@Article{duriez:tm:2006,
  author    = {Duriez, Christian and Dubois, Frederic and Kheddar, Abderrahmane and Andriot, Claude},
  title     = {Realistic haptic rendering of interactive deformable objects in virtual environments},
  journal   = {IEEE-ASME Transactions on Mechatronics},
  year      = {2006},
  volume    = {12},
  number    = {1},
  pages     = {36--47},
  month     = {January},
  doi       = {10.1109/TVCG.2006.13},
  url       = {https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1541998},
  keywords  = {Computer hatics, Signorini\textquotesingle s law, Coulomb\textquotesingle s friction law, corotational deformable objects, Delassus operator, Gauss-Seidel type resolution, real-time simulation},
  abstract  = {A new computer haptics algorithm to be used in general interactive manipulations of deformable virtual objects is presented. In multimodal interactive simulations, haptic feedback computation often comes from contact forces. Subsequently, the fidelity of haptic rendering depends significantly on contact space modeling. Contact and friction laws between deformable models are often simplified in up to date methods. They do not allow a "realistic" rendering of the subtleties of contact space physical phenomena (such as slip and stick effects due to friction or mechanical coupling between contacts). In this paper, we use Signorini\textquotesingle s contact law and Coulomb\textquotesingle s friction law as a computer haptics basis. Real-time performance is made possible thanks to a linearization of the behavior in the contact space, formulated as the so-called Delassus operator, and iteratively solved by a Gauss-Seidel type algorithm. Dynamic deformation uses corotational global formulation to obtain the Delassus operator in which the mass and stiffness ratio are dissociated from the simulation time step. This last point is crucial to keep stable haptic feedback. This global approach has been packaged, implemented, and tested. Stable and realistic 6D haptic feedback is demonstrated through a clipping task experiment.},
  publisher = {IEEE-INST Electrical Electronics Engineers Inc},
  address   = {445 Hoes Lane, Piscataway, NJ 08855-4141, USA}
}