Physics-Based Animation

Oleksiy Busaryev, Tamal K. Dey, Huamin Wang

The fractures of thin plates often exhibit complex physical behaviors in the real world. In particular, fractures caused by tearing are different from fractures caused by in-plane motions. In this paper, we study how to make thin-plate fracture animations more realistic from three perspectives. We propose a stress relaxation method, which is applied to avoid shattering artifacts after generating each fracture cut. We formulate a fracture-aware remeshing scheme based on constrained Delaunay triangulation, to adaptively provide more fracture details. Finally, we use our multi-layered model to simulate complex fracture behaviors across thin layers. Our experiment shows that the system can efficiently and realistically simulate the fractures of multi-layered thin plates.

Adaptive Fracture Simulation of Multi-Layered Thin Plates

Zhili Chen, Renguo Feng, Huamin Wang

Real-world cloth exhibits complex behaviors when it contacts deformable bodies. In this paper, we study how to improve the simulation of cloth-body interactions from three perspectives: collision, friction, and air pressure. We propose an efficient and robust algorithm to detect the collisions between cloth and deformable bodies, using the surface traversal technique. We develop a friction measurement device and we use it to capture frictional data from real-world experiments. The derived friction model can realistically handle complex friction properties of cloth, including anisotropy and nonlinearity. To produce pressure effects caused by the air between cloth and deformable bodies, we define an air mass field on the cloth layer and we use real-world air permeability data to animate it over time. Our results demonstrate the efficiency and accuracy of our system in simulating objects with a three-layer structure (i.e., a cloth layer, an air layer, and an inner body layer), such as pillows, comforters, down jackets, and stuffed toys.

Modeling Friction and Air Effects between Cloth and Deformable Bodies

Ryoichi Ando, Nils Thürey and Chris Wojtan

We introduce a new method for efficiently simulating liquid with extreme amounts of spatial adaptivity. Our method combines several key components to drastically speed up the simulation of large-scale fluid phenomena: We leverage an alternative Eulerian tetrahedral mesh discretization to significantly reduce the complexity of the pressure solve while increasing the robustness with respect to element quality and removing the possibility of locking. Next, we enable subtle free-surface phenomena by deriving novel second-order boundary conditions consistent with our discretization. We couple this discretization with a spatially adaptive Fluid-Implicit Particle (FLIP) method, enabling efficient, robust, minimally-dissipative simulations that can undergo sharp changes in spatial resolution while minimizing artifacts. Along the way, we provide a new method for generating a smooth and detailed surface from a set of particles with variable sizes. Finally, we explore several new sizing functions for determining spatially adaptive simulation resolutions, and we show how to couple them to our simulator. We combine each of these elements to produce a simulation algorithm that is capable of creating animations at high maximum resolutions while avoiding common pitfalls like inaccurate boundary conditions and inefficient computation.

Highly Adaptive Liquid Simulations on Tetrahedral Meshes

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

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

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

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

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

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

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