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

Deformation embedding for point-based elastoplastic simulation

pre-printWe present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space-the least-squares best fit of the material's rest state into three dimensions. Nearest neighbor queries in the embedded space efficiently update particle neighborhoods to account for plastic flow. These queries are simpler and more efficient than remeshing strategies employed in mesh-based finite element methods.We also introduce a new estimate for the volume of a particle, allowing particle masses to vary spatially and temporally with fixed density. Our approach can handle simultaneous extreme elastic and plastic deformations. We demonstrate our approach on a variety of examples that exhibit a wide range of material behaviors

Conformation constraints for efficient viscoelastic fluid simulation

The simulation of high viscoelasticity poses important computational challenges. One is the difficulty to robustly measure strain and its derivatives in a medium without permanent structure. Another is the high stiffness of the governing differential equations. Solutions that tackle these challenges exist, but they are computationally slow. We propose a constraint-based model of viscoelasticity that enables efficient simulation of highly viscous and viscoelastic phenomena. Our model reformulates, in a constraint-based fashion, a constitutive model of viscoelasticity for polymeric fluids, which defines simple governing equations for a conformation tensor. The model can represent a diverse palette of materials, spanning elastoplastic, highly viscous, and inviscid liquid behaviors. In addition, we have designed a constrained dynamics solver that extends the position-based dynamics method to handle efficiently both position-based and velocity-based constraints. We show results that range from interactive simulation of viscoelastic effects to large-scale simulation of high viscosity with competitive performance

Visual Simulation of Multiple Unmixable Fluids

International audienceWe present a novel grid-based method for simulating multiple unmixable fluids moving and interacting. Unlike previous methods that can only represent the interface between two fluids (usually between liquid and gas), this method can handle an arbitrary number of fluids through multiple independent level sets coupled with a constrain condition. To capture the fluid surface more accurately, we extend the particle level set method to a multi-fluid version. It shares the advantages of the particle level set method, and has the ability to track the interfaces of multiple fluids. To handle the dynamic behavior of different fluids existing together, we use a multiphase fluid formulation based on a smooth weight function

Liquid surface tracking with error compensation

Our work concerns the combination of an Eulerian liquid simulation with a high-resolution surface tracker (e.g. the level set method or a Lagrangian triangle mesh). The naive application of a high-resolution surface tracker to a low-resolution velocity field can produce many visually disturbing physical and topological artifacts that limit their use in practice. We address these problems by defining an error function which compares the current state of the surface tracker to the set of physically valid surface states. By reducing this error with a gradient descent technique, we introduce a novel physics-based surface fairing method. Similarly, by treating this error function as a potential energy, we derive a new surface correction force that mimics the vortex sheet equations. We demonstrate our results with both level set and mesh-based surface trackers

Master of Science

thesisWe present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space-the least-squares best fit of the material's rest state into three dimensions. Together with plastic offsets that map embedded space to rest space, the embedded space allows us to robustly estimate the deformation gradient, compute elastic forces, and account for plastic flow. We additionally introduce an estimate for the volume of a particle, opening the door for nonuniform sampling, and describe a technique to increase the robustness of point-based elastic simulation. Our approach can handle arbitrarily large elastic deformations and extreme plastic deformations. Because the approach is point-based, there is no need for complex remeshing-the corresponding operation is a simple neighborhood query in embedded space. We demonstrate our approach on a variety of examples that display a wide range of material behaviors