## Large Steps in Cloth Simulation (1998)

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Citations: | 435 - 5 self |

### BibTeX

@MISC{Baraff98largesteps,

author = {David Baraff and Andrew Witkin},

title = {Large Steps in Cloth Simulation},

year = {1998}

}

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### Abstract

The bottle-neck 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 fast...

### Citations

1963 |
Matrix Computations
- Golub, Loan
(Show Context)
Citation Context ...terative techniques such as Gauss-Seidel relaxation or conjugate gradients. (For a square system of n nodes, the resulting linear system has bandwidth √ n. In this case, banded Choleski factorization =-=[6]-=- requires time O(n 2 ).) As previously discussed, Terzopoulos et al. made use of an ADI method for larger cloth simulations. Following Terzopoulos et al.’s treatment of deformable surfaces, work by Ca... |

721 | Deformable models
- Terzopoulos, Fleischer
- 1988
(Show Context)
Citation Context ...g. 1 Introduction Physically-based cloth animation has been a problem of interest to the graphics community for more than a decade. Early work by Terzopoulos et al. [17] and Terzopoulos and Fleischer =-=[15, 16]-=- on deformable models correctly characterized cloth simulation as a problem in deformable surfaces, and applied techniques from the mechanical engineering and finite element communities to the problem... |

705 |
Numerical Recipes
- Press, Teukolsky, et al.
- 1993
(Show Context)
Citation Context ...fortunate. Cloth strongly resists stretching motions while being comparatively permissive in allowing bending or shearing motions. This results in a “stiff” underlying differential equation of motion =-=[12]-=-. Explicit methods are ill-suited to solving stiff equations because they require many small steps to stably advance the simulation forward in time. 2 In practice, the computational cost of an explici... |

307 | An introduction to the conjugate gradient method without the agonizing pain
- Shewchuk
- 1994
(Show Context)
Citation Context ... use of the “normal equations”; but this involves multiplying the matrix of equation (14) with its transpose which doubles the cost of each iteration while squaring the condition number of the system =-=[14]-=-—a less than desirable plan. We decided that using a CG method to solve the unsymmetric problem was not acceptable. Note that without constraints, applying a CG method to equation (6) is not difficult... |

213 | Fast contact force computation for nonpenetrating rigid bodies
- BARAFF
- 1994
(Show Context)
Citation Context ...ticles’ accelerations are inherently dependent on one another through the matrix A of equation (16). This means that the correct approach to determing constraint release is combinatoric, as in Baraff =-=[2]-=-. We reject this approach as impractical given the dimension of A. Instead, we allow contacts to release when the constraint force between a particle and a solid switches from a repulsive force to an ... |

194 |
Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture", SIGGRAPH 88
- Terzopoulos, Fleischer
- 1988
(Show Context)
Citation Context ... Series, 1998 v direction is measured by ‖wv‖. (Some previous continuum formulations have modeled stretch energy along an axis as essentially (wT u wu − 1) 2 , which is a quartic function of position =-=[15, 16, 17, 4]-=-. We find this to be needlessly stiff; worse, near the rest state, the force gradient—a quadratic function of position—is quite small, which partially negates the advantage implicit integration has in... |

184 | Deformation constraints in a mass-spring model to describe rigid cloth behavior
- Provot
- 1995
(Show Context)
Citation Context ...f the problem—obtain similarly realistic results, while dropping the computational cost to approximately 20–30 minutes per frame on an SGI R8000 processor. No mention is made of damping terms. Provot =-=[13]-=- focuses on improving the performance of explicit methods by a post-step modification of nodal positions. He iteratively adjusts nodal positions to eliminate unwanted stretch; the convergence properti... |

128 |
Constraints methods for flexible models
- Platt, Barr
- 1988
(Show Context)
Citation Context ...sed a simple viscous damping function which dissipated kinetic energy, independent of the type of motion. Carignan et al. [4]improved upon this somewhat, borrowing a formulation due to Platt and Barr =-=[11]-=-; however, their damping function—a linear function of velocity—does not match the quartic energy functions of their continuum formulation. In this section we describe a general treatment for damping ... |

119 | Predicting the drape of woven cloth using interacting particles
- Breen, House, et al.
- 1984
(Show Context)
Citation Context ...plied techniques from the mechanical engineering and finite element communities to the problem. Since then, other research groups (notably Carignan et al. [4] and Volino et al. [20, 21]; Breen et al. =-=[3]-=-; and Eberhardt et al.[5]) have taken up the challenge of cloth. Although specific details vary (underlying representations, numerical solution methods, collision detection and constraint methods, etc... |

95 | Dynamic NURBS with Geometric Constraints for Interactive Sculpting
- TERZOPOULOS, QIN
- 1994
(Show Context)
Citation Context ...elow the solid object’s surface. This is unacceptable. 50SIGGRAPH 98, Orlando, July 19–24 COMPUTER GRAPHICS Proceedings, Annual Conference Series, 1998 One solution is to use Baumgarte stabilization =-=[18]-=-, which schedules the particle’s acceleration so that the position and velocity error of the particle with respect to the surface decay asymptotically to zero. We experimented with this technique, but... |

90 |
Versatile and efficient techniques for simulating cloth and other deformable objects
- Volino, Courchesne, et al.
- 1995
(Show Context)
Citation Context ...rmable surfaces, and applied techniques from the mechanical engineering and finite element communities to the problem. Since then, other research groups (notably Carignan et al. [4] and Volino et al. =-=[20, 21]-=-; Breen et al. [3]; and Eberhardt et al.[5]) have taken up the challenge of cloth. Although specific details vary (underlying representations, numerical solution methods, collision detection and const... |

87 |
Rapid, stable fluid dynamics for computer graphics
- KASS, MILLER
- 1990
(Show Context)
Citation Context ...tation differs greatly from the implementation by Terzopoulos et al. [15, 17], which for large simulations 1 Additional use of implicit methods in animation and dynamics work includes Kass and Miller =-=[8]-=-, Terzopoulos and Qin [18], and Tu [19]. 2 Even worse, the number of time steps per frame tends to increase along with the problem size, for an explicit method. Cloth simulations of size n— meaning x ... |

85 | Dressing animated synthetic actors with complex deformable clothes
- Carignan, Yang, et al.
- 1992
(Show Context)
Citation Context ... Series, 1998 v direction is measured by ‖wv‖. (Some previous continuum formulations have modeled stretch energy along an axis as essentially (wT u wu − 1) 2 , which is a quartic function of position =-=[15, 16, 17, 4]-=-. We find this to be needlessly stiff; worse, near the rest state, the force gradient—a quadratic function of position—is quite small, which partially negates the advantage implicit integration has in... |

85 |
A Fast, Flexible, Particle-System Model for Cloth Draping
- Eberhardt, Weber, et al.
(Show Context)
Citation Context ... mechanical engineering and finite element communities to the problem. Since then, other research groups (notably Carignan et al. [4] and Volino et al. [20, 21]; Breen et al. [3]; and Eberhardt et al.=-=[5]-=-) have taken up the challenge of cloth. Although specific details vary (underlying representations, numerical solution methods, collision detection and constraint methods, etc.), there is a deep commo... |

66 |
Dynamic simulation of non-penetrating rigid bodies
- Baraff
- 1992
(Show Context)
Citation Context ... the cloth particles to the current (possibly illegal) state and check for either particle/triangle or edge/edge crossings. To avoid O(n 2 ) comparisons, we use a coherency-based boundingbox approach =-=[1]-=- to cull out the majority of pairs. When collisions between a cloth vertex and triangle, or two cloth edges are detected, we insert a strong damped spring force to push the cloth apart. A dissipative ... |

54 |
Computer Graphics Techniques for Modeling Cloth
- Ng, Grimsdale
(Show Context)
Citation Context ... positions to eliminate unwanted stretch; the convergence properties of this method are unclear. A more comprehensive discussion on cloth research can be found in the survey paper by Ng and Grimsdale =-=[9]-=-. 2 Simulation Overview In this section, we give a brief overview of our simulator’s architecture and introduce some notation. The next section derives the linear system used to step the simulator for... |

25 | Artificial Animals for Computer Animation: biomechanics, locomotion, perception and behavior
- Tu
- 1996
(Show Context)
Citation Context ...entation by Terzopoulos et al. [15, 17], which for large simulations 1 Additional use of implicit methods in animation and dynamics work includes Kass and Miller [8], Terzopoulos and Qin [18], and Tu =-=[19]-=-. 2 Even worse, the number of time steps per frame tends to increase along with the problem size, for an explicit method. Cloth simulations of size n— meaning x ∈ IR O(n) —generally require O(n) expli... |

22 |
An evolving system for simulating clothes on virtual actors
- Volino, Thalmann, et al.
(Show Context)
Citation Context ...rmable surfaces, and applied techniques from the mechanical engineering and finite element communities to the problem. Since then, other research groups (notably Carignan et al. [4] and Volino et al. =-=[20, 21]-=-; Breen et al. [3]; and Eberhardt et al.[5]) have taken up the challenge of cloth. Although specific details vary (underlying representations, numerical solution methods, collision detection and const... |

11 |
Three dimensional apparel cad system
- Okabe, Imaoka, et al.
- 1992
(Show Context)
Citation Context ...lied on explicit numerical integration (such as Euler’s method or Runge-Kutta methods) to advance the simulation, or, in the case of of energy minimization, analogous methods such as steepest-descent =-=[3, 10]-=-. This is unfortunate. Cloth strongly resists stretching motions while being comparatively permissive in allowing bending or shearing motions. This results in a “stiff” underlying differential equatio... |

5 |
An Introduction To Physically Based Modeling, chapter Introduction to Continuum Dynamics for Computer Graphics
- Kass
- 1995
(Show Context)
Citation Context ...ailure, the ability to make arbitrary small changes in a particle’s position continued to attract our attention. The entire process of implicit integration can be considered to be a filtering process =-=[7]-=-, and we postulated that a mechanism for filtering energy changes caused by displacing particles might make position alteration a viable technique. We considered that perhaps some sort of extra implic... |