#### DMCA

## Energy Conservation for the Simulation of Deformable Bodies

Citations: | 2 - 0 self |

### Citations

883 | Elastically deformable models.
- Terzopoulos, Platt, et al.
- 1987
(Show Context)
Citation Context ...rgy as desired. Index Terms—Computer Graphics, Physically-based Modeling ✦ 1 INTRODUCTION DEFORMABLE models have been used in computer graphics for over twenty years, dating back to the early work of =-=[1]-=-–[3]. While our work will focus on massspring models, the main ideas should be extendable to finite element methods (such as those in [4] and [5]), though we do not evaluate FEMs within the scope of t... |

576 | WITKIN A.: Large steps in cloth simulation
- BARAFF
- 1998
(Show Context)
Citation Context ...s (such as those in [4] and [5]), though we do not evaluate FEMs within the scope of this paper. Many authors have explored various time integration schemes, such as fully implicit methods (e.g. [2], =-=[6]-=-), semi-implicit schemes (e.g. [7], [8]), and explicit schemes (e.g. [9]). Damping plays a much larger role in a numerical simulation than one might otherwise first expect. Implicit time integration s... |

543 |
Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations (2nd edn)
- Hairer, Lubich, et al.
- 2006
(Show Context)
Citation Context ...ry energy conservative time integration schemes in addition to those already mentioned above. We refer the interested reader to a selection of papers on the topic (e.g. [17]–[21]) as well as the book =-=[22]-=-. We note that the energy conserving time integration scheme that we propose in Section 2 is not intended to directly compete against the plethora of methods in the literature, but rather is used to i... |

300 | J.: Robust treatment of collisions, contact and friction for cloth animation
- BRIDSON, FEDKIW, et al.
- 2002
(Show Context)
Citation Context ...though we do not evaluate FEMs within the scope of this paper. Many authors have explored various time integration schemes, such as fully implicit methods (e.g. [2], [6]), semi-implicit schemes (e.g. =-=[7]-=-, [8]), and explicit schemes (e.g. [9]). Damping plays a much larger role in a numerical simulation than one might otherwise first expect. Implicit time integration schemes possess inherent damping, w... |

203 | Graphical Modeling and Animation of Brittle Fracture
- O’BRIEN, HODGINS
- 1999
(Show Context)
Citation Context ...aphics for over twenty years, dating back to the early work of [1]–[3]. While our work will focus on massspring models, the main ideas should be extendable to finite element methods (such as those in =-=[4]-=- and [5]), though we do not evaluate FEMs within the scope of this paper. Many authors have explored various time integration schemes, such as fully implicit methods (e.g. [2], [6]), semi-implicit sch... |

176 | H.-S.: Stable but responsive cloth.
- CHOI, KO
- 2002
(Show Context)
Citation Context ...a much larger role in a numerical simulation than one might otherwise first expect. Implicit time integration schemes possess inherent damping, which can lead to undesirable artifacts as discussed by =-=[10]-=-. Other authors, such as [11], stressed the desirability of schemes that add a known quantitative amount of damping independent of the time step, as opposed to an unknown quantity of scheme-inherent d... |

141 |
Simulation of clothing with folds and wrinkles
- Bridson, Marino, et al.
- 2003
(Show Context)
Citation Context ...h we do not evaluate FEMs within the scope of this paper. Many authors have explored various time integration schemes, such as fully implicit methods (e.g. [2], [6]), semi-implicit schemes (e.g. [7], =-=[8]-=-), and explicit schemes (e.g. [9]). Damping plays a much larger role in a numerical simulation than one might otherwise first expect. Implicit time integration schemes possess inherent damping, which ... |

114 |
Invertible Finite Elements for Robust Simulation of Large Deformation
- Irving, Teran, et al.
- 2004
(Show Context)
Citation Context ...or over twenty years, dating back to the early work of [1]–[3]. While our work will focus on massspring models, the main ideas should be extendable to finite element methods (such as those in [4] and =-=[5]-=-), though we do not evaluate FEMs within the scope of this paper. Many authors have explored various time integration schemes, such as fully implicit methods (e.g. [2], [6]), semi-implicit schemes (e.... |

111 | SCHRÖDER P.: Discrete shells.
- GRINSPUN, HIRANI, et al.
- 2003
(Show Context)
Citation Context ...rings in an energy conserving way. Figure 10 shows a simple example of these energy conserving bending springs. It is feasible that these ideas could be extended to other bending models, such as [8], =-=[29]-=-, [30]. Moreover, we imagine one could extend these energy conservation techniques to other models based on mass-spring systems, such as the hard and soft constraints in [26] (see also [31]). 4 OUR NE... |

97 | Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems
- Kane, Marsden, et al.
(Show Context)
Citation Context ...t from any number of contemporary energy conservative time integration schemes in addition to those already mentioned above. We refer the interested reader to a selection of papers on the topic (e.g. =-=[17]-=-–[21]) as well as the book [22]. We note that the energy conserving time integration scheme that we propose in Section 2 is not intended to directly compete against the plethora of methods in the lite... |

88 | Untangling cloth
- Baraff, Witkin, et al.
(Show Context)
Citation Context ... other techniques for handling self-collisions, referring the interested reader to [35], and stress that similar energy conservation techniques could be applied to these other methods. In particular, =-=[36]-=- showed that under various situations, such as when cloth is pinched in the armpit of a character (between two bodies), it is sometimes desirable to allow interpenetration of cloth, which can be untan... |

65 | A Crystalline, Red Green Strategy for Meshing Highly Deformable Objects With Tetrahedra,”
- Molino
- 2003
(Show Context)
Citation Context ...use the restlength and Young’s modulus may be different for each altitude, simply switching springs while using the same P Eres is not sufficient. To handle 3.1 Altitude Springs Following the work of =-=[24]-=- and [25], we use altitude springs when simulating triangles and tetrahedra for volume preservation. For simplicity, we will consider Fig. 8. A single tetrahedron with edge and altitude springs is str... |

58 |
Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Computer Methods in Applied Mechanics and Engineering
- Simo, Tarnow, et al.
- 1992
(Show Context)
Citation Context ...hod proposed in Section 4 does not require iteration, but instead achieves exact energy conservation through solving a single quadratic formula. This is in the spirit of the projection-type method in =-=[23]-=-, but since our approach is different our method lendsIEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 3 itself to the simulation of more complex phenomena such as damping, collisions, and se... |

51 | Variational time integrators - Lew, Marsden, et al. |

49 | A High Performance Solver for the Animation of Deformable Objects using Advanced Numerical Methods - Hauth, Etzmuß - 2001 |

41 |
FEDKIW R.: Hybrid simulation of deformable solids
- SIFAKIS, SHINAR, et al.
- 2007
(Show Context)
Citation Context ...ite edge. An equal and opposite spring force is applied to the particle and the virtual node, and the virtual node distributes its forces barycentrically to the particles of the edge. As discussed in =-=[26]-=-, the inverse mass and velocity of this virtual node are defined as „ 1 w2 1 = + mv m1 w2 « 2 (36) m2 vv = w1v1 + w2v2 (37) where nodes 1 and 2 form the edge along which the virtual node lies, and w1 ... |

40 | A simple geometric model for elastic deformations
- CHAO, PINKALL, et al.
- 2010
(Show Context)
Citation Context ...rator seen in [14] exhibits either high speed oscillations when exactly conserving energy or loss of energy when damping is added to make the simulation more visually appealing. results. For example, =-=[12]-=- states “in application practice, one generally wishes to have damping” but stresses the importance of damping independent of the time step in contrast to numerical damping, similar in vein to argumen... |

36 |
A mass spring model for hair simulation
- SELLE, LENTINE, et al.
- 2008
(Show Context)
Citation Context ... what one gets with a normal spring, except that one of the endpoints is replaced by the weighted sum of two nodes. The equation for ∆P E is easily modified in a similar fashion. However, as noted in =-=[27]-=-, if all three altitude springs in a triangle are used at once, one might encounter negative barycentric weights. To prevent these degenerate cases, we only ever use the shortest altitude spring, whic... |

31 |
Energy-preserving integrators for fluid animation.
- MULLEN, CRANE, et al.
- 2009
(Show Context)
Citation Context ...ly wishes to have damping” but stresses the importance of damping independent of the time step in contrast to numerical damping, similar in vein to arguments in [10]. Similarly in the case of fluids, =-=[13]-=- states “completely inviscid [undamped] flows may look unnatural” and “fluid animation in computer graphics requires a small amount of viscosity to render the motion more realistic.” We take this one ... |

30 | Dynamic local remeshing for elastoplastic simulation
- Wicke, Ritchie, et al.
- 2010
(Show Context)
Citation Context ...at energy is conserved when altitude springs are added and removed from the simulation. As future work, it would be interesting to try to adapt this scheme to a method that handles remeshing, such as =-=[28]-=-. Figure 10 shows a simulation with energy conserving triangle altitude springs, and Figure 8 shows the extension of this method to energy conserving tetrahedron altitude springs. Figure 9 shows the t... |

29 | variational integrators for computer animation
- Kharevych, Yang, et al.
- 2006
(Show Context)
Citation Context ...ical simulation than one might otherwise first expect. Implicit time integration schemes possess inherent damping, which can lead to undesirable artifacts as discussed by [10]. Other authors, such as =-=[11]-=-, stressed the desirability of schemes that add a known quantitative amount of damping independent of the time step, as opposed to an unknown quantity of scheme-inherent damping present in many implic... |

28 | Asynchronous contact mechanics - Harmon, Vouga, et al. - 2009 |

27 | Two-way coupling of rigid and deformable bodies.
- Shinar
- 2008
(Show Context)
Citation Context ... to use our algorithm for energy conservation at all, monitoring the energy difference during collisions and identifying any time steps where the energy increases would be important. As in [6], [26], =-=[33]-=-, we use collisions as constraints on vn+1 in the conjugate gradients solve during the velocity update in step V above. In this case, we would again like to determine the ∆KE due to using these collis... |

26 | Adaptive physics based tetrahedral mesh generation using level sets. (in review).
- MOLINO, BRIDSON, et al.
- 2004
(Show Context)
Citation Context ...estlength and Young’s modulus may be different for each altitude, simply switching springs while using the same P Eres is not sufficient. To handle 3.1 Altitude Springs Following the work of [24] and =-=[25]-=-, we use altitude springs when simulating triangles and tetrahedra for volume preservation. For simplicity, we will consider Fig. 8. A single tetrahedron with edge and altitude springs is stretched an... |

24 | Volume contact constraints at arbitrary resolution
- Allard, Faure, et al.
(Show Context)
Citation Context ...o note that similar energy conservation approaches can be applied to other collision handling schemes. For more on collision handling techniques, we refer the interested reader to the recent paper of =-=[34]-=-. 5.1 Self-Collisions As the amount of deformation in a mesh becomes more significant, it becomes important to handle selfcollisions, which we handle using the method of [7]. We first note that self-c... |

19 |
Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion, II. Motion of a system of particles
- LaBudde, Greenspan
- 1976
(Show Context)
Citation Context ... energy conservation, we begin our exposition in Section 2 with a bottom-up approach to energy conservation for non-linear elastic systems similar to some of the earliest papers on the topic, such as =-=[15]-=- which considered the motion of a single particle and the subsequent paper [16] that considered systems of particles. This leads us one step at a time towards a conclusion similar to theirs, that an i... |

16 |
MAGNENAT-THALMANN N.: Simple linear bending stiffness in particle systems
- VOLINO
- 2006
(Show Context)
Citation Context ...in an energy conserving way. Figure 10 shows a simple example of these energy conserving bending springs. It is feasible that these ideas could be extended to other bending models, such as [8], [29], =-=[30]-=-. Moreover, we imagine one could extend these energy conservation techniques to other models based on mass-spring systems, such as the hard and soft constraints in [26] (see also [31]). 4 OUR NEW SCHE... |

15 | Subspace self-collision culling.
- BARBIC, JAMES
- 2010
(Show Context)
Citation Context ...in Section 4. In Figure 15, we show an energy conserving simulation with self collisions. We note that there are many other techniques for handling self-collisions, referring the interested reader to =-=[35]-=-, and stress that similar energy conservation techniques could be applied to these other methods. In particular, [36] showed that under various situations, such as when cloth is pinched in the armpit ... |

12 | FEDKIW R.: Energy stability and fracture for frame rate rigid body simulations
- SU, SCHROEDER
- 2009
(Show Context)
Citation Context ...energy correction allows for momentum conservation. Note that what we are doing here is we have a momentum that we like, but we want a better total energy. This is similar to the energy correction in =-=[32]-=-, where angular momentum is conserved but a new rigid body orientation is obtained that conserves energy. Through various tests, we found the best results are produced when damping forces are used in ... |

11 | Efficient yarn-based cloth with adaptive contact linearization
- Kaldor, James, et al.
- 2010
(Show Context)
Citation Context ...work. It would be interesting to see if we could extend our methods, especially the energy conserving global fix in Section 4, to consider other models for cloth, such as the yarn based model seen in =-=[37]-=-. In the attached videos, a slight artifact is apparent in the bouncing sphere videos when the stiffness is high, causing the sphere to bounce off-center. We hypothesize that this is due to the discre... |

9 | Stability of asynchronous variational integrators - Fong, Darve, et al. |

8 |
Deformable models,” Vis
- Teropoulos, Fleischer
(Show Context)
Citation Context ...ethods (such as those in [4] and [5]), though we do not evaluate FEMs within the scope of this paper. Many authors have explored various time integration schemes, such as fully implicit methods (e.g. =-=[2]-=-, [6]), semi-implicit schemes (e.g. [7], [8]), and explicit schemes (e.g. [9]). Damping plays a much larger role in a numerical simulation than one might otherwise first expect. Implicit time integrat... |

6 | Point cloud glue: constraining simulations using the procrustes transform
- TWIGG, KAČIĆ-ALESIĆ
- 2010
(Show Context)
Citation Context ...ch as [8], [29], [30]. Moreover, we imagine one could extend these energy conservation techniques to other models based on mass-spring systems, such as the hard and soft constraints in [26] (see also =-=[31]-=-). 4 OUR NEW SCHEME In Section 2 we outlined a force based iterative approach to conserving energy in a mass-spring system which relied on an energy budgeting process where exact changes in kinetic an... |

5 |
M.: Forcestepping integrators in lagrangian mechanics
- GONZALEZ, SCHMIDT, et al.
(Show Context)
Citation Context ...m any number of contemporary energy conservative time integration schemes in addition to those already mentioned above. We refer the interested reader to a selection of papers on the topic (e.g. [17]–=-=[21]-=-) as well as the book [22]. We note that the energy conserving time integration scheme that we propose in Section 2 is not intended to directly compete against the plethora of methods in the literatur... |

2 |
momentum conserving methods of arbitrary order for the numerical integration of equations of motion i. motion of a system of particles
- “Energy
- 1976
(Show Context)
Citation Context ...roach to energy conservation for non-linear elastic systems similar to some of the earliest papers on the topic, such as [15] which considered the motion of a single particle and the subsequent paper =-=[16]-=- that considered systems of particles. This leads us one step at a time towards a conclusion similar to theirs, that an iterative approach is required (one of their methods requires iteration and the ... |