This paper proposes a real-time simulation technique for thin shells undergoing large deformation. Shells are thin objects such as leaves and papers that can be abstracted as 2D structures. Development of a satisfactory physical model that runs in real-time but produces visually convincing animation of thin shells has been remaining a challenge in computer graphics. Rather than resorting to shell theory which involves the most complex formulations in continuum mechanics, we adopt the energy functions from the discrete shells proposed by Grinspun et al. [GHDS03]. For real-time integration of the governing equation, we develop a modal warping technique for shells. This new simulation framework results from making extensions to the original modal warping technique [CK05] which was developed for the simulation of 3D solids. We report experimental results, which show that the proposed method runs in real-time even for large meshes, and that it can simulate large bending and/or twisting deformations with acceptable realism.
Month: June 2007
Animation of Chemically Reactive Fluids using a Hybrid Simulation Method
Chemical phenomena abound in the real world, and often comprise indispensable elements of visual effects that are routinely created in the film industry. In this paper, we present a hybrid technique for simulating chemically reactive fluids, based on the theory of chemical kinetics. Our method makes synergistic use of both Eulerian grid-based methods and Lagrangian particle methods to simulate real and hypothetical chemical mechanisms effectively and efficiently. We demonstrate that by modeling chemical reactions using a particle system, an established, physically based fluid system can be extended easily to generate a wide range of chemical phenomena, ranging from catalysis and erosion to fire and explosions, with only a small additional cost.
Animation of Chemically Reactive Fluids Using a Hybrid Simulation Method
Cubic Shells
Hinge-based bending models are widely used in the physically-based animation of cloth, thin plates and shells. We propose a hinge-based model that is simpler to implement, more efficient to compute, and offers a greater number of effective material parameters than existing models. Our formulation builds on two mathematical observations: (a) the bending energy of curved flexible surfaces can be expressed as a cubic polynomial if the surface does not stretch; (b) a general class of anisotropic materials—those that are orthotropic—is captured by appropriate choice of a single stiffness per hinge. Our contribution impacts a general range of surface animation applications, from isotropic cloth and thin plates to orthotropic fracturing thin shells.
Real-time Simulations of Bubbles and Foam within a Shallow-Water Framework
Bubbles and foam are important fluid phenomena on scales that we encounter in our lives every day. While different techniques to handle these effects were developed in the past years, they require a full 3D fluid solver with free surfaces and surface tension. We present a shallow water based particle model that is coupled with a smoothed particle hydrodynamics simulation to demonstrate that real-time simulations of bubble and foam effects are possible with high frame rates. A shallow water simulation is used to represent the overall water volume. It is coupled to a particle-based bubble simulation with a flow field of spherical vortices. This bubble simulation is interacting with a smoothed particle hydrodynamics simulation including surface tension to handle foam on the fluid surface. The realism and performance of our approach is demonstrated with several test cases that run with high frame rates on a standard PC.
Real-time Simulations of Bubbles and Foam within a Shallow-Water Framework
Legendre Fluids: A Unified Framework for Analytic Reduced Space Modeling and Rendering of Participating Media
In this paper, we present a unified framework for reduced space modeling and rendering of dynamic and nonhomogenous participating media, like snow, smoke, dust and fog. The key idea is to represent the 3D spatial variation of the density, velocity and intensity fields of the media using the same analytic basis. In many situations, natural effects such as mist, outdoor smoke and dust are smooth (low frequency) phenomena, and can be compactly represented by a small number of coefficients of a Legendre polynomial basis. We derive analytic expressions for the derivative and integral operators in the Legendre coefficient space, as well as the triple product integrals of Legendre polynomials. These mathematical results allow us to solve both the Navier-Stokes equations for fluid flow and light transport equations for single scattering efficiently in the reduced Legendre space. Since our technique does not depend on volume grid resolution, we can achieve computational speedups as compared to spatial domain methods while having low memory and pre-computation requirements as compared to datadriven approaches. Also, analytic definition of derivatives and integral operators in the Legendre domain avoids the approximation errors inherent in spatial domain finite difference methods. We demonstrate many interesting visual effects resulting from particles immersed in fluids as well as volumetric scattering in non-homogenous and dynamic participating media, such as fog and mist.
Time-critical distributed contact for 6-DoF haptic rendering of adaptively sampled reduced deformable models
Real-time evaluation of distributed contact forces for rigid or deformable 3D objects is important for providing multi-sensory feedback in emerging real-time applications, such as 6-DoF haptic force-feedback rendering. Unfortunately, at very high temporal rates (1 kHz for haptics), there is often insufficient time to resolve distributed contact between geometrically complex objects.
In this paper, we present a spatially and temporally adaptive sample-based approach to approximate contact forces under hard real-time constraints. The approach is CPU based, and supports contact between a rigid and a reduced deformable model with complex geometry. Penalty-based contact forces are efficiently resolved using a multi-resolution point-based representation for one object, and a signed-distance field for the other. Hard realtime approximation of distributed contact forces uses multi-level progressive point-contact sampling, and exploits temporal coherence, graceful degradation and other optimizations. We present several examples of 6-DoF haptic rendering of geometrically complex rigid and deformable objects in distributed contact at real-time kilohertz rates.
Adaptive Deformations with Fast Tight Bounds
Simulation of deformations and collision detection are two highly intertwined problems that are often treated separately. This is especially true in existing elegant adaptive simulation techniques, where standard collision detection algorithms cannot leverage the adaptively selected degrees of freedom.We propose a seamless integration of multi-grid algorithms and collision detection that identifies boundary conditions while inherently exploiting adaptivity. We realize this integration through multiscale bounding hierarchies, a novel unified hierarchical representation, together with an adaptive multigrid algorithm for irregular meshes and an adaptivity-aware hierarchical collision detection algorithm. Our solution produces detailed deformations with adapted computational cost, but it also enables robust interactive simulation of self-colliding deformable objects with high-resolution surfaces.
Screen Space Meshes
We present a simple yet powerful approach for the generation and rendering of surfaces defined by the boundary of a three-dimensional point cloud. First, a depth map plus internal and external silhouettes of the surface are generated in screen space. These are used to construct a 2D screen space triangle mesh with a new technique that is derived from Marching Squares. The resulting mesh is transformed back to 3D world space for the computation of occlusions, reflections, refraction, and other shading effects. One of the main applications for screen space meshes is the visualization of Lagrangian, particle-based fluids models. Our new method has several advantages over the full 3D Marching Cubes approach. The algorithm only generates surface where it is visible, view-dependent level of detail comes for free, and interesting visual effects are possible by filtering in screen space.
CORDE: Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects
Simulating one-dimensional elastic objects such as threads, ropes or hair strands is a difficult problem, especially if material torsion is considered. In this paper, we present CORDE(french ’rope’), a novel deformation model for the dynamic interactive simulation of elastic rods with torsion. We derive continuous energies for a dynamically deforming rod based on the Cosserat theory of elastic rods. We then discretize the rod and compute energies per element by employing finite element methods. Thus, the global dynamic behavior is independent of the discretization. The dynamic evolution of the rod is obtained by numerical integration of the resulting Lagrange equations of motion. We further show how this system of equations can be decoupled and efficiently solved. Since the centerline of the rod is explicitly represented, the deformation model allows for accurate contact and self-contact handling. Thus, we can reproduce many important looping phenomena. Further, a broad variety of different materials can be simulated at interactive rates. Experiments underline the physical plausibility of our deformation model.
CORDE: Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects
Weakly Compressible SPH for Free Surface Flows
We present a weakly compressible form of the Smoothed Particle Hydrodynamics method (SPH) for fluid flow based on the Tait equation. In contrast to commonly employed projection approaches that strictly enforce incompressibility, time-consuming solvers for the Poisson equation are avoided by allowing for small, user-defined density fluctuations. We also discuss an improved surface tension model that is particularly appropriate for single-phase free-surface flows. The proposed model is compared to existing models and experiments illustrate the accuracy of the approach for free surface flows. Combining the proposed methods, volume-preserving low-viscosity liquids can be efficiently simulated using SPH. The approach is appropriate for medium-scale and small-scale phenomena. Effects such as splashing and breaking waves are naturally handled.