Modeling the geometry of solid materials cracking and shattering into elaborately shaped pieces is a painstaking task, which is often impractical to tune by hand when a large number of fragments are produced. In Walt Disney's animated feature film Bolt, cracking and shattering objects were prominent visual elements in a number of action sequences. We designed a system to facilitate the modeling of cracked and shattered objects, enabling the automatic generation of a large number of fragments while retaining the flexibility to artistically control the density and complexity of the crack formation, or even manually controlling the shape of the resulting pieces where necessary. Our method resolves every fragment exactly into a separate triangulated surface mesh, producing pieces that line up perfectly even upon close inspection, and allows straightforward transfer of texture and look properties from the un-fractured model.
Hair simulation remains one of the most challenging aspects of creating virtual characters. Most research focuses on handling the massive geometric complexity of hundreds of thousands of interacting hairs. This is accomplished either by using brute force simulation or by reducing degrees of freedom with guide hairs. This paper presents a hybrid Eulerian/Lagrangian approach to handling both self and body collisions with hair efficiently while still maintaining detail. Bulk interactions and hair volume preservation is handled efficiently and effectively with a FLIP based fluid solver while intricate hair-hair interaction is handled with Lagrangian self-collisions. Thus the method has the efficiency of continuum/guide based hair models with the high detail of Lagrangian self-collision approcahes.
Abstract:One of the most fundamental challenges in plastic surgery is the alteration of the geometry and topology of the skin. The specific decisions made by the surgeon concerning the size and shape of the tissue to be removed and the subsequent closure of the resulting wound may have a dramatic affect on the quality of life for the patient after the procedure is completed. The plastic surgeon must look at the defect created as an organic puzzle, designing the optimal pattern to close the hole aesthetically and efficiently. In the past, such skills were the distillation of years of hands-on practice on live patients, while relevant reference material was limited to two-dimensional illustrations. Practicing this procedure on a personal computer has been largely impractical to date, but recent technological advances may come to challenge this limitation. We present a comprehensive realtime virtual surgical environment, based on finite element modeling and simulation of tissue cutting and manipulation. Our system demonstrates the fundamental building blocks of plastic surgery procedures on a localized tissue flap, and provides a proof of concept for larger simulation systems usable in the authoring of complex procedures on elaborate subject geometry.
Abstract:The immersed boundary method is an algorithm for simulating the interaction of immersed elastic bodies or boundaries with a viscous incompressible fluid. The immersed elastic material is represented in the fluid equations by a system or held of applied forces. The particular case of Stokes flow with applied forces on a periodic domain involves two related mathematical complications. One of these is that an arbitrary constant vector may be added to the fluid velocity, and the other is the constraint that the integral of the applied force must be zero. Typically, forces defined on a freely floating elastic immersed boundary or body satisfy this constraint, but there are many important classes of forces that do not. For example, the so called "tether" forces that are used to prescribe the simulated configuration of an immersed boundary, possibly in a time-dependent manner, typically do not sum to zero. Another type of force that does not have zero integral is a uniform force density that may be used to simulate an overall pressure gradient driving flow through a system. We present a method for periodic Stokes flow that when used with tether points admits the use of all forces irrespective of their integral over the domain. A byproduct of this method is that the additive constant velocity associated with periodic Stokes flow is uniquely determined. Indeed, the additive constant is chosen at each time step so that the sum of the tether forces balances the sum of any other forces that may be applied.
Abstract:Peristaltic pumping by wavelike contractions is a fundamental biomechanical mechanism for fluid and material transport and is used in the esophagus, intestine, oviduct, and ureter. While peristaltic pumping of a Newtonian fluid is well understood, in many important settings, as in the fluid dynamics of reproduction, the fluids have non-Newtonian responses. Here, we present a numerical method for simulating an Oldroyd-B fluid coupled to contractile, moving walls. A marker and cell grid-based projection method is used for the fluid equations and an immersed boundary method is used for coupling to a Lagrangian representation of the deforming walls. We examine numerically the peristaltic transport of a highly viscous Oldroyd-B fluid over a range of Weissenberg numbers and peristalsis wavelengths and amplitudes.
Abstract:We present a novel algorithm for collision processing on triangulated meshes. Our method robustly maintains a collision free state on complex geometries while resorting to collision resolution at time intervals often comparable to the frame rate. Our approach is motivated by the behavior of a thin layer of fluid inserted in the empty space between nearly-colliding parts of the simulated surface, acting as a cushioning mechanism. Point-triangle or edge-edge pairs on a collision course are naturally resolved by the incompressible response of this fluid buffer. This response is formulated into a globally coupled nonlinear system which we solve using Newton iteration and symmetric, positive definite solvers. The globally coupled treatment of collisions allows us to resolve up to two orders of magnitude more collisions than traditional greedy algorithms (e.g. Gauss-Seidel collision response) and take substantially larger time steps without compromising the visual quality of the simulation.
Abstract:We propose a novel approach to fracturing (and denting) brittle materials. To avoid the computational burden imposed by the stringent time step restrictions of explicit methods or with solving nonlinear systems of equations for implicit methods, we treat the material as a fully rigid body in the limit of infinite stiffness. In addition to a triangulated surface mesh and level set volume for collisions, each rigid body is outfitted with a tetrahedral mesh upon which finite element analysis can be carried out to provide a stress map for fracture criteria. We demonstrate that the commonly used stress criteria can lead to arbitrary fracture (especially for stiff materials) and instead propose the notion of a time averaged stress directly into the FEM analysis. When objects fracture, the virtual node algorithm provides new triangle and tetrahedral meshes in a straightforward and robust fashion. Although each new rigid body can be rasterized to obtain a new level set, small shards can be difficult to accurately resolve. Therefore, we propose a novel collision handling technique for treating both rigid bodies and rigid body thin shells represented by only a triangle mesh.
Abstract:We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. In order to leverage existing algorithms for nonconvex bodies, multiple collisions, large contact groups, stacking, etc., we use maximal rather than generalized coordinates and take an impulse-based approach that allows us to treat articulation, contact, and collision in a unified manner. Traditional constraint handling methods are subject to drift, and we propose a novel prestabilization method that does not require tunable potentially stiff parameters as does Baumgarte stabilization. This differs from poststabilization in that we compute allowable trajectories before moving the rigid bodies to their new positions, instead of correcting them after the fact when it can be difficult to incorporate the effects of contact and collision. A poststabilization technique is used for momentum and angular momentum. Our approach works with any black box method for specifying valid joint constraints and no special considerations are required for arbitrary closed loops or branching. Moreover, our implementation is linear both in the number of bodies and in the number of auxiliary contact and collision constraints, unlike many other methods that are linear in the number of bodies, but not in the number of auxiliary constraints
Abstract: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.