the mesh and are not (e.g., existing growth-based methods are unable to adapt to non-axis-aligned geometry and as such tend to provide a poor representation of the walkable space in complex environments). We introduce the Planar Adaptive Space Filling Volumes (PASFV) algorithm, Volumetric Adaptive Space Filling Volumes (VASFV) algorithm, and the Iterative Wavefront Edge Expansion Cell Decomposition (Wavefront) algorithm. These algorithms provide growth-based spatial decompositions for navigation mesh generation in either 2D (PASFV) or 3D (VASFV). These algorithms generate quick (on demand) decompositions (Wavefront), use quad/cube base spatial structures to provide more regular regions in the navigation mesh instead of triangles, and offer full coverage decompositions to avoid gaps in the navigation mesh by adapting to non-axis-aligned geometry. We have shown experimentally that the decompositions offered by PASFV and VASFV are superior both in character navigation ability, number of regions, and coverage in comparison to the existing and commonly used techniques of Space Filling Volumes, Hertel-Melhorn decomposition, Delaunay Triangulation, and Automatic Path Node Generation. Finally, we show that our Wavefront algorithm retains the superior performance of the PASFV and VASFV algorithms while providing faster decompositions that contain fewer degenerate and near degenerate regions. Unlike traditional navigation mesh generation techniques, the PASFV and VASFV algorithms have a real time extension (Dynamic Adaptive Space Filling Volumes, DASFV) which allows the navigation mesh to adapt to changes in the geometry of the environment at runtime. In addition, it is possible to use a navigation mesh for applications above and beyond character path planning and navigation. These multiple uses help to increase the return on the investment in creating a navigation mesh for a game or simulation environment. In particular, we will show how to use a navigation mesh for the acceleration of collision detection

A Material Point Method for Elastoplasticity with Ductile Fracture and Frictional Contact

Simulating physical materials with dynamic movements to photo-realistic resolution has always been one of the most crucial and challenging topics in Computer Graphics. This dissertation considers large-strain elastoplasticity theory applied to the low-to-medium stiffness regime, with topological changes and codimensional objects incorporated. We introduce improvements to the Material Point Method (MPM) for two particular objectives, simulating fracturing ductile materials and incorporation of MPM and Lagrangian Finite Element Method (FEM).Our first contribution, simulating ductile fracture, utilizes traditional particle-based MPM [SSC13, SCS94] as well as the Lagrangian energy formulation of [JSS15] which uses a tetrahedron mesh, rather than particle-based estimation of the deformation gradient and potential energy. We model failure and fracture via elastoplasticity with damage. The material is elastic until its deformation exceeds a Rankine or von Mises yield condition. At that point, we use a softening model that shrinks the yield surface until it reaches the damage thresh- old. Once damaged, the material Lam ́e coefficients are modified to represent failed material. This approach to simulating ductile fracture with MPM is successful, as MPM naturally captures the topological changes coming from the fracture. However, rendering the crack surfaces can be challenging. We design a novel visualization technique dedicated to rendering the material’s boundary and its intersection with the evolving crack surfaces. Our approach uses a simple and efficient element splitting strategy for tetrahedron meshes to create crack surfaces. It employs an extrapolation technique based on the MPM simulation. For traditional particle-based MPM, we use an initial Delaunay tetrahedralization to connect randomly sampled MPM particles. Our visualization technique is a post-process and can run after the MPM simulation for efficiency. We demonstrate our method with several challenging simulations of ductile failure with considerable and persistent self-contact and applications with thermomechanical models for baking and cooking.Our second contribution, hybrid MPM–Lagrangian-FEM, aims to simulate elastic objects like hair, rubber, and soft tissues. It utilizes a Lagrangian mesh for internal force computation and a Eulerian grid for self-collision, as well as coupling with external materials. While recent MPM techniques allow for natural simulation of hyperelastic materials represented with Lagrangian meshes, they utilize an updated Lagrangian discretization and use the Eulerian grid degrees of freedom to take variations of the potential energy. It often coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts. We develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM, e.g., sand, snow, etc. Furthermore, while recent MPM advances allow for resolution of frictional contact with codimensional simulation of hyperelasticity, they do not generalize to the case of volumetric materials. We show that our hybrid approach resolves these issues. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling

IST Austria Thesis

This thesis describes a brittle fracture simulation method for visual effects applications. Building upon a symmetric Galerkin boundary element method, we first compute stress intensity factors following the theory of linear elastic fracture mechanics. We then use these stress intensities to simulate the motion of a propagating crack front at a significantly higher resolution than the overall deformation of the breaking object. Allowing for spatial variations of the material's toughness during crack propagation produces visually realistic, highly-detailed fracture surfaces. Furthermore, we introduce approximations for stress intensities and crack opening displacements, resulting in both practical speed-up and theoretically superior runtime complexity compared to previous methods. While we choose a quasi-static approach to fracture mechanics, ignoring dynamic deformations, we also couple our fracture simulation framework to a standard rigid-body dynamics solver, enabling visual effects artists to simulate both large scale motion, as well as fracturing due to collision forces in a combined system. As fractures inside of an object grow, their geometry must be represented both in the coarse boundary element mesh, as well as at the desired fine output resolution. Using a boundary element method, we avoid complicated volumetric meshing operations. Instead we describe a simple set of surface meshing operations that allow us to progressively add cracks to the mesh of an object and still re-use all previously computed entries of the linear boundary element system matrix. On the high resolution level, we opt for an implicit surface representation. We then describe how to capture fracture surfaces during crack propagation, as well as separate the individual fragments resulting from the fracture process, based on this implicit representation. We show results obtained with our method, either solving the full boundary element system in every time step, or alternatively using our fast approximations. These results demonstrate that both of these methods perform well in basic test cases and produce realistic fracture surfaces. Furthermore we show that our fast approximations substantially out-perform the standard approach in more demanding scenarios. Finally, these two methods naturally combine, using the full solution while the problem size is manageably small and switching to the fast approximations later on. The resulting hybrid method gives the user a direct way to choose between speed and accuracy of the simulation

Être en apesanteur :

Résumé Le dispositif de réalité virtuelle Être en apesanteur faisant l’objet de cet article est issu du projet du Labex Arts-H2H Le Corps Infini qui réunissait différentes formes d’expression artistique du corps en apesanteur dans l’espace scénique du cirque. Cette installation est à la fois un processus de recherche création et un des fruits des expérimentations réalisées autour du projet. Elle nous a conduit à s’interroger sur les caractéristiques diégétiques d’un monde virtuel suggérant des perceptions d’apesanteur, et en quoi des interactions avec des matières fluides et volatiles pourraient venir renforcer cette sensation d’incarnation dans ce monde. Lors de la performance Le Corps Infini, le monde virtuel Être en apesanteur invitait le public à vivre le point de vue aérien des circassiennes, et une sensation de gravité altérée. En explorant un environnement onirique sans pesanteur, le spectateur entre dans un état d’énaction lorsque ses gestes s’incarnent progressivement dans son corps virtuel. Porté par une balancelle, il se met dans une posture quasi fœtale, comme s’il était soutenu par la main d’une personne, tel un embryon dans sa poche amniotique.Abstract The artistic installation Being in weightlessness studied in this article is born from the Labex Art & H2H Infinite Body project which is gathering multiple artistic representations of bodies in suspension in the circus scenic space. This installation is both a research-creation process and a result of experimentations produced around the project. It led us to question diegetic characteristics of a zero-gravity virtual world and how interactions with fluids and volatile materials could improve feelings of incarnation in this world. Being in weightlessness invited the public to experience weightless feelings from the aerial viewpoint of the Circassians during the Infinite Body performance. By exploring an environment without gravity, the spectator enters a state of enaction while his gestures are gradually embodied in his virtual body. Comfortably suspended in a spherical swing, he puts himself in an almost fetal position as if it was supported by an invisible hand, like an embryo in its amniotic sac

A Materials Science Driven Pattern Generation Solution to Fracturing Computer Generated Glass for Films and Games

Believably and realistically fracturing computer generated glass for visual effects has been previously solved through various methods such as algorithmic approaches, utilizing texture maps, or finite element analysis. These solutions can achieve some believable results but often at the cost of one or more of the following: simulation time, preparation time, art directability, consistency with materials science research, or the requirement of creating or utilizing fixed assets or maps. In this thesis I present a novel method that draws from the appropriate literature and focuses on quickly generating accurate fracture patterns. The method takes inputs such as the artist’s animation of an impact and desired object properties, and outputs fracture patterns used for breaking objects apart based on input values, materials science literature, and fracture mechanics. After determining all of the fracture pattern variables such as the number of radial and concentric cracks, the artist is able to override the computed parameters to retain control and art directability. Implementation of this method was performed using MAXScript, the built-in scripting language for Autodesk 3ds Max. The result is a computationally fast and mechanically accurate tool while retaining art directability to fulfill film storyboards or game design

Analysis and Generation of Quality Polytopal Meshes with Applications to the Virtual Element Method

This thesis explores the concept of the quality of a mesh, the latter being intended as the discretization of a two- or three- dimensional domain. The topic is interdisciplinary in nature, as meshes are massively used in several fields from both the geometry processing and the numerical analysis communities. The goal is to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. In other words, a good quality mesh that is also cheap to handle, overcoming the typical trade-off between quality and computational cost. To reach this goal, we first need to answer the question: ''How, and how much, does the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depend on the particular mesh adopted to model the problem? And which geometrical features of the mesh most influence the result?'' We present a comparative study of the different mesh types, mesh generation techniques, and mesh quality measures currently available in the literature related to both engineering and computer graphics applications. This analysis leads to the precise definition of the notion of quality for a mesh, in the particular context of numerical simulations of partial differential equations with the virtual element method, and the consequent construction of criteria to determine and optimize the quality of a given mesh. Our main contribution consists in a new mesh quality indicator for polytopal meshes, able to predict the performance of the virtual element method over a particular mesh before running the simulation. Strictly related to this, we also define a quality agglomeration algorithm that optimizes the quality of a mesh by wisely agglomerating groups of neighboring elements. The accuracy and the reliability of both tools are thoroughly verified in a series of tests in different scenarios