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65
Large steps in cloth simulation
 SIGGRAPH 98 Conference Proceedings
, 1998
"... The bottleneck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particle ..."
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Cited by 435 (5 self)
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The bottleneck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particles with an implicit integration method. The simulator models cloth as a triangular mesh, with internal cloth forces derived using a simple continuum formulation that supports modeling operations such as local anisotropic stretch or compression; a unified treatment of damping forces is included as well. The implicit integration method generates a large, unbanded sparse linear system at each time step which is solved using a modified conjugate gradient method that simultaneously enforces particles ’ constraints. The constraints are always maintained exactly, independent of the number of conjugate gradient iterations, which is typically small. The resulting simulation system is significantly faster than previous accounts of cloth simulation systems in the literature. Keywords—Cloth, simulation, constraints, implicit integration, physicallybased modeling. 1
Stable Fluids
, 1999
"... Building animation tools for fluidlike motions is an important and challenging problem with many applications in computer graphics. The use of physicsbased models for fluid flow can greatly assist in creating such tools. Physical models, unlike key frame or procedural based techniques, permit an a ..."
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Cited by 424 (8 self)
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Building animation tools for fluidlike motions is an important and challenging problem with many applications in computer graphics. The use of physicsbased models for fluid flow can greatly assist in creating such tools. Physical models, unlike key frame or procedural based techniques, permit an animator to almost effortlessly create interesting, swirling fluidlike behaviors. Also, the interaction of flows with objects and virtual forces is handled elegantly. Until recently, it was believed that physical fluid models were too expensive to allow realtime interaction. This was largely due to the fact that previous models used unstable schemes to solve the physical equations governing a fluid. In this paper, for the first time, we propose an unconditionally stable model which still produces complex fluidlike flows. As well, our method is very easy to implement. The stability of our model allows us to take larger time steps and therefore achieve faster simulations. We have used our model in conjuction with advecting solid textures to create many fluidlike animations interactively in two and threedimensions.
Practical animation of liquids
 Graphical Models and Image Processing
, 1996
"... We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the NavierStokes equations which couple momentum and mass con ..."
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Cited by 344 (23 self)
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We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the NavierStokes equations which couple momentum and mass conservation to completely describe fluid motion. Our starting point is an environment containing an arbitrary distribution of fluid, and submerged or semisubmerged obstacles. Velocity and pressure are defined everywhere within this environment, and updated using a set of finite difference expressions. The resulting vector and scalar fields are used to drive a height field equation representing the liquid surface. The nature of the coupling between obstacles in the environment and free variables allows for the simulation of a wide range of effects that were not possible with previous computergraphics fluid models. Wave effects such as reflection, refraction and diffraction, as well as rotational effects such as eddies, vorticity, and splashing are a natural consequence of solving the system. In addition, the Lagrange equations of motion are used to place buoyant dynamic objects into a scene, and track the position of spray and foam during the animation process. Typical disadvantages to dynamic simulations such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the finite difference discretization, and by appending terms to the NavierStokes equations to include forcing functions. Free surfaces in our system are represented as either a collection of massless particles in 2D, or a height field which is suitable for many of the water rendering algorithms presented by researchers in recent years.
Linear Algebra Operators for GPU Implementation of Numerical Algorithms
 ACM Transactions on Graphics
, 2003
"... In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for ..."
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Cited by 239 (9 self)
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In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism and efficient communication on modern GPUs. Besides performance gains due to improved numerical computations, graphics algorithms benefit from this model in that the transfer of computation results to the graphics processor for display is avoided. We demonstrate the effectiveness of our approach by implementing direct solvers for sparse matrices, and by applying these solvers to multidimensional finite difference equations, i.e. the 2D wave equation and the incompressible NavierStokes equations.
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
 ACM Trans. Graph
, 2003
"... Permission to make digital/hard copy of part of all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given ..."
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Cited by 219 (3 self)
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Permission to make digital/hard copy of part of all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given that copying is by permission
Animation and Rendering of Complex Water Surfaces
, 2002
"... We present a new method for the animation and rendering of photorealistic water effects. Our method is designed to produce visually plausible three dimensional effects, for example the pouring of water into a glass (see figure 1) and the breaking of an ocean wave, in a manner which can be used in a ..."
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Cited by 211 (21 self)
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We present a new method for the animation and rendering of photorealistic water effects. Our method is designed to produce visually plausible three dimensional effects, for example the pouring of water into a glass (see figure 1) and the breaking of an ocean wave, in a manner which can be used in a computer animation environment. In order to better obtain photorealism in the behavior of the simulated water surface, we introduce a new "thickened" front tracking technique to accurately represent the water surface and a new velocity extrapolation method to move the surface in a smooth, waterlike manner. The velocity extrapolation method allows us to provide a degree of control to the surface motion, e.g. to generate a windblown look or to force the water to settle quickly. To ensure that the photorealism of the simulation carries over to the final images, we have integrated our method with an advanced physically based rendering system.
Simulating Water and Smoke with an Octree Data Structure
, 2004
"... We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric ..."
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Cited by 155 (14 self)
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We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a nonsymmetric linear system which is more computationally challenging to invert. The semiLagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.
Scan Primitives for GPU Computing
 GRAPHICS HARDWARE 2007
, 2007
"... The scan primitives are powerful, generalpurpose dataparallel primitives that are building blocks for a broad range of applications. We describe GPU implementations of these primitives, specifically an efficient formulation and implementation of segmented scan, on NVIDIA GPUs using the CUDA API.Us ..."
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Cited by 114 (8 self)
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The scan primitives are powerful, generalpurpose dataparallel primitives that are building blocks for a broad range of applications. We describe GPU implementations of these primitives, specifically an efficient formulation and implementation of segmented scan, on NVIDIA GPUs using the CUDA API.Using the scan primitives, we show novel GPU implementations of quicksort and sparse matrixvector multiply, and analyze the performance of the scan primitives, several sort algorithms that use the scan primitives, and a graphical shallowwater fluid simulation using the scan framework for a tridiagonal matrix solver.
Fluid Control Using the Adjoint Method
 ACM TRANS. GRAPH. (SIGGRAPH PROC
, 2004
"... We describe a novel method for controlling physicsbased fluid simulations through gradientbased nonlinear optimization. Using a technique known as the adjoint method, derivatives can be computed efficiently, even for large 3D simulations with millions of control parameters. In addition, we introdu ..."
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Cited by 70 (1 self)
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We describe a novel method for controlling physicsbased fluid simulations through gradientbased nonlinear optimization. Using a technique known as the adjoint method, derivatives can be computed efficiently, even for large 3D simulations with millions of control parameters. In addition, we introduce the first method for the full control of freesurface liquids. We show how to compute adjoint derivatives through each step of the simulation, including the fast marching algorithm, and describe a new set of control parameters specifically designed for liquids.
Dynamic simulation of splashing fluids
 IN PROC. OF COMPUTER ANIMATION
, 1995
"... In this paper we describe a method for modeling the dynamic behavior of splashing fluids. The model simulates the behavior of a fluid when objects impact or float on its surface. The forces generated by the objects create waves and splashes on the surface of the fluid. To demonstrate the realism an ..."
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Cited by 66 (5 self)
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In this paper we describe a method for modeling the dynamic behavior of splashing fluids. The model simulates the behavior of a fluid when objects impact or float on its surface. The forces generated by the objects create waves and splashes on the surface of the fluid. To demonstrate the realism and limitations of the model, images from a computergenerated animation are presented and compared with video frames of actual splashes occuring under similar initial conditions.