Interactive Continuous Collision Detection for Polygon Soups

Xin Huang

11/20/2007

Introduction

• Discrete CD– Miss collision between sampled time

instances

• Continuous Collision Detection (CCD)

Introduction

• Continuous Collision Detection (CCD)– Consider continuous motion– Report first time of contact (TOC)

• Well applied in– Cloth simulation– Rigid body Dynamics– Local planning

Motivation

• CCD in Local Planning– CCD is used to check collision along the interpolating

trajectory between two free nearby samples – Perform the CCD query for samples near contact

space is vital in local planning

Related work (1)

• Schwarzer [2002]: Exact collision checkingUse adaptive bisection approachCan be used for polygon soupsCalculate un-directional motion bound Work not well when separation distance is very small

Related work (2)

• [Redon 2002]Use interval arithmetic to compute the motion boundContinuous OBB testWork not well when the motion has large rotationDoes not perform adaptive bisection, suffer from a large

number of bisection steps when objects are far apart

Related work (3)

• [Zhang 06]: Extend conservative advancementCompute continuous motion by linear interpolatingPerform hierarchy advancement based on convex hull

treeBenefit from motion coherence supported by swift++

As reported, perform more efficiently than [Redon 2002]

Challenge

• Exact CCD– Small separation distance

• [Redon 2002]– Large Rotation

• [Zhang 06]– Polygon soups– High number of convex pieces

Disassembly Plan (D-Plan)

• Efficient collision free path computation

• CAD/CAM models– non-manifold or polygon soups with no

connectivity or topology information– have tight spaces and multiple narrow

passages in configuration spaces

Some challenging benchmarks

200K+ polygons

12,236 vertices11,569 trianglesObstacle

Robot 16,781 vertices15,197 triangles

•Application in Assembly Maintainability: extract the part,

there are many non-manifold parts in the robot

Goal

• Perform fast continuous collision detection for polygon soups in local planning for part disassembly

Main Approaches

• Perform conservative advancement (CA) for polygon soups

• Directional motion bound computation

• Hierarchical CA for BVH

• Explore motion coherence to accelerate

Conservative Advancement

• CA for Convex Polytopes– computes an upper bound of TOC by

repeatedly advancing A by dt toward B while avoiding collision

– When close enough, if TOC<1, then report collision; else report collision free

Conservative Advancement

• CA for non-convex objects– Convex decomposition– Assume the closed mesh

• CA for polygon soups– Using SSV based on PQP– Compute the motion bound for SSV– Compute the motion bound for triangle– Can process polygon soups

Directional motion bound computation

• Calculate linear motion interpolation– : U = V + W*R

• Project the motion along the direction of the closest distance d

• Compute the directional motion for BV and Triangle in Leaf BV

d

U

Hierarchical CA for BVH

• Bound volume traversal trees– Given two BVHs (HA, HB), starting from the root

nodes, recursively perform pairwise TOC computation– If TOC(na, nb) < TOCcurrent, the recursive traversal

continues; otherwise it stops

Explore motion coherence

• Temporal coherence in contact space sampling and constraint motion

• Motion coherence during each step of CA

• Compute the initial TOC according to the closest features stored in last iteration

Explore motion coherence• Further benefit motion coherence by exploring

local tree containing the closest features• The initial small TOC will help culling many BV

pair Tests and Triangle pair test

Algorithm

1. Build the Bound Volume traversal tree for object A and B2. Compute the initial TOC using local tree motion coherence3. Traverse the BVH tree to compute TOC4. If the current node in traversal tree is leaf node, compute

the distance and directional motion bound between the two triangles to calculate TOC

5. If the current node is not leaf node, go to step 3 to traverse its child node if the TOC of the two BV is less than current minimal TOC

6 .Advance the object A by TOC until TOC > 1 or distance between the two objects is less than threshold

7. Return TOC

Demo

Experiments analysis

• The alpha model (1K triangles)

Experiments analysis

• Test motion coherence

No motion coherence Enable motion coherence

Conclusion

• Implement the CCD for polygon soups using conservative advancementPerform the hierarchy conservative advancement for

polygon soups based on PQPCalculate the directional motion bound for SSV using

linear interpolatingExplore motion coherence

Future work

• Compute the motion bound for constrained motion

• Perform continuous collision detection for sliding motion

References

• Xinyu Zhang, Minkyoung Lee, Young J. Kim: Interactive continuous collision detection for non-convex polyhedra. The Visual Computer 22(9-11): 749-760 (2006)

• Gottschalk, S., Lin, M., Manocha, D.: OBB-Tree: A hierarchical structure for rapid interference detection. In: H. Rushmeier (ed.) SIGGRAPH 96 Conference Proceedings, Annual Conference Series, pp. 171–180. ACM SIGGRAPH, Addison Wesley (1996).

• Kim, B., Rossignac, J.: Collision prediction for polyhedra under screw motions. In: ACM Conference on Solid Modeling and Applications (2003)

• Larsen, E., Gottschalk, S., Lin, M., Manocha, D.: Fast proximity queries with swept sphere volumes. Tech. Rep. TR99-018, Department of Computer Science, University of North Carolina (1999)

• Schwarzer, F., Saha, M., Latombe, J.C.: Exact collision checking of robot paths. In: Workshop on Algorithmic Foundations of Robotics (WAFR) (2002)

References

• Lin, M., Manocha, D.: Collision and proximity queries. In: Handbook of Discrete and Computational Geometry (2003)

• Mirtich, B.: Timewarp rigid body simulation. SIGGRAPH 00 Conference Proceedings pp. 193–200 (2000)

• Mirtich, B.V.: Impulse-based dynamic simulation of rigid body systems. Ph.D. thesis, University of California, Berkeley (1996)

• Redon, S., Kheddar, A., Coquillart, S.: Fast continuous collision detection between rigid bodies. Proc. of Eurographics (Computer Graphics Forum) (2002)

• Xinyu Zhang, Stephane Redon, Minkyoung Lee, Young J. Kim: Continuous collision detection for articulated models using Taylor models and temporal culling. ACM Trans. Graph. 26(3): 15 (2007)