This paper is concerned with the animation and control of vehicles with complex dynamics such as helicopters, boats, and cars. Motivated by recent developments in discrete geometric mechanics we develop a general framework for integrating the dynamics of holonomic and nonholonomic vehicles by preserving their state-space geometry and motion invariants. We demonstrate that the resulting integration schemes are superior to standard methods in numerical robustness and efficiency, and can be applied to many types of vehicles. In addition, we show how to use this framework in an optimal control setting to automatically compute accurate and realistic motions for arbitrary user-specified constraints.
Linear Time Super-Helices
Thin elastic rods such as cables, phone coils, tree branches, or hair, are common objects in the real world but computing their dynamics accurately remains challenging. The recent Super-Helix model, based on the discrete equations of Kirchhoff for a piecewise helical rod, is one of the most promising models for simulating non-stretchable rods that can bend and twist. However, this model suffers from a quadratic complexity in the number of discrete elements, which, in the context of interactive applications, makes it limited to a few number of degrees of freedom – or equivalently to a low number of variations in curvature along the mean curve. This paper proposes a new, recursive scheme for the dynamics of a Super-Helix, inspired by the popular algorithm of Featherstone for serial multibody chains. Similarly to Featherstone’s algorithm, we exploit the recursive kinematics of a Super-Helix to propagate elements inertias from the free end to the clamped end of the rod, while the dynamics is solved within a second pass traversing the rod in the reverse way. Besides the gain in linear complexity, which allows us to simulate a rod of complex shape much faster than the original approach, our algorithm makes it straightforward to simulate tree-like structures of Super-Helices, which turns out to be particularly useful for animating trees and plants realistically, under large displacements.
Continuum-based Strain Limiting
We present Continuum-based Strain Limiting (CSL) – a new method for limiting deformations in physically-based cloth simulations. Recent developments have led to methods which excel at simulating nearly inextensible materials, but the efficient simulation of general biphasic textiles and their anisotropic behavior remains challenging. Other approaches use softer materials and enforce limits on edge elongations, leading to discretization-dependent behavior. Moreover, they offer no explicit control over shearing and stretching unless specifically aligned meshes are used, which makes them less attractive for practical animation of anisotropic textiles. Based on a continuum deformation measure, our method allows accurate deformation control using individual thresholds for all types of strain. We impose deformation limits element-wise and cast the problem as a system of linear equations. We show how to further improve efficiency using an approximate formulation. CSL can be combined with any type of cloth simulator and, as a velocity filter, integrates seamlessly into standard collision handling frameworks.
Simulation of Two-Phase Flow with Sub-Scale Droplets and Bubble Effects
We present a new Eulerian-Lagrangian method for physics-based simulation of fluid flow, which includes automatic generation of sub-scale spray and bubbles. The Marker Level Set method is used to provide a simple geometric criterion for free marker generation. A filtering method, inspired from Weber number thresholding, further controls the free marker generation (in a physics-based manner). Two separate models are used, one for sub-scale droplets, the other for sub-scale bubbles. Droplets are evolved in a Newtonian manner, using a density extension drag force field, while bubbles are evolved using a model based on Stokes’ Law. We show that our model for sub-scale droplet and bubble dynamics is simple to couple with a full (macro-scale) Navier-Stokes two-phase flow model and is quite powerful in its applications. Our animations include coarse grained multiphase features interacting with fine scale multiphase features.
Simulation of Two-Phase Flow with Sub-Scale Droplets and Bubble Effects
Real-Time Fluid Simulation Using Discrete Sine/Cosine Transforms
Recent advances in fluid simulations have yielded exceptionally realistic imagery. However, most algorithms have computational requirements that are prohibitive for real-time simulations. Using Fourier based solutions mitigates this issue, although due to wraparound, boundary conditions are not naturally available, leading to inconsistencies near the boundary. We show that slip boundary conditions can be imposed by solving the mass conservation step using cosine and sine transforms instead of the Fourier transform.
Further, we show that measures against density dissipation can be computed using cosine transforms and we describe a new method to compute surface tension in the same domain. This combination of related algorithms leads to real-time simulations with boundary conditions.
Real-Time Fluid Simulation Using Discrete Sine/Cosine Transforms
Implicit Contact Handling for Deformable Objects
We present an algorithm for robust and efficient contact handling of deformable objects. By being aware of the internal dynamics of the colliding objects, our algorithm provides smooth rolling and sliding, stable stacking, robust impact handling, and seamless coupling of heterogeneous objects, all in a unified manner. We achieve dynamicsawareness through a constrained dynamics formulation with implicit complementarity constraints, and we present two major contributions that enable an efficient solution of the constrained dynamics problem: a time stepping algorithm that robustly ensures non-penetration and progressively refines the formulation of constrained dynamics, and a new solver for large mixed linear complementarity problems, based on iterative constraint anticipation. We show the application of our algorithm in challenging scenarios such as multi-layered cloth moving at high velocities, or colliding deformable solids simulated with large time steps.
Mixing Fluids and Granular Materials
Fluid animations in computer graphics show interactions with various kinds of objects. However, fluid flowing through a granular material such as sand is still not possible within current frameworks. In this paper, we present the simulation of fine granular materials interacting with fluids. We propose a unified Smoothed Particle Hydrodynamics framework for the simulation of both fluid and granular material. The granular volume is simulated as a continuous material sampled by particles. By incorporating previous work on porous flow in this simulation framework we are able to fully couple fluid and sand. Fluid can now percolate between sand grains and influence the physical properties of the sand volume. Our method demonstrates various new effects such as dry soil transforming into mud pools by rain or rigid sand structures being eroded by waves.
Scalable Real-Time Animation of Rivers
Many recent games and applications target the interactive exploration of realistic large scale worlds. These worlds consist mostly of static terrain models, as the simulation of animated fluids in these virtual worlds is computation- ally expensive. Adding flowing fluids, such as rivers, to these virtual worlds would greatly enhance their realism, but causes specific issues: as the user is usually observing the world at close range, small scale details such as waves and ripples are important. However, the large scale of the world makes classical methods impractical for simulating these effects. In this paper, we present an algorithm for the interactive simulation of realistic flowing fluids in large virtual worlds. Our method relies on two key contributions: the local computation of the velocity field of a steady flow given boundary conditions, and the advection of small scale details on a fluid, following the velocity field, and uniformly sampled in screen space.
Hydraulic Erosion Using Smoothed Particle Hydrodynamics
This paper presents a new technique for modification of 3D terrains by hydraulic erosion. It efficiently couples fluid simulation using a Lagrangian approach, namely the Smoothed Particle Hydrodynamics (SPH) method, and a physically-based erosion model adopted from an Eulerian approach. The eroded sediment is associated with the SPH particles and is advected both implicitly, due to the particle motion, and explicitly, through an additional velocity field, which accounts for the sediment transfer between the particles. We propose a new donor-acceptor scheme for the explicit advection in SPH. Boundary particles associated to the terrain are used to mediate sediment exchange between the SPH particles and the terrain itself. Our results show that this particle-based method is efficient for the erosion of dense, large, and sparse fluid. Our implementation provides interactive results for scenes with up to 25,000 particles.
Parallel Simulation of Inextensible Cloth
This paper presents an efficient simulation method for parallel cloth simulation. The presented method uses an impulse-based approach for the simulation. Cloth simulation has many application areas like computer animation, computer games or virtual reality. Simulation methods often make the assumption that cloth is an elastic material. In this way the simulation can be performed very efficiently by using spring forces. These methods disregard the fact that many textiles cannot be stretched significantly. The simulation of inextensible textiles with methods based on spring forces leads to stiff differential equations which cause a loss of performance. In contrast to that, in this paper a method is presented that simulates cloth by using impulses. The mesh of a cloth model is subdivided into strips of constraints. The impulses for each strip can be computed in linear time. The strips that have no common particle are independent from each other and can be solved in parallel. The impulse-based method allows the realistic simulation of inextensible textiles in real-time.