Simulation of deformable models with the Poisson equation.
In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Taylor & Francis
2006
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| Online Access: | http://hdl.handle.net/20.500.11937/8279 |
| _version_ | 1848745610934484992 |
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| author | Zhong, Yongmin Shirinzadeh, B. Alici, G. Smith, J. |
| author_facet | Zhong, Yongmin Shirinzadeh, B. Alici, G. Smith, J. |
| author_sort | Zhong, Yongmin |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated as the source injected into the Poisson system, as described by the law of conservation of energy. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. An autonomous cellular neural network (CNN) model is established by using the analogy between the Poisson equation and CNN to solve the Poisson model for the real-time requirement of soft object deformation. A method is presented to derive the internal forces from the potential energy distribution. The proposed methodology models non-linear materials with the non-linear Poisson equation and thus non-linear CNN, rather than geometric non-linearity. It not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients. A haptic virtual reality system has been developed for deformation simulation with force feedback. Examples are presented to demonstrate the efficiency of the proposed methodology. |
| first_indexed | 2025-11-14T06:20:06Z |
| format | Journal Article |
| id | curtin-20.500.11937-8279 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:20:06Z |
| publishDate | 2006 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-82792017-09-13T14:36:23Z Simulation of deformable models with the Poisson equation. Zhong, Yongmin Shirinzadeh, B. Alici, G. Smith, J. Poisson equation Haptic feedback and analogy systems CNN Deformation In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated as the source injected into the Poisson system, as described by the law of conservation of energy. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. An autonomous cellular neural network (CNN) model is established by using the analogy between the Poisson equation and CNN to solve the Poisson model for the real-time requirement of soft object deformation. A method is presented to derive the internal forces from the potential energy distribution. The proposed methodology models non-linear materials with the non-linear Poisson equation and thus non-linear CNN, rather than geometric non-linearity. It not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients. A haptic virtual reality system has been developed for deformation simulation with force feedback. Examples are presented to demonstrate the efficiency of the proposed methodology. 2006 Journal Article http://hdl.handle.net/20.500.11937/8279 10.1080/10255840600908503 Taylor & Francis restricted |
| spellingShingle | Poisson equation Haptic feedback and analogy systems CNN Deformation Zhong, Yongmin Shirinzadeh, B. Alici, G. Smith, J. Simulation of deformable models with the Poisson equation. |
| title | Simulation of deformable models with the Poisson equation. |
| title_full | Simulation of deformable models with the Poisson equation. |
| title_fullStr | Simulation of deformable models with the Poisson equation. |
| title_full_unstemmed | Simulation of deformable models with the Poisson equation. |
| title_short | Simulation of deformable models with the Poisson equation. |
| title_sort | simulation of deformable models with the poisson equation. |
| topic | Poisson equation Haptic feedback and analogy systems CNN Deformation |
| url | http://hdl.handle.net/20.500.11937/8279 |