Stable 6-DOF Haptic Rendering with Inner Sphere Trees

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

2. BVHs vs Voxels • BVHs • Easy to build • Fast, robust and exact • Complicated to compute penetration depth • Not fast enough for haptic applications Mendoza et al, 2006],[ [Zhang et al, 2007], … • Voxel based algorithms • Fast enough for haptic interactions • Independent of object complexity • Memory consuming • Aliasing artifacts [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. w1 w2 Batch Neural Gas Clustering 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. BVH Traversal: Penetration Volume Queries v1 v2 Penetration volume = 0 Penetration volume = v1 Penetration volume = v1 + v2 Related Work Our Approach Details Collision Response Results Extensions Conclusion

10. BVH Traversal: Proximity Queries d1 distance < d1 Related Work Our Approach Details Collision Response Results Extensions Conclusion

11. Collision Response Part 2: Torques Collision Response Part 1: Forces s2redÅ s2blue Pi,j niblue -niblue sjredÅ siblue ftotalblue= fiblue  (si, sj) = (Pi,j – Cm) £ fi fiblue=(sjredÅ siblue)(–niblue) total =  (si, sj) = (Pc – Cm) £ f 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 Separation List Visual Rendering Thread Haptic Simulation Thread Collision Detection Thread Positions Positons 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.