Month: April 2013

A Two-Continua Approach to Eulerian Simulation of Water Spray

Michael B. Nielsen, Ole Osterby

Physics based simulation of the dynamics of water spray – water droplets dispersed in air – is a means to increase the visual plausibility of computer graphics modeled phenomena such as waterfalls, water jets and stormy seas. Spray phenomena are frequently encountered by the visual effects industry and often challenge state of the art methods. Current spray simulation pipelines typically employ a combination of Lagrangian (particle) and Eulerian (volumetric) methods – the Eulerian methods being used for parts of the spray where individual droplets are not apparent. However, existing Eulerian methods in computer graphics are based on gas solvers that will for example exhibit hydrostatic equilibrium in certain scenarios where the air is expected to rise and the water droplets fall. To overcome this problem, we propose to simulate spray in the Eulerian domain as a two-way coupled two-continua of air and water phases co-existing at each point in space. The fundamental equations originate in applied physics and we present a number of contributions that make Eulerian two-continua spray simulation feasible for computer graphics applications. The contributions include a Poisson equation that fits into the operator splitting methodology as well as (semi-)implicit discretizations of droplet diffusion and the drag force with improved stability properties. As shown by several examples, our approach allows us to more faithfully capture the dynamics of spray than previous Eulerian methods.

A Two-Continua Approach to Eulerian Simulation of Water Spray

Non-Polynomial Galerkin Projection on Deforming Meshes

Matt Stanton, Yu Sheng, Martin Wicke, Federico Perazzi, Amos Yuen, Srinivasa Narasimhan, Adrien Treuille

This paper extends Galerkin projection to a large class of non-polynomial functions typically encountered in graphics. We demonstrate the broad applicability of our approach by applying it to two strikingly different problems: fluid simulation and radiosity rendering, both using deforming meshes. Standard Galerkin projection cannot efficiently approximate these phenomena. Our approach, by contrast, enables the compact representation and approximation of these complex non-polynomial systems, including quotients and roots of polynomials. We rely on representing each function to be model-reduced as a composition of tensor products, matrix inversions, and matrix roots. Once a function has been represented in this form, it can be easily model-reduced, and its reduced form can be evaluated with time and memory costs dependent only on the dimension of the reduced space.

Non-Polynomial Galerkin Projection on Deforming Meshes

Position Based Fluids

Miles Macklin, Matthias Müller

In fluid simulation, enforcing incompressibility is crucial for realism; it is also computationally expensive. Recent work has improved efficiency, but still requires time-steps that are impractical for real-time applications. In this work we present an iterative density solver integrated into the Position Based Dynamics framework (PBD). By formulating and solving a set of positional constraints that enforce constant density, our method allows similar incompressibility and convergence to modern smoothed particle hydrodynamic (SPH) solvers, but inherits the stability of the geometric, position based dynamics method, allowing large time steps suitable for real-time applications. We incorporate an artificial pressure term that improves particle distribution, creates surface tension, and lowers the neighborhood requirements of traditional SPH. Finally, we address the issue of energy loss by applying vorticity confinement as a velocity post process.

Position Based Fluids

Real-Time Dynamic Fracture with Volumetric Approximate Convex Decompositions

Matthias Mueller, Nuttapong Chentanez, Tae-Yong Kim

We propose a new fast, robust and controllable method to simulate the dynamic destruction of large and complex objects in real time. The common method for fracture simulation in computer games is to pre-fracture models and replace objects by their pre-computed parts at run-time. This popular method is computationally cheap but has the disadvantages that the fracture pattern does not align with the impact location and that the number of hierarchical fracture levels is fixed. Our method allows dynamic fracturing of large objects into an unlimited number of pieces fast enough to be used in computer games. We represent visual meshes by volumetric approximate convex decompositions (VACD) and apply user-defined fracture patterns dependent on the impact location. The method supports partial fracturing meaning that fracture patterns can be applied locally at multiple locations of an object. We propose new methods for computing a VACD, for approximate convex hull construction and for detecting islands in the convex decomposition after partial destruction in order to determine support structures.

Real-Time Dynamic Fracture with Volumetric Approximate Convex Decompositions

Robust Inside-Outside Segmentation using Generalized Winding Numbers

Alec Jacobson, Ladislav Kavan, Olga Sorkine-Hornung

Solid shapes in computer graphics are often represented with boundary descriptions, e.g. triangle meshes, but animation, physically-based simulation, and geometry processing are more realistic and accurate when explicit volume representations are available. Tetrahedral meshes which exactly contain (interpolate) the input boundary description are desirable but difficult to construct for a large class of input meshes. Character meshes and CAD models are often composed of many connected components with numerous self-intersections, non-manifold pieces, and open boundaries, precluding existing meshing algorithms. We propose an automatic algorithm handling all of these issues, resulting in a compact discretization of the input’s inner volume. We only require reasonably consistent orientation of the input triangle mesh. By generalizing the winding number for arbitrary triangle meshes, we define a function that is a perfect segmentation for watertight input and is well-behaved otherwise. This function guides a graphcut segmentation of a constrained Delaunay tessellation (CDT), providing a minimal description that meets the boundary exactly and may be fed as input to existing tools to achieve element quality. We highlight our robustness on a number of examples and show applications of solving PDEs, volumetric texturing and elastic simulation.

Robust Inside-Outside Segmentation using Generalized Winding Numbers

Interactive Authoring of Simulation-Ready Plants

Yili Zhao, Jernej Barbič

Physically based simulation can produce quality motion of plants, but requires an authoring stage to convert plant “polygon soup” triangle meshes to a format suitable for physically based simulation. We give a system that can author complex simulation-ready plants in a manner of minutes. Our system decomposes the plant geometry, establishes a hierarchy, builds and connects simulation meshes, and detects instances. It scales to anatomically realistic geometry of adult plants, is robust to non-manifold input geometry, gaps between branches or leaves, free-flying leaves not connected to any branch, spurious geometry, and plant self-collisions in the in- put configuration. We demonstrate the results using a FEM model reduction simulator that can compute large-deformation dynamics of complex plants at interactive rates, subject to user forces, gravity or randomized wind. We also provide plant fracture (with pre-specified patterns), inverse kinematics to easily pose plants, as well as interactive design of plant material properties. We authored and simulated over 100 plants from diverse climates and geographic regions, including broadleaf (deciduous) trees and conifers, bushes and flowers. Our largest simulations involve anatomically realistic adult trees with hundreds of branches and over 100,000 leaves.

Interactive Authoring of Simulation-Ready Plants

Liquid Surface Tracking with Error Compensation

Morten Bojsen-Hansen, Chris Wojtan

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.

Liquid Surface Tracking with Error Compensation

Folding and Crumpling Adaptive Sheets

Rahul Narain, Tobias Pfaff, and James F. O’Brien

We present a technique for simulating plastic deformation in sheets of thin materials, such as crumpled paper, dented metal, and wrinkled cloth. Our simulation uses a framework of adaptive mesh refinement to dynamically align mesh edges with folds and creases. This framework allows efficient modeling of sharp features and avoids bend locking that would be otherwise caused by stiff in-plane behavior. By using an explicit plastic embedding space we prevent remeshing from causing shape diffusion. We include several examples demonstrating that the resulting method realistically simulates the behavior of thin sheets as they fold and crumple.

Folding and Crumpling Adaptive Sheets

Near-exhaustive Precomputation of Secondary Cloth Effects

Doyub Kim, Woojong Koh, Rahul Narain, Kayvon Fatahalian, Adrien Treuille, James F. O’Brien

The central argument against data-driven methods in computer graphics rests on the curse of dimensionality: it is intractable to precompute “everything” about a complex space. In this paper, we challenge that assumption by using several thousand CPU-hours to perform a massive exploration of the space of secondary clothing effects on a character animated through a large motion graph. Our system continually explores the phase space of cloth dynamics, incrementally constructing a secondary cloth motion graph that captures the dynamics of the system. We find that it is possible to sample the dynamical space to a low visual error tolerance and that secondary motion graphs containing tens of gigabytes of raw mesh data can be compressed down to only tens of megabytes. These results allow us to capture the effect of high-resolution, off-line cloth simulation for a rich space of character motion and deliver it efficiently as part of an interactive application.

Near-exhaustive Precomputation of Secondary Cloth Effects

Eulerian-on-Lagrangian Simulation

Ye Fan, Joshua Litven, David I.W. Levin, Dinesh K. Pai

We describe an Eulerian-on-Lagrangian solid simulator that reduces or eliminates many of the problems experienced by fully Eulerian methods but retains its advantages. Our method does not require the construction of an explicit object discretization and the fixed nature of the simulation mesh avoids tangling during large deformations. By introducing Lagrangian modes to the simulation we enable unbounded simulation domains and reduce the time-step restrictions which can plague Eulerian simulations. Our method features a new solver that can resolve contact between multiple objects while simultaneously distributing motion between the Lagrangian and Eulerian modes in a least-squares fashion. Our method successfully bridges the gap between Lagrangian and Eulerian simulation methodologies without having to abandon either one.

Eulerian-on-Lagrangian Simulation