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DESCRIPTION
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Haptics and Virtual Reality
M. Zareinejad
Lecture 9:
Implicit surface Deformable Object
Implicit surface
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Implicit surface and gradient map
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Implicit surface
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Constrained by a Plane
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Surface Tracking
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Surface Tracking
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Surface Tracking
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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.
Outline
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Deformable Object
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Haptic interaction with deformable objects
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Haptic interaction with deformable objects
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Haptic interaction with 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.
Haptic simulation of deformable objects
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Soft Tissue properties
Relationship between stress and strain
Possible Models:
Linear elasticityNonlinear elasticityViscoelasticity
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ViscoelasticityCreep and creep recovery Stress Relaxation
Kelvin Maxwell Zener
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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 vs. meshless simulation of deformation
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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.
Mesh-based simulation of deformation
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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.
Mass-spring models of deformation
ji
jiijji
iNjiji PP
PPlPPkF 0
)(
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Triangular mesh T2 mesh
Spring-mass-type meshes
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Mass-spring models of deformation