1. Stable 6-DOF Haptic Rendering with Inner Sphere Trees René Weller, Gabriel Zachmann Clausthal University, Germany {weller,zach}@in.tu-clausthal.de IDETC/CIE 2009, Aug-Sep 2009, San Diego, CA

2. Related Work Our Approach Details Collision Response Results Extensions Conclusion BVHs vs Voxels  BVHs  Easy to build  Fast, robust and exact -Complicated to compute penetration depth -Not fast enough for haptic applications  Voxel based algorithms  Fast enough for haptic interactions  Independent of object complexity -Memory consuming -Aliasing artifacts Mendoza et al, 2006],[ [Zhang et al, 2007], … [McNeely et al., 1999] Related Work Our Approach Details Collision Response Results Extensions Conclusion

3. Goal: Keep the Best of Both Worlds  Keep a single consistent data structures for moving and fixed objects  Near constant running time  Low memory usage  Continuous feedback forces Related Work Our Approach Details Collision Response Results Extensions Conclusion

4. Our Novel Approach: Inner Sphere Trees  Fill the object with non-overlapping spheres  Build sphere hierarchy  Support for approximative separation distance and penetration volume  Penetration volume defines a new approach for penalty forces Related Work Our Approach Details Collision Response Results Extensions Conclusion

5. Sphere Packing Related Work Our Approach Details Collision Response Results Extensions Conclusion

6. Hierarchy Creation Related Work Our Approach Details Collision Response Results Extensions Conclusion

7. Batch Neural Gas Clustering w1w1 w2w2 Related Work Our Approach Details Collision Response Results Extensions Conclusion

8. Hierarchy Creation in 3D Related Work Our Approach Details Collision Response Results Extensions Conclusion

9. Penetration volume = v 1 + v 2 Penetration volume = 0Penetration volume = v 1 BVH Traversal: Penetration Volume Queries v1v1 v2v2 Related Work Our Approach Details Collision Response Results Extensions Conclusion

10. distance < d 1 d1d1 BVH Traversal: Proximity Queries Related Work Our Approach Details Collision Response Results Extensions Conclusion

11.  (s i, s j ) = (P i,j – C m ) £ f i f i blue =(s j red Å s i blue )(–n i blue )  total =   (s i, s j )f total blue =  f i blue  = (P c – C m ) £ f n i blue -n i blue s j red Å s i blue Collision Response Part 1: Forces s 2 red Å s 2 blue Collision Response Part 2: Torques P i,j Related Work Our Approach Details Collision Response Results Extensions Conclusion

12. Results: Forces / Torques Related Work Our Approach Details Collision Response Results Extensions Conclusion

13. Results: Penetration Volume Related Work Our Approach Details Collision Response Results Extensions Conclusion

14. Results: Proximity-Queries Related Work Our Approach Details Collision Response Results Extensions Conclusion

15. Multithreaded Time Critical Approach Haptic Simulation Thread Collision Detection Thread Visual Rendering Thread Positons Separation List Positions Related Work Our Approach Details Collision Response Results Extensions Conclusion

16. Time Critical Traversal: Separation List Related Work Our Approach Details Collision Response Results Extensions Conclusion

17. Expected Overlap Volume Related Work Our Approach Details Collision Response Results Extensions Conclusion

18. Applications  12 full dynamically moving objects  3.5M of triangles  1KHz simulation rate  Old Pentium IV 3GHz computer Related Work Our Approach Details Collision Response Results Extensions Conclusion

19. Conclusions  Inner Sphere Trees with support for  Proximity queries  Penetration volume computation  Independent of object complexity  Fast run time with high accuracy  Accuracy loss < 1% at 1 KHz refresh rate  Stable multithreaded time critical algorithm  BVH-like low memory usage and consistency  Continuous forces and torques => No Aliasing Related Work Our Approach Details Collision Response Results Extensions Conclusion

20. Future Work  Derive exact error bounds to get the optimal number of inner spheres  GPU implementation  Other bounding volumes  Other objects  Thin sheets  Deformable objects Related Work Our Approach Details Collision Response Results Extensions Conclusion

21. Acknowledgments  DFG grant ZA292/1-1  BMBF grant Avilus / 01 IM 08 001 U.