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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
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
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
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
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Sphere Packing
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Hierarchy Creation
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
wi :=
P m
j = 0h¸ (ki j )xjP m
j = 0h¸ (ki j )
Batch Neural Gas Clustering
w1
w2
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Hierarchy Creation in 3D
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Penetration volume = v1 + v2Penetration volume = 0Penetration volume = v1
BVH Traversal: Penetration Volume Queries
v1
v2
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
distance < d1
d1
BVH Traversal: Proximity Queries
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
(si, sj) = (Pi,j – Cm) £ fi fiblue=(sj
redÅ siblue)(–ni
blue)total = (si, sj)ftotalblue= fi
blue= (Pc – Cm) £ f
niblue
-niblue
sjred Å si
blue
Collision Response Part 1: Forces
s2red Å s2
blue
Collision Response Part 2: Torques
Pi,j
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Results: Forces / Torques
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Results: Penetration Volume
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Results: Proximity-Queries
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Multithreaded Time Critical Approach
HapticSimulation
Thread
CollisionDetectionThread
VisualRendering
Thread
Positons
Separation List
Positions
Related Work Our Approach Details Collision Response Results Extensions Conclusion
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
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Expected Overlap Volume
Related Work Our Approach Details Collision Response Results Extensions Conclusion
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
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
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
Related Work Our Approach Details Collision Response Results Extensions Conclusion
Acknowledgments
DFG grant ZA292/1-1
BMBF grant Avilus / 01 IM 08 001 U.