Stable 6-DOF Haptic Rendering with Inner Sphere Trees 19.05.2018 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

BVHs vs Voxels BVHs Voxel based algorithms 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

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

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

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

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

Batch Neural Gas Clustering w1 w2 Related Work Our Approach Details Collision Response Results Extensions Conclusion

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

BVH Traversal: Penetration Volume Queries Penetration volume = v1 + v2 Penetration volume = 0 Penetration volume = v1 Related Work Our Approach Details Collision Response Results Extensions Conclusion

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

Collision Response Part 1: Forces Collision Response Part 2: Torques Collision Response Part 1: Forces s2red Å s2blue Pi,j niblue -niblue sjred Å 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

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

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

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

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

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

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

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

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

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

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