fastcd: fracturing-aware stable collision detection jae-pil heo 1, joon-kyung seong 1, duksu kim 1,...
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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
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Collision Detection (CD)
●Collision detection is an essential part of various applications● Physically-based simulation● Games● Robotics
cloth simulation Quake 4 KAIST Hubo
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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
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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
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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
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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
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Benchmarks
Cloth-Ball Exploding-Dragon
Breaking-Walls
video
# of topology changes
0fixed topology
4dynamic topology
8dynamic topology
complexity
92K 252K -> 252K 42K -> 140K
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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
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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
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Outline
● Background
● Dual-Cone Method
● BVH Update Method
● Comparison
● Conclusion
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Outline
● Background
● Dual-Cone Method
● BVH Update Method
● Comparison
● Conclusion
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Bounding Volume Hierarchies (BVHs)
●Organize bounding volumes as a tree
● Leaf nodes have triangles
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BVH-based CD
A
B C
X
Y Z
Collision test pair queue
(A,X)
●BVH traversal
A X
Dequeue
BV overlap test
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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?
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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
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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
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Conservativeness of Dual-Cone
●Dual-Cone method does not provide culling for a whole surface, since it is too conservative
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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)
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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
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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
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Dual-Cone Method
●Pros● Low culling overhead
O(1) for each node [Provot 1997]● Efficiently constructed and updated
for fracturing models
●Cons● Approximate culling
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Outline
● Background
● Dual-Cone Method
● BVH Update Method
● Comparison
● Conclusion
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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
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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
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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
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Metric Validation
● Estimated # of tests vs Observed # of tests
● Linear Correlation : 0.71 ● for various models ( 0.28 ~ 0.76 , average 0.48 )
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Selective Restructuring using Our Metric
nowv
recentvcompute25.1
recent
now
v
v
25.1recent
now
v
vrecentv
CD Compute deform
-restructure-update
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Result of Selective Restructuring
● LM metric : [Larsson and Akenine-Möller 2006]
●Performance degradations at topological changes unstable
252K triangles, dynamic topology
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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
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Result of Fast BVH Construction
●Performance degradations at fracturing events are reduced
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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
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Comparison (Discrete-CD)
● 20x faster than optimized spatial hashing [Teschner et al, 2003] (S-Hash)
● Stable performance
42~140K triangles, dynamic topology
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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
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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
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Fracturing Benchmarks
●Our fracturing benchmarks are at:http://sglab.kaist.ac.kr/models
●Our project page:http://sglab.kaist.ac.kr/FASTCD
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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
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Thanks for your attention.
Any question or feedback?