FASTCD: Fracturing-Aware Stable Collision Detection

Jae-Pil Heo1, Joon-Kyung Seong1, Duksu Kim1,Miguel A. Otaduy2, Jeong-Mo Hong3,

Min Tang4, and Sung-Eui Yoon1

1KAIST, 2URJC Madrid, 3Dongguk Univ, 4Zhejiang Univ.

http://sglab.kaist.ac.kr/FASTCD

2

Collision Detection (CD)

●Collision detection is an essential part of various applications● Physically-based simulation● Games● Robotics

cloth simulation Quake 4 KAIST Hubo

3

Inter- and Self- Collisions

● Inter-collisions● Collisions between two objects

● Self-collisions (intra-collisions)● Collisions between

different parts of one object● Takes much longer

computation time (~100x)than inter-collisions

from Govindaraju’s work

4

CD for Fracturing Models

● Fracturing ● changes topology (connectivity) of a mesh

pre-computed information and acceleration structures become useless

● places many objects in close proximity CD cost is increasing

● Fracturing is one of the most challenging scenarios of collision detection

5

Goals

●Design a collision detection method that provides followings:● efficient performance for detecting inter-

and self-collisions● stable performance with deforming

models that have geometric and topological changes

6

Our Contributions

●A novel culling method for self-collision detection, dual-cone method, which is suitable for fracturing models

●A BVH selective restructuring method based on a novel cost estimation metric and a fast BVH construction technique for fracturing models

7

Benchmarks

Cloth-Ball Exploding-Dragon

Breaking-Walls

video

# of topology changes

0fixed topology

4dynamic topology

8dynamic topology

complexity

92K 252K -> 252K 42K -> 140K

8

Previous Work (1/2)

●BVH update methods● Refit

● [Teschner et al, 2005]

● Reconstruction ● [Wald et al, 2006]

● Selective restructuring● [Larsson et al, 2006], [Yoon et al, 2006]

● Selective restructuring for progressively fracturing models● [Otaduy et al, 2006]

● Less attention to topology changing models

9

Previous Work (2/2)

●Culling techniques for self-CD● Reduce redundant tests (low level culling)

● [Curtis et al. 2008]● [Tang et al. 2010]

● Easily combined with our method

● Detect self-collision free regions (high level culling)● [Volino and Thalmann 1994]● [Tang et al, 2008]● [Sara et al, 2010]

● Do not directly consider topology changes

10

Outline

● Background

● Dual-Cone Method

● BVH Update Method

● Comparison

● Conclusion

11

Outline

● Background

● Dual-Cone Method

● BVH Update Method

● Comparison

● Conclusion

12

Bounding Volume Hierarchies (BVHs)

●Organize bounding volumes as a tree

● Leaf nodes have triangles

13

BVH-based CD

A

B C

X

Y Z

Collision test pair queue

(A,X)

●BVH traversal

A X

Dequeue

BV overlap test

14

BVH-based CD

A

B C

X

Y Z

Collision test pair queue

(B,Y)

BV overlap test

Dequeue Refine

Self-CD

●BVH traversal

(B,Z) (C,Y) (C,Y) (B,C) (Y,Z)

What if “A” does not have any self-collisions?

15

Self-Collision Free Conditions [Volino and Thalmann

1994]

● surface is rather flat● Surface Normal Cone (SNC)

bounds surface normals● apex angle of SNC α < 90º● Efficiently constructed

and updated with BVHs [Provot 1997]

●No self-intersection on projected contour( contour test )● Quadratic time complexity● Dual-Cone method reduces this overhead

SNC

α

16

Intuition of Dual-Cone Method

●Consider the curvature of projected contour

●Binormal: perpendicular to both surface normal and contour

●Binormal Cone (BNC) bounds binormals

●No self-intersection on contour axis angle of BNC β < 90º

●Dual-Cone: SNC and BNCContour with

self-intersection

Contour without self-intersection

β

β

17

Conservativeness of Dual-Cone

●Dual-Cone method does not provide culling for a whole surface, since it is too conservative

18

Dual-Cone Method with BVH

● Combine with BVH to provide practical culling

● Ignore virtual contour● virtual contour: caused by bounding volume split (---)● Can bring counter-example● Did not miss any collisions in our complex benchmarks

C

C C CC: No Self-Collision (culling)

19

Dual-Cone Method

●Dual-Cone● SNC: surface normal cone● BNC: binormal cone

●Contour test can be replacedwith a test that whether axis of SNC is inside BNC or not

C

C

20

Result of Dual-Cone Method

Contour Test

Miss Collisions ?

Culling Ratio

FPS

No Test Yes 49% 3.40

VT94 No 48% 2.54

Dual-Cone No 46% 3.24

● Dynamic topology model● About 100x performance improvement at fracturing events

prior method need pre-computations

● Fixed topology model

● Did not miss collisions● Comparable performance with “No Test”

Low culling overhead

21

Dual-Cone Method

●Pros● Low culling overhead

O(1) for each node [Provot 1997]● Efficiently constructed and updated

for fracturing models

●Cons● Approximate culling

22

Outline

● Background

● Dual-Cone Method

● BVH Update Method

● Comparison

● Conclusion

23

Selective Restructuring of BVHs

● As models deform, culling efficiency of their BVHs can be getting lower● should be restructured

● How to determine efficiency of BVH?● LM metric : Overlap volume of sibling nodes

[Larsson and Akenine-Möller 2006]

●Our cost metric measures expected number of intersection tests !

Deform Restructuring

24

Cost Estimation Metric (1/2)

● = expected # of intersection tests from node for self-collision detection

● Recurrence formula

● Replace with cost terms

● No self-collision at (Dual-Cone )

● Dual-Cone operator

A

nL nR

n

),()()()( RLRL nnInterCDnSelfCDnSelfCDnSelfCD

),()()()( RLRL nnCostInternTSnTSnTS

n 0)( nTS

not)or collision -self (no 1or 0)( nD

),()()()()()( RLRRLL nnCostInternTSnDnTSnDnTS

)(nTSn

25

Cost Estimation Metric (2/2)

● Cost estimation metric for inter-collision detection [Yoon and Manocha 2006]

● We approximate

● Finally we obtain

● Metric values can be computed in bottom-up BVH refitting process

)(nTI

),()()()()()( RLRRLL nnCostInternTSnDnTSnDnTS

)()(),( RLRL nTInTInnCostInter

)()()()()()()( RLRRLL nTInTInTSnDnTSnDnTS

26

Metric Validation

● Estimated # of tests vs Observed # of tests

● Linear Correlation : 0.71 ● for various models ( 0.28 ~ 0.76 , average 0.48 )

27

Selective Restructuring using Our Metric

nowv

recentvcompute25.1

recent

now

v

v

25.1recent

now

v

vrecentv

CD Compute deform

-restructure-update

28

Result of Selective Restructuring

● LM metric : [Larsson and Akenine-Möller 2006]

●Performance degradations at topological changes unstable

252K triangles, dynamic topology

29

Fast BVH Construction Method

● At a fracturing event, BVH for fractured part should be re-constructed● causes noticeable performance degradation

● Propose BVH construction method based on grid and hashing instead of typical NlogN methods

● Constructed hierarchy haslow culling efficiency, but requires less construction time● Overall performance improved

at fracturing events

30

Result of Fast BVH Construction

●Performance degradations at fracturing events are reduced

31

Comparison (Continuous-CD)

● 260x faster than T-CCD [Tang et al. 2008] at topology changes

● Our method shows stable performance

● Characteristics of benchmarks!

252K triangles, dynamic topology

32

Comparison (Discrete-CD)

● 20x faster than optimized spatial hashing [Teschner et al, 2003] (S-Hash)

● Stable performance

42~140K triangles, dynamic topology

33

Limitations

●Dual-Cone method combined with BVHs is an approximate method

●BVH selective restructuring method using our cost estimation metric does not guarantee to always improve the performance

● Finalize with positive

34

Conclusion

● Stable CD methods for fracturing models● Dual-cone culling method for self-collision

detection● BVH selective-restructuring method using

our cost estimation metric measuring estimated # of intersection tests

● Fast BVH construction method that reduces performance degradations at fracturing events

● 260x performance improvement at fracturing event over prior BVH based CD method

● 20x performance improvement over optimized spatial hashing

35

Fracturing Benchmarks

●Our fracturing benchmarks are at:http://sglab.kaist.ac.kr/models

●Our project page:http://sglab.kaist.ac.kr/FASTCD

36

Acknowledgments

●Members of Scalable Graphics Lab, KAIST

●Anonymous reviewers

● Funding agencies● MEST, NSFC, Spanish Dept. of

Science and Innovation, BK, KAIST, IITA, KRF, MSRA, ADD, MKE, KSEF

37

Thanks for your attention.

Any question or feedback?