1. Eurohaptics 2002 jcorso@cs.jhu.edu © Interactive Haptic Display of Deformable Surfaces Based on the Medial Axis Transform Jason J. Corso, Jatin Chhugani, Allison Okamura The Johns Hopkins University Eurohaptics 2002

2. jcorso@cs.jhu.edu © Interaction Definition of interactive changes –Graphics: 15 – 30 Hz –Haptics: 1000 Hz Definition of rendering changes –Graphics: pixel-wise (NxN) –Haptics: single-point (typically) How do these differences affect algorithms?

3. Eurohaptics 2002 jcorso@cs.jhu.edu © Talk Outline Overview and Related Work The Medial Axis Transform Object Modeling Object Interaction Implementation and Results Conclusions

4. Eurohaptics 2002 jcorso@cs.jhu.edu © Overview Of Our Work Interactive deformation and haptic rendering of viscoelastic surfaces Medial Axis Transform Compact representation Efficient rendering with low memory usage

5. Eurohaptics 2002 jcorso@cs.jhu.edu © Related Work Physically-Based Modeling –Spectrum: –ArtDefo uses BEM [Pai 99,00] –Medical Simulations often use FEM/BEM D-NURBS – physics based generalization that is coupled with FEM [Terzopoulos 94]

6. Eurohaptics 2002 jcorso@cs.jhu.edu © Related Work Graphics-Based Deformation –Free-Form [Coquillart 97] –Volumetric Approaches [Avila 96] –Adaptively Sampled Distance Fields [Frisken 01] NURBS Surfaces for haptic rendering –Surface-Surface Interaction [Cohen 98]

7. Eurohaptics 2002 jcorso@cs.jhu.edu © Medial Axis Transform

8. Eurohaptics 2002 jcorso@cs.jhu.edu © Medial Axis Transform MAT proposed by Blum [67] A multilocal,multiscale representation for graphics [Pizer, UNC] Automatically generate a volumetric representation of a polygonal mesh [Gagvani] Okamura developed a robotic system to acquire MAT models of real rigid- body objects [01].

9. Eurohaptics 2002 jcorso@cs.jhu.edu © Medial Axis Transform Foundation: shape skeletons Geometric abstraction of curves Skeleton called medial axis (2D) Each point on skeleton is associated with a locally maximal disk. These medial points coupled with their radii define the MAT.

10. Eurohaptics 2002 jcorso@cs.jhu.edu © Object Modeling An object is comprised of –The discretized skeleton –Radii of circles centered along skeleton –Stiffness, mass, damping, etc

11. Eurohaptics 2002 jcorso@cs.jhu.edu © Object Modeling Interpolate a spline through skeleton (SK) (include position, radius, etc). Interpolate an envelope spline (SC) through contour.

12. Eurohaptics 2002 jcorso@cs.jhu.edu © Object Modeling

13. Eurohaptics 2002 jcorso@cs.jhu.edu © Talk Outline Overview and Related Work The Medial Axis Transform Object Modeling Object Interaction Implementation and Results Conclusions

14. Eurohaptics 2002 jcorso@cs.jhu.edu © Object Interaction Nearest Point Localization Collision Detection Force/Deformation Calculation Spline Deformation Perform Rendering

15. Eurohaptics 2002 jcorso@cs.jhu.edu © Nearest Point Localization Perform a binary search over domain of the skeleton spline. Evaluates circle nearest Q

16. Eurohaptics 2002 jcorso@cs.jhu.edu © Collision Detection If ||PQ|| < R intersect then intersection

17. Eurohaptics 2002 jcorso@cs.jhu.edu © Object Deformation D = R intersect - ||PQ|| SK and SC are deformed appropriately.

18. Eurohaptics 2002 jcorso@cs.jhu.edu © Object Deformation D = R intersect - ||PQ|| SK and SC are deformed appropriately.

19. Eurohaptics 2002 jcorso@cs.jhu.edu © Object Deformation D = R intersect - ||PQ|| SK and SC are deformed appropriately.

20. Eurohaptics 2002 jcorso@cs.jhu.edu © Spline Deformation Given d, a deformation vector, deform the most influential control points.

21. Eurohaptics 2002 jcorso@cs.jhu.edu © Haptic Rendering Interact with circles through springs and dampers. Shear forces incorporated

22. Eurohaptics 2002 jcorso@cs.jhu.edu © Dynamic Deformation Second order system Treat circles as masses, each with a spring and a damper.

23. Eurohaptics 2002 jcorso@cs.jhu.edu © Graphic Rendering View-dependent adaptive tessellation Tessellate with maximum screen- space deviation of 3 pixels. Contour splines must be re- tessellated every frame to reflect the deformation.

24. Eurohaptics 2002 jcorso@cs.jhu.edu © Implementation - DeforMAT In C++ on 700MHz PIII with 384MB GeForce2 and OpenGL (with the GLU NURBS Tessellator) for graphics 2D – Immersion IE2000 3D – SensAble 3DOF Phantom

25. Eurohaptics 2002 jcorso@cs.jhu.edu © Results The complexity of the environment being graphically rendered is on average 10 5 triangles independent of MAT complexity.

26. Eurohaptics 2002 jcorso@cs.jhu.edu © Video

27. Eurohaptics 2002 jcorso@cs.jhu.edu © Conclusions A new algorithm for interactively deforming viscoelastic bodies at haptic interactive rates; i.e. 1KHz Couples efficient computation for haptic feedback with view-dependent graphics Minimal memory footprint

28. Eurohaptics 2002 jcorso@cs.jhu.edu © Future Work Incorporate bifurcation Non-ordered Medial Axes/Surfaces Analysis of Area/Volume preservation Extension of graphical rendering algorithms Direct performance comparison Analysis of parameter estimation –Robot to gather data

29. Eurohaptics 2002 jcorso@cs.jhu.edu © Acknowledgments Samuel Khor for starting the work on haptic rendering using shape skeletons at Hopkins Budi Purnomo for his many suggestions with respect to spline deformation