Stable 6-DOF Haptic Rendering with Inner Sphere Trees René Weller, Gabriel Zachmann Clausthal...

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]



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



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



Sphere Packing



Hierarchy Creation



wi :=

P m

j = 0h¸ (ki j )xjP m

j = 0h¸ (ki j )

Batch Neural Gas Clustering

w1

w2



Hierarchy Creation in 3D



Penetration volume = v1 + v2Penetration volume = 0Penetration volume = v1

BVH Traversal: Penetration Volume Queries

v1

v2



distance < d1

d1

BVH Traversal: Proximity Queries



(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



Results: Forces / Torques



Results: Penetration Volume



Results: Proximity-Queries



Multithreaded Time Critical Approach

HapticSimulation

Thread

CollisionDetectionThread

VisualRendering

Thread

Positons

Separation List

Positions



Time Critical Traversal: Separation List



Expected Overlap Volume



Applications

12 full dynamically moving

objects

3.5M of triangles

1KHz simulation rate

Old Pentium IV 3GHz computer



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



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



Acknowledgments

DFG grant ZA292/1-1

BMBF grant Avilus / 01 IM 08 001 U.

Stable 6-DOF Haptic Rendering with Inner Sphere Trees René Weller, Gabriel Zachmann Clausthal...

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