1. M. Zareinejad 1

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13.  Haptic interaction with deformable objects: ◦ Overview. ◦ Mesh-based simulation of deformation:  The Mass-Spring method.  The ChainMail method.  Continuum mechanics methods:  The Finite Element Method (FEM).  The Boundary Element Method (BEM).  The Cellular Neural Network (CNN) method. 13 Deformable Object

14. 14 Haptic interaction with deformable objects

15. 15 Haptic interaction with deformable objects

16. 16 Haptic interaction with deformable objects

17.  Goals: ◦ Speed.  30Hz for visual feedback.  500-1000 Hz for haptic feedback. ◦ Stability. ◦ Physical accuracy.  critical for medical applications: surgical training, planning and outcome prediction.  Challenges: ◦ Governing physical laws. ◦ Material coupling, e.g., elastic tissue & fluid. ◦ Inhomogeneities & anisotropies. ◦ Non-linear deformations. ◦ Geometry changes, e.g., cutting, suturing. 17

18.  Relationship between stress and strain  Possible Models: Linear elasticity Nonlinear elasticity Viscoelasticity 18

19. Viscoelasticity Creep and creep recovery Stress Relaxation Kelvin MaxwellZener 19

20.  Mesh-based techniques: ◦ Connectivity among object nodes. ◦ Difficult to handle:  large deformations (fluid flow).  connectivity changes (cuts, fractures). ◦ Example: Finite Element Method (FEM) models.  Meshless techniques: ◦ No connectivity among object nodes. ◦ Easy to handle:  fluid flows.  cuts, fractures, etc. ◦ Example: Smoothed Particle Hydrodynamics (SPH) models, Method of Finite Spheres (Kim, De, Srinivasan ‘03). 20

21.  Surface models of deformation: ◦ Object represented by points on its boundary G. ◦ Not good for incompressibility, bending.  Volumetric models of deformation: ◦ Object represented by all points in W. 21

22.  Object = mass nodes connected by a network of linear springs.  Force on node P i :  Advantages: ◦ Easy to implement. ◦ Consistent with the data structures used for graphic rendering. ◦ Suitable for static or dynamic simulations. 22

23. Triangular mesh T2 mesh Spring-mass-type meshes 23

24. 24 Mass-spring models of deformation Mass-spring models of deformation