Efficient Deformations Using Custom Coordinate Systems

Physics-based deformable object simulations have been playing an increasingly important role in 3D computer graphics. They have been adopted for humanoid character animations as well as special effects such as fire and explosion. However, simulations of large, complex systems can consume large amounts of computation and mostly remain offline, which prohibits their use for interactive applications.We present several highly efficient schemes for deformable object simulation using custom spatial coordinate systems. Our choices span the spectrum of subspace to full space and both Lagrangian and Eulerian viewpoints.Subspace methods achieve massive speedups over their “full space” counterparts by drastically reducing the degrees of freedom involved in the simulation. A long standing difficulty in subspace simulation is incorporating various non-linearities. They introduce expensive computational bottlenecks and quite often cause novel deformations that are outside the span of the subspace.We address these issues in articulated deformable body simulations from a Lagrangian viewpoint. We remove the computational bottleneck of articulated self-contact handling by deploying a pose-space cubature scheme, a generalization of the standard “cubature” approximation. To handle novel deformations caused by arbitrary external collisions, we introduce a generic approach called subspace condensation, which activates full space simulation on the fly when an out-of-basis event is encountered. Our proposed frameworkefficiently incorporates various non-linearities and allows subspace methods to be used in cases where they previously would not have been considered.Deformable solids can interact not only with each other, but also with fluids. Wedesign a new full space method that achieves a two-way coupling between deformable solids and an incompressible fluid where the underlying geometric representation is entirely Eulerian. No-slip boundary conditions are automatically satisfied by imposing a global divergence-free condition. We are able to simulate multiple solids undergoing complex, frictional contact while simultaneously interacting with a fluid. The complexity of the scenarios we are able to simulate surpasses those that we have seen from any previous method

Doctor of Philosophy

dissertationPhysical simulation has become an essential tool in computer animation. As the use of visual effects increases, the need for simulating real-world materials increases. In this dissertation, we consider three problems in physics-based animation: large-scale splashing liquids, elastoplastic material simulation, and dimensionality reduction techniques for fluid simulation. Fluid simulation has been one of the greatest successes of physics-based animation, generating hundreds of research papers and a great many special effects over the last fifteen years. However, the animation of large-scale, splashing liquids remains challenging. We show that a novel combination of unilateral incompressibility, mass-full FLIP, and blurred boundaries is extremely well-suited to the animation of large-scale, violent, splashing liquids. Materials that incorporate both plastic and elastic deformations, also referred to as elastioplastic materials, are frequently encountered in everyday life. Methods for animating such common real-world materials are useful for effects practitioners and have been successfully employed in films. We describe a point-based method for animating elastoplastic materials. Our primary contribution is a simple method for computing the deformation gradient for each particle in 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. One of the most significant drawbacks of physics-based animation is that ever-higher fidelity leads to an explosion in the number of degrees of freedom

Sparse Surface Constraints for Combining Physics-based Elasticity Simulation and Correspondence-Free Object Reconstruction

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable real-world data sources such as sparse observations without correspondences. We introduce a novel Lagrangian-Eulerian optimization formulation, including a cost function that penalizes differences to observations during an optimization run. This formulation matches correspondence-free, sparse observations from a single-view depth sequence with a finite element simulation of deformable bodies. In conjunction with an efficient hexahedral discretization and a stable, implicit formulation of collisions, our method can be used in demanding situation to recover a variety of material parameters, ranging from Young's modulus and Poisson ratio to gravity and stiffness damping, and even external boundaries. In a number of tests using synthetic datasets and real-world measurements, we analyse the robustness of our approach and the convergence behavior of the numerical optimization scheme

IST Austria Thesis

Fabrication of curved shells plays an important role in modern design, industry, and science. Among their remarkable properties are, for example, aesthetics of organic shapes, ability to evenly distribute loads, or efficient flow separation. They find applications across vast length scales ranging from sky-scraper architecture to microscopic devices. But, at the same time, the design of curved shells and their manufacturing process pose a variety of challenges. In this thesis, they are addressed from several perspectives. In particular, this thesis presents approaches based on the transformation of initially flat sheets into the target curved surfaces. This involves problems of interactive design of shells with nontrivial mechanical constraints, inverse design of complex structural materials, and data-driven modeling of delicate and time-dependent physical properties. At the same time, two newly-developed self-morphing mechanisms targeting flat-to-curved transformation are presented. In architecture, doubly curved surfaces can be realized as cold bent glass panelizations. Originally flat glass panels are bent into frames and remain stressed. This is a cost-efficient fabrication approach compared to hot bending, when glass panels are shaped plastically. However such constructions are prone to breaking during bending, and it is highly nontrivial to navigate the design space, keeping the panels fabricable and aesthetically pleasing at the same time. We introduce an interactive design system for cold bent glass façades, while previously even offline optimization for such scenarios has not been sufficiently developed. Our method is based on a deep learning approach providing quick and high precision estimation of glass panel shape and stress while handling the shape multimodality. Fabrication of smaller objects of scales below 1 m, can also greatly benefit from shaping originally flat sheets. In this respect, we designed new self-morphing shell mechanisms transforming from an initial flat state to a doubly curved state with high precision and detail. Our so-called CurveUps demonstrate the encodement of the geometric information into the shell. Furthermore, we explored the frontiers of programmable materials and showed how temporal information can additionally be encoded into a flat shell. This allows prescribing deformation sequences for doubly curved surfaces and, thus, facilitates self-collision avoidance enabling complex shapes and functionalities otherwise impossible. Both of these methods include inverse design tools keeping the user in the design loop

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

Fast Complementary Dynamics via Skinning Eigenmodes

We propose a reduced-space elasto-dynamic solver that is well suited for augmenting rigged character animations with secondary motion. At the core of our method is a novel deformation subspace based on Linear Blend Skinning that overcomes many of the shortcomings prior subspace methods face. Our skinning subspace is parameterized entirely by a set of scalar weights, which we can obtain through a small, material-aware and rig-sensitive generalized eigenvalue problem. The resulting subspace can easily capture rotational motion and guarantees that the resulting simulation is rotation equivariant. We further propose a simple local-global solver for linear co-rotational elasticity and propose a clustering method to aggregate per-tetrahedra non-linear energetic quantities. The result is a compact simulation that is fully decoupled from the complexity of the mesh.Comment: 20 pages, 24 figure

Real-time simulation of surgery by Proper Generalized Decomposition techniques

La simulación quirúrgica por ordenador en tiempo real se ha convertido en una alternativa muy atractiva a los simuladores quirúrgicos tradicionales. Entre otras ventajas, los simuladores por ordenador consiguen ahorros importantes de tiempo y de costes de mantenimiento, y permiten que los estudiantes practiquen sus habilidades quirúrgicas en un entorno seguro tantas veces como sea necesario. Sin embargo, a pesar de las capacidades de los ordenadores actuales, la cirugía computacional sigue siendo un campo de investigación exigente. Uno de sus mayores retos es la alta velocidad a la que se tienen que resolver complejos problemas de mecánica de medios continuos para que los interfaces hápticos puedan proporcionar un sentido del tacto realista (en general, se necesitan velocidades de respuesta de 500-1000 Hz).Esta tesis presenta algunos métodos numéricos novedosos para la simulación interactiva de dos procedimientos quirúrgicos habituales: el corte y el rasgado (o desgarro) de tejidos blandos. El marco común de los métodos presentados es el uso de la Descomposición Propia Generalizada (PGD en inglés) para la generación de vademécums computacionales, esto es, metasoluciones generales de problemas paramétricos de altas dimensiones que se pueden evaluar a velocidades de respuesta compatibles con entornos hápticos.En el caso del corte, los vademécums computacionales se utilizan de forma conjunta con técnicas basadas en XFEM, mientras que la carga de cálculo se distribuye entre una etapa off-line (previa a la ejecución interactiva) y otra on-line (en tiempo de ejecución). Durante la fase off-line, para el órgano en cuestión se precalculan tanto un vademécum computacional para cualquier posición de una carga, como los desplazamientos producidos por un conjunto de cortes. Así, durante la etapa on-line, los resultados precalculados se combinan de la forma más adecuada para obtener en tiempo real la respuesta a las acciones dirigidas por el usuario. En cuanto al rasgado, a partir de una ecuación paramétrica basada en mecánica del daño continuo, se obtiene un vademécum computacional. La complejidad del modelo se reduce mediante técnicas de Descomposición Ortogonal Propia (POD en inglés), y el vademécum se incorpora a una formulación incremental explícita que se puede interpretar como una especie de integrador temporal.A modo de ejemplo, el método para el corte se aplica a la simulación de un procedimiento quirúrgico refractivo de la córnea conocido como queratotomía radial, mientras que el método para el rasgado se centra en la simulación de la colecistectomía laparoscópica (la extirpación de la vesícula biliar mediante laparoscopia). En ambos casos, los métodos implementados ofrecen excelentes resultados en términos de velocidades de respuesta y producen simulaciones muy realistas desde los puntos de vista visual y háptico.The real-time computer-based simulation of surgery has proven to be an appealing alternative to traditional surgical simulators. Amongst other advantages, computer-based simulators provide considerable savings on time and maintenance costs, and allow trainees to practice their surgical skills in a safe environment as often as necessary. However, in spite of the current computer capabilities, computational surgery continues to be a challenging field of research. One of its major issues is the high speed at which complex problems in continuum mechanics have to be solved so that haptic interfaces can render a realistic sense of touch (generally, feedback rates of 500–1 000 Hz are required). This thesis introduces some novel numerical methods for the interactive simulation of two usual surgical procedures: cutting and tearing of soft tissues. The common framework of the presented methods is the use of the Proper Generalised Decomposition (PGD) for the generation of computational vademecums, i. e. general meta-solutions of parametric high-dimensional problems that can be evaluated at feedback rates compatible with haptic environments. In the case of cutting, computational vademecums are used jointly with XFEM-based techniques, and the computing workload is distributed into an off-line and an on-line stage. During the off-line stage, both a computational vademecum for any position of a load and the displacements produced by a set of cuts are pre-computed for the organ under consideration. Thus, during the on-line stage, the pre-computed results are properly combined together to obtain in real-time the response to the actions driven by the user. Concerning tearing, a computational vademecum is obtained from a parametric equation based on continuum damage mechanics. The complexity of the model is reduced by Proper Orthogonal Decomposition (POD) techniques, and the vademecum is incorporated into an explicit incremental formulation that can be viewed as a sort of time integrator. By way of example, the cutting method is applied to the simulation of a corneal refractive surgical procedure known as radial keratotomy, whereas the tearing method focuses on the simulation of laparoscopic cholecystectomy (i. e. the removal of the gallbladder). In both cases, the implemented methods offer excellent performances in terms of feedback rates, and produce.<br /

Lagrangian-on-Lagrangian Garment Design

Since the discovery of elastomeric materials, such as spandex or lycra, skintight clothing has revolutionized many different areas of the clothing industry, such as body-shaping clothing, athletic wear, and medical garments, among others. Often, this kind of clothing is designed to fulfill a given purpose, such as providing comfort, mobility, or improving recovery in the case of an athlete, provide support or exert some desired pressure in the case of medical garments, or actively deform the body to acquire some desired shape. Additionally, some designs aim to improve the life of the garment by, for example, minimizing tractions across the seams. While many tight-skin garments are sold in the market for generic body shapes, many of the purposes here mentioned are only achievable through a personalized fitting. To this end, we introduce a novel model, where the cloth is modeled as a membrane, parameterized as a function of the body. The cloth, is then able to slide on the body and deform it while staying always in contact. We call this model Lagrangian-on-Lagrangian. Based on this model, we develop an optimization framework, based on sensitivity analysis, capable of developing sewable patterns such that, when worn by a person, satisfy a given design target. With the framework, we include several design targets such as, body shape, stretch, pressure, sliding under motion, and seam traction. We evaluate our method on a variety of applications, as well as body shapes

Droplets, splashes and sprays: highly detailed liquids in visual effects production.

An often misunderstood or under-appreciated feature of the visual effects pipeline is the sheer quantity of components and layers that go into a single shot, or even, single effect. Liquids, often combining waves, splashes, droplets and sprays, are a particular example of this. Whilst there has been a huge amount of research on liquid simulation in the last decade or so, little has been successful in reducing the number of layers or elements required to create a plausible final liquid effect. Furthermore, the finer-scale phenomena of droplets and sprays, often introduced in this layered approach and crucial for plausibility, are some of the least well catered-for in the existing toolkit. In lieu of adequate tooling, creation of these elements relies heavily on non-physical methods, bespoke setups and artistic ingenuity. This project explores physically-based methods for creating these phenomena, demonstrat- ing improved levels of detail and plausibility over existing non-physical approaches. These provide an alternative to existing workflows that are heavily reliant on artistic input, allowing artists to focus efforts on creative direction rather than trying to recreate physical plausibility. We explore various approaches to increasing the level of detail captured in physically-based liquid simulations, developing a collection of tools that improve existing workflows. First, we investigate the potential of a re-simulation approach to increasing artist iteration on fluid simulations using previous simulation data. Following this, a novel droplet interaction model for ballistic particle simulations is developed to introduce higher levels of detail in simulations of liquid droplets and sprays. This allows physically-plausible interactions between droplet particles to be modelled efficiently and helps to create realistic droplet and spray behaviours. Then, to maximise the quality of the results of these and other particle-based simulations, we develop a high quality particle surfacing algorithm to handle the varied nature of inputs common in production. Finally, we discuss the development of an expression language to manipulate point and volume data commonly used in creating these simulations, as well as elsewhere throughout visual effects. This research was driven directly by production requirements in partnership with a world- leading visual effects studio, DNEG. Projects have been developed to immediately integrate into production, using efficient, industry-standard, open technologies such as OpenVDB. It is shown that the toolkit for splashing liquids, even at fine-scales, can be improved by incorporating greater physical motivation further demonstrating the importance of physical simulation in visual effects and suggesting effects similarly reliant on artistic input (e.g. character/skin deformation) may benefit from increased physical correctness

Particle method approach in mechanics of solids and granular materials

It is well recognized that matter has a discrete nature, but this aspect is usually considered only at the nano and microscale, on the other hand at the meso and macroscale levels compact matter is represented with a continuous model. At the macroscopic scales can be usefully adopted a discrete model of solids, without losing accuracy in the description of the main mechanical involved phenomena; when a multiscale study of solids is necessary the discrete approach, tailored to the scale of observation of interest, allows complete and exhaustive descriptions of many phenomena. This PhD thesis presents a general computational particle method suitable for analyzing the dynamic behaviour of compact solids as well as granular matters. The particle interaction is modelled through proper force functionals related to the nature of the material being analyzed (solid, granular or their interaction); such an approach is also adopted for the boundary and for the particle-particle contacts, so a unified mechanical model can be simply adopted for the simulation of a very wide class of mechanical problems under static or dynamic conditions. In particular the failure of brittle solids under dynamic dynamic impact can be easily predicted, avoiding the necessity of complex remeshing operations, stress field enrichment or the introduction of discontinuous displacement field, as typically required by numerical continuous approaches such as the finite element method. Moreover the discrete approach allows to simply model mechanical problems involving large displacements, friction or frictionless interactions with elastic boundaries, fragmentation and clustering of the failed material as well as cohesion in particle-like matters. Some examples aimed at demonstrating the versatility of the developed approach are finally presented: in particular the problems involving the failure of continuous solid elements under impact loading, confined particle flows and solid-granular materials interaction are simulated through the proposed approach and the related results are critically discussed and, when available, compared with literature data