Quasi-Rigid Objects in Contact Mark Pauly Dinesh PaiLeo Guibas Stanford UniversityRutgers UniversityStanford University

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Contacts in Simulation Bio-medical applications: surgery simulation artifical joints, dental implants Mechanical design: wear and tear of industrial parts Physics-based animation: movies games

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Existing Models Rigid body dynamics small number of state variables efficient collision detection contact sensitivity problem (a stool with hundreds of legs) Fully deformable (e.g. FEM, mass-spring) accurate modeling of complex materials (elasticity, plasticity) too costly for models that hardly deform

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Quasi-Rigid Objects Physical model point force applied to object only leads to small, local deformation analytical system response model to define displacements due to point force linear elasticity: Global system response by superposition forces and displacements evaluated on surface only

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Quasi-Rigid Objects Surface model point cloud representation for modeling consistent, highly dynamic contact surface

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Physical Model Boussinesq approximation infinite elastic half-space Poisson’s ratio shear modulus force at x displacement at y due to force at x

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Physical Model Boussinesq approximation system response function

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Physical Model Linear elasticity superposition total displacement at y

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Volume Preservation Condition:

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Volume Preservation

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Approximate system response at discrete nodes (point samples) Discretization force at node j shape function displacement at node i

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Discretization system response matrix vector of displacements [u 1,...,u N ] T vector of tractions [p 1,...,p N ] T matrix coefficient

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Contact Collision detection static bounding volume hierarchies (small deformations) Contact resolution compute forces and displacements that resolve contact Contact surface find contact surface that is consistent for both models

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Contact Resolution Collision detection determines points that potentially experience displacements (active nodes) find corresponding point for each active node active nodes corresponding nodes

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Contact Resolution Separation of active nodes initial separation final separation

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Contact Resolution Condition for contact resolution: non-negative separation: s i ≥ 0 non-negative force: p i ≥ 0

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Linear Complementarity Problem (LCP) solved using Lemke’s method Contact Resolution

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Contact Surface Consistent conforming contact surface Adaptive moving least squares (MLS) approximation requires no re-meshing or zippering

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Simulation Treat objects as rigid while in free motion Integrate contact forces to compute total wrench

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Example Model acquisition laser-range scan Hierarchy construction recursive clustering efficient multi-level computation

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Example Simulation

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Example MeasurementSimulation X2 FootSensor (xSensor Corp.) 37 x 13 sensors, 1.94 sensors/cm2 Validation

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Bio-medical Applications Simulate friction effects to predict attrition  design of artificial joints

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Computer Animation Quasi-rigid body simulation

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Computer Animation Explicit representation of contact surface allows accurate simulation of friction effects

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Computer Animation Explicit representation of contact surface allows accurate simulation of friction effects

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Conclusion Quasi-rigid objects bridge the gap between rigid bodies and fully deformable models Simple and efficient model for contact resolution Limitations: small deformations linear elasticity sharp corners

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Future Work Coupling with low-resolution FEM model Acquired system response functions Incorporate friction into LCP Application: Contact simulation in knee joint

Quasi-Rigid Objects in ContactSCA 04Mark Pauly Acknowledgements NSF grants CARGO , ITR , IIS , EIA , ARO grant DAAD Anonymous reviewers