Dynamic Real-Time Deformations using Space & Time Adaptive Sampling Gilles Debunne Marie-Paule Cani Gilles Debunne Marie-Paule Cani Mathieu Desbrun Alan H. Barr Mathieu Desbrun Alan H. Barr

Goal Physical model Position Display 30 Hz Force feedback 1000 Hz Dynamic animation of deformable objects: Realistic Real-time

Motivation : surgery simulation © Epidaure

Difficulties We must combine: Visual realism  Complex computations Haptic feedback, stiff objects  Very small time steps (~1000 Hz) True real-time simulation  1 second of animation computed in 1 second or less

Consequences Only ~100 nodes for volume sampling  Optimal placement of samples required Separate surface and internal 3D model  Must be linked

Surface display vs. internal model Displayed surface ~10,000 triangles 30 Hz Internal physical model ~100 points ~1000 Hz

How to link with the surface Internal physical model Displayed surface

Adaptive sampling High sampling rate in high deformation zones Optimal use of the resources Reach and ensure real-time

Challenges Locally adapt sampling: When ? Where ? How ? Find a physical model: Dynamic behavior independent of discretization

Overview Multiresolution animation Choice of a physical model Results

Previous work Switch techniques according to visual impact Dynamic, cinematic… [Berka 97, Chenney & Forsyth 97, Carlson & Hodgins 97] Adaptive discretization Mass-springs [Hutchinson 96, Ganovelli & al 00] Finite Elements [O’Brien & Hodgins 99, Zhuang 99] No simplification

Our method: multiresolution Local adaptivity Refinement and simplification In 3D, mesh subdivision reduces quality

Different discretization rates Coarse Fine

Made of tetrahedra Independent from each other Optimized quality Meshes of the object Coarse Fine User’s tool

Active nodes Active coarse nodes Active fine nodes Force computed from neighbors’ displacements

Interface between meshes Interface zone Active coarse zone Active fine zone

Active Interface points Interface Similar to Domain Decomposition

Active Interface

C1C1 C2C2 J K C3C3 J,K interpolated from C 1 C 2 C 3 Active Interface Fine Coarse

Transmitting deformation information I F3F3 F2F2 F1F1 I interpolated from F 1 F 2 F 3 Fine Coarse Active Interface

Sampling adaptation Based on local deformation amplitude Node replaced by its children in the finer resolution

Definition of children Voronoï region Children Precomputed hierarchy

Active children Children become active Interface parent

Resulting mesh structure Active Interface Simulation at different time steps

Overview Multiresolution animation Choice of a physical model Results

Sampling-independent dynamic simulation Identical vibration modesTestbed No damping Measure of vertical displacement over time Goal

Different discretizations Level 0 Level 1 Level points 4 3 points5 3 points

Particle systems Mass-springs systems [Hutch96, BW98, GCS00] F

Mass-spring system « As close as possible » to Finite Elements [Gel98] Amplitude varies No smoothness z Coarse Medium Fine

Continuous models Discretization of a continuous equation Stress and strain tensors (Cauchy, Green) Finite Elements [TW88, GMTT89, BNC96, JP99] Explicit Finite Elements [Cot97, OH99]

Classical Finite Elements Object Finite Elements Large matricial system + Accuracy - Speed

Continuous models Discretization of a continuous equation Stress and strain tensors (Cauchy, Green) Finite Elements [TW88, GMTT89, BNC96, JP99] Explicit Finite Elements [Cot97, OH99]

- Accuracy + Speed Explicit Finite Elements Object Finite Elements Independent matricial systems

Continuous models Discretization of a continuous equation Stress and strain tensors (Cauchy, Green) Finite Elements [TW88, GMTT89, BNC96, JP99] Explicit Finite Elements [Cot97, OH99]

Cauchy tensor Mass-tensor [Cot97] Oscillations of the amplitude

Multiresolution ! (Behaves almost independently of the resolution) Green tensor [OH99]

Multiresolution is preserved With Rayleigh damping

Multiresolution in time Courant criterion (CFL) Depending on material’s stiffness, sampling Stability When force integration may diverge Synchronization with the display dt i = dt display 2i2i

Real-Time simulation Computation and display are synchronized Wait t 1/30 th sec simulated time 1/30 th sec, time experienced by the user Force feedback 1000Hz

Overview Multiresolution animation Choice of a physical model Results

Video

Conclusion Multiresolution in physically-based animation Real-time simulation guaranteed Force feedback at 1000 Hz Display at 30 Hz Multiresolution speedup factor :

Perspectives Hierarchical collision detection Cuts of the object Validation by surgeons The surgeon robot © Serre