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## Elastically Deformable Models (1987)

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### Other Repositories/Bibliography

Venue: | Computer Graphics |

Citations: | 1 - 0 self |

### Citations

1796 |
A Practical Guide to Splines
- Boor
- 1978
(Show Context)
Citation Context ... in progress. 205s~t~ SIGGRAPH '87, Anaheim, July 27-31, 1987 2. Related Graphics Models Interestingly, the classical spline representations of shape have characterizations based in elasticity theory =-=[7]-=-. However, in adopting splines as a representation of curve and surface shape, the graphics literature has deemphaslzed the physical basis of splines. The cubic interpolating spline, for instance, is ... |

901 | The rendering equation
- Kajiya
- 1986
(Show Context)
Citation Context ...ey [20] and Fournier and Reeves [11] to model water waves, as well as Kajiya and yon Herzen [17] and Yaeger et aL [28] for cloud simulation. Also, the physics of imaging has been applied to rendering =-=[16, 15]-=-. Well [26] used catenaries to approximate cloth, while Feynman [10] used a more sophisticated thin plate flexure model for the same purpose. Terzopoulos [23] employed deformable models based on varia... |

743 |
Differential Geometry of Curves and Surfaces
- Carmo, M
- 1976
(Show Context)
Citation Context ...is of Deformation Elasticity theory involves the analysis of deformation [18, 12]. We will define measures of deformation using concepts from the differential geometry of curves, surfaces, and solids =-=[8]-=-. One requirement of our present approach is that the measures should be insensitive to rigid body motion since it imparts no deformation. The shape of a body is determined by the Euclidean distances ... |

698 | R.: Free-form deformation of solid geometric models
- SEDERBERG, PARRY
- 1986
(Show Context)
Citation Context ...les to reconstruct surfaces from scattered visual constraints. To create deformable models, Barr [3] subjected solid primitives to prescribed deformations using Jaeobian matrices. Sederberg and Parry =-=[21]-=- imposed similar deformations to solids modeled as freeform surfaces. We extend these approaches by adding equations governing the eycolution of deformations. Our models are compatible with and comple... |

518 |
Theory of Elasticity
- Landau, Lifshitz
- 1995
(Show Context)
Citation Context ...deformable models. These energies are employed to define the internal elastic forces of the models (see Section 6).s4.1. Analysis of Deformation Elasticity theory involves the analysis of deformation =-=[18, 12]-=-. We will define measures of deformation using concepts from the differential geometry of curves, surfaces, and solids [8]. One requirement of our present approach is that the measures should be insen... |

365 |
Global and local deformations of solid primitives
- Barr
- 1984
(Show Context)
Citation Context ...re model for the same purpose. Terzopoulos [23] employed deformable models based on variational principles to reconstruct surfaces from scattered visual constraints. To create deformable models, Barr =-=[3]-=- subjected solid primitives to prescribed deformations using Jaeobian matrices. Sederberg and Parry [21] imposed similar deformations to solids modeled as freeform surfaces. We extend these approaches... |

276 |
Regularization of inverse visual problems involving discontinuities
- Terzopoulos
- 1986
(Show Context)
Citation Context ...ves, surfaces, and solids. Our work in this paper can be viewed as an extension, including physically-based dynamics, of the mixed-order generalized splines employed in computer vision by Terzopoulos =-=[24]-=-. Special purpose physical models have begun to capture the attention of the computer graphics community. Fluid mechanics was used by Peachey [20] and Fournier and Reeves [11] to model water waves, as... |

255 | Von Herzen, “Ray Tracing Volume Densities
- Kajiya, P
- 1984
(Show Context)
Citation Context ...ls have begun to capture the attention of the computer graphics community. Fluid mechanics was used by Peachey [20] and Fournier and Reeves [11] to model water waves, as well as Kajiya and yon Herzen =-=[17]-=- and Yaeger et aL [28] for cloud simulation. Also, the physics of imaging has been applied to rendering [16, 15]. Well [26] used catenaries to approximate cloth, while Feynman [10] used a more sophist... |

200 |
Foundations of Solid Mechanics
- Fung
- 1965
(Show Context)
Citation Context ...deformable models. These energies are employed to define the internal elastic forces of the models (see Section 6).s4.1. Analysis of Deformation Elasticity theory involves the analysis of deformation =-=[18, 12]-=-. We will define measures of deformation using concepts from the differential geometry of curves, surfaces, and solids [8]. One requirement of our present approach is that the measures should be insen... |

144 |
A Simple Model of Ocean Waves
- Fournier, Reeves
- 1986
(Show Context)
Citation Context ...er vision by Terzopoulos [24]. Special purpose physical models have begun to capture the attention of the computer graphics community. Fluid mechanics was used by Peachey [20] and Fournier and Reeves =-=[11]-=- to model water waves, as well as Kajiya and yon Herzen [17] and Yaeger et aL [28] for cloud simulation. Also, the physics of imaging has been applied to rendering [16, 15]. Well [26] used catenaries ... |

136 |
A radiosity method for non-diffuse environments
- IMMEL, COHEN, et al.
- 1986
(Show Context)
Citation Context ...ey [20] and Fournier and Reeves [11] to model water waves, as well as Kajiya and yon Herzen [17] and Yaeger et aL [28] for cloud simulation. Also, the physics of imaging has been applied to rendering =-=[16, 15]-=-. Well [26] used catenaries to approximate cloth, while Feynman [10] used a more sophisticated thin plate flexure model for the same purpose. Terzopoulos [23] employed deformable models based on varia... |

117 |
Computational Geometry for Design and Manufacture
- Faux, Pratt
- 1979
(Show Context)
Citation Context ...ints in the deformed body in Euclidean 3-space is given by dl = E Gijdaidaj, (2) i,j where the symmetric matrix Or Or Gij (r(a))= Oa"-~'Oaj (3) is known as the metric tensor or first fundamental form =-=[9]-=- (the dot indicates the scalar product of two vectors). Two 3-dimensional solids have the same shape (differ only by a rigid body motion) if their 3 x 3 metric tensors are identical functions of a = l... |

106 |
The dynamics of articulated rigid bodies for purposes of animation
- Armstrong, Green
- 1985
(Show Context)
Citation Context ...ntary to the constraint-based modeling approach for rigid primitives proposed by Barzel and Barr [4], as well as with the dynamics-based approaches of Wilhelms and Barsky [27] and Armstrong and Green =-=[1]-=- to animating articulated rigid bodies. Finally, since computer vision is the inverse problem of computer graphics, the models presented in this paper are of value for reconstructing mathematical repr... |

89 |
Multilevel computational processes for visual surface reconstruction
- Terzopoulos
- 1983
(Show Context)
Citation Context ...imaging has been applied to rendering [16, 15]. Well [26] used catenaries to approximate cloth, while Feynman [10] used a more sophisticated thin plate flexure model for the same purpose. Terzopoulos =-=[23]-=- employed deformable models based on variational principles to reconstruct surfaces from scattered visual constraints. To create deformable models, Barr [3] subjected solid primitives to prescribed de... |

80 |
Modeling waves and surf
- Peachey
- 1986
(Show Context)
Citation Context ...ed splines employed in computer vision by Terzopoulos [24]. Special purpose physical models have begun to capture the attention of the computer graphics community. Fluid mechanics was used by Peachey =-=[20]-=- and Fournier and Reeves [11] to model water waves, as well as Kajiya and yon Herzen [17] and Yaeger et aL [28] for cloud simulation. Also, the physics of imaging has been applied to rendering [16, 15... |

40 |
Using dynamic analysis to animate articulated bodies such as humans and robots. Graphics Interface
- Wilhelms, Barsky
- 1985
(Show Context)
Citation Context ... compatible with and complementary to the constraint-based modeling approach for rigid primitives proposed by Barzel and Barr [4], as well as with the dynamics-based approaches of Wilhelms and Barsky =-=[27]-=- and Armstrong and Green [1] to animating articulated rigid bodies. Finally, since computer vision is the inverse problem of computer graphics, the models presented in this paper are of value for reco... |

40 |
The Finite Element Method, Third Edition
- Zienkiewicz
- 1977
(Show Context)
Citation Context ...87 model equations. In the present paper we have employed finite difference discretization techniques. We are presently implementing more sophisticated discretizations using the finite element method =-=[29]-=-. We have also experimented with higher-order time integration procedures such as a fourth-order Runge-Kutta method [6]. Our results indicate that adaptive time-step control can be beneficial in incre... |

32 |
Combining Physical and Visual Simulation - Creation of the Planet Jupiter for the Film
- Yaeger, Upson, et al.
(Show Context)
Citation Context ...re the attention of the computer graphics community. Fluid mechanics was used by Peachey [20] and Fournier and Reeves [11] to model water waves, as well as Kajiya and yon Herzen [17] and Yaeger et aL =-=[28]-=- for cloud simulation. Also, the physics of imaging has been applied to rendering [16, 15]. Well [26] used catenaries to approximate cloth, while Feynman [10] used a more sophisticated thin plate flex... |

22 |
Matching deformable models to images: Direct and iterative solutions
- Terzopoulos
- 1987
(Show Context)
Citation Context ...nce computer vision is the inverse problem of computer graphics, the models presented in this paper are of value for reconstructing mathematical representations of non-rigid objects from their images =-=[25]-=-. 3. Dynamics of Deformable Models We begin the mathematical development by giving the equations of motion governing the dynamics of our deformable models under the influence of applied forces. The eq... |

11 |
Nonlinear elasticity
- Stoker
- 1968
(Show Context)
Citation Context ... we can use such expressions to simulate nonlinear elastic phenomena such as the (~ @ Computer Graphics, Volume 21, Number 4, July 1987 Figure 5. Membrane shrinking around a jack. i bending of shells =-=[22]-=-. Unfortunately, the discrete nonlinear approximations, especially the 191i terms in (17), tend to be poorly conditioned numerically. One way to improve conditioning is to hnearize the second term of ... |

5 |
Modeling the appearance of cloth. MSc thesis
- Feynman
- 1986
(Show Context)
Citation Context ...jiya and yon Herzen [17] and Yaeger et aL [28] for cloud simulation. Also, the physics of imaging has been applied to rendering [16, 15]. Well [26] used catenaries to approximate cloth, while Feynman =-=[10]-=- used a more sophisticated thin plate flexure model for the same purpose. Terzopoulos [23] employed deformable models based on variational principles to reconstruct surfaces from scattered visual cons... |

3 |
Geometric Modeling and Fluid Dynamic Analysis of Swimming Spermatozoa
- Barr
- 1983
(Show Context)
Citation Context ... is the velocity of the surface relative to some constant stream velocity u. The force is a flow field projected onto the normal of the surface, is linear in the velocity, and models a viscous medium =-=[2]-=-. We simulate collision dynamics between elastic models and immobile impenetrable objects by creating a potential energy cexp(-f(r)/e) around each object, where f is the object's inside/outside functi... |

1 |
Dynamic Constraints, MSc thesis
- Barzel
- 1987
(Show Context)
Citation Context ... adding equations governing the eycolution of deformations. Our models are compatible with and complementary to the constraint-based modeling approach for rigid primitives proposed by Barzel and Barr =-=[4]-=-, as well as with the dynamics-based approaches of Wilhelms and Barsky [27] and Armstrong and Green [1] to animating articulated rigid bodies. Finally, since computer vision is the inverse problem of ... |

1 |
The synthesis of cloth objects
- Well
- 1986
(Show Context)
Citation Context ...rnier and Reeves [11] to model water waves, as well as Kajiya and yon Herzen [17] and Yaeger et aL [28] for cloud simulation. Also, the physics of imaging has been applied to rendering [16, 15]. Well =-=[26]-=- used catenaries to approximate cloth, while Feynman [10] used a more sophisticated thin plate flexure model for the same purpose. Terzopoulos [23] employed deformable models based on variational prin... |