Haptics and Virtual Reality Lecture 9: • Implicit surface • Deformable Object M. Zareinejad
Outline • Deformable Object • 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.
Haptic simulation of deformable objects • 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.
Soft Tissue properties • Relationshipbetweenstressandstrain • PossibleModels: • Linearelasticity • Nonlinearelasticity • Viscoelasticity
Viscoelasticity Creepandcreeprecovery StressRelaxation Kelvin Maxwell Zener
Mesh vs. meshless simulation of deformation • 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).
Mesh-based simulation of deformation • 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.
Mass-spring models of deformation • Object = mass nodes connected by a network of linear springs. • Force on node Pi: • Advantages: • Easy to implement. • Consistent with the data structures used for graphic rendering. • Suitable for static or dynamic simulations.
Spring-mass-type meshes T2 mesh Triangular mesh