Fast Collision Detection for Deformable Models using Representative-Triangles

Fast Collision Detection for Deformable Models using Representative-Triangles

Sean Curtis1, Rasmus Tamstorf 2, & Dinesh Manocha1

I3D 2008February 15, 2008

1 University of North Carolina at Chapel Hill 2 Walt Disney Animation Studios

Faster Collision Detection

• Seven layers of cloth and body with 50K triangles.

• 3.3X collision detection speed-up with Representative Triangles.

Previous Work

• General surveys– Ericson 2004; Lin and Manocha 2003;

Teschner et al. 2005.

Previous Work

• Triangle-pair Culling– BVH - BV types

• Sphere, Swept-sphere, AABB, OBB, k-DOP, hybrid, etc.

• Bradshaw and O’Sullivan. 2004; Gottschalk et al. 1996; Hubbard 1993; Klosowski et al. 1998; van den Bergen 1997; etc.

Previous Work

• Triangle-pair Culling– BVH Management

• Restructuring, rebuilding, lazy construction, etc.

• Larsson and Akenine-Möller 2006; Otaduy et al. 2007, Yoon et al. 2007; Zachmann and Weller 2006.

Previous Work

• Triangle-pair Culling– BVH Management

• Restructuring, rebuilding, lazy construction, etc.

• Larsson and Akenine-Möller 2006; Otaduy et al. 2007, Yoon et al. 2007; Zachmann and Weller 2006.

– Specialized culling techniques• Normal cones, GPU-based culling, etc.

• Govindaraju et al. 2005; Provot 1997; Sud et al. 2006.

Previous Work

• Feature-based Collision Detection– Voronoi regions (convex and non-convex)

• Ehmann and Lin 2001; Lin and Canny 1991; Mirtich 1998.

Previous Work

• Feature-based Collision Detection– Voronoi regions (convex and non-convex)

• Ehmann and Lin 2001; Lin and Canny 1991; Mirtich 1998.

– Feature BVs• Hutter and Fuhrmann 2007.

Previous Work

• Continuous Collision Detection– Reduction of elementary tests– Govindaraju et al. 2005; Hutter and Fuhrmann

2007; Tang et al. 2007; Wong 2005, etc.

Continuous Collision Detection (CCD)

• Time of collision.

t = i+1t = i



t = i+1t = i+Δtt = i



• Test between features (vertices, edges and faces.)

Edge-EdgeVertex-Face

Triangles vs. Features

• Triangles used for culling.



• CD operates on features.



• CD operates on features.

• This leads to:– Less efficient culling– Elementary test duplication

Culling Efficiency

• Features usually occupy significantly less space than their corresponding triangles.

Culling Efficiency

• Features usually occupy significantly less space than their corresponding triangles.

• Based on triangle BVs:– 15 elementary tests

Culling Efficiency

• Features can occupy significantly less space than their corresponding triangles.


• Based on feature BVs:– 1 EE test

Culling Efficiency



• Based on feature BVs:– 1 EE test

Culling Efficiency



• Based on feature BVs:– 2 EE tests

Culling Efficiency




Culling Efficiency




Culling Efficiency




Culling Efficiency




Culling Efficiency




Culling Efficiency




Culling Efficiency



• Based on feature BVs:– 2 EE tests– 0 VF tests

Culling Efficiency




Culling Efficiency




Culling Efficiency



• Based on feature BVs:– 2 EE tests– 1 VF test

Culling Efficiency




Culling Efficiency




Elementary Test Duplication

• The intersecting vertex is shared by six triangles.

Elementary Test Duplication

• The intersecting vertex is shared by six triangles.

• The VF test could be spawned by six different triangle pairs.

Representative Triangles (R-Tris)

• R-Tris definition

• R-Tris usage

• R-Tris properties

• Computing R-Tris (assignment)

R-Tri Definition

• An augmented triangle that “represents” some subset of its features and their corresponding feature BVs.

R-Tri DefinitionFeature Assignment

• The pattern in which each feature is assigned to an R-Tri is an assignment scheme.

R-Tri DefinitionFeature Assignment

• The pattern in which each feature is assigned to an R-Tri is an assignment scheme.

• Assignment scheme– Not unique.– Every feature is assigned to one and only one

triangle, incident to the feature.

R-Tri Usage

• Given a pair of R-Tris that are potentially colliding:

– Find corresponding feature pairs.

R-Tri Usage



– Test feature BVs.

R-Tri Usage




R-Tri Usage




R-Tri Usage




R-Tri Usage



– Test feature BVs.– Spawn elementary tests.

R-Tri Usage


– Find corresponding feature pairs.– Test feature BVs.– Spawn elementary tests.

• Improves culling and eliminates duplicates.

R-Tris Properties

• General– Compatible with any triangle-pair culling

algorithm (including grids, BVHs, sweep & prune, GPU occlusion queries, etc.)

R-Tris Properties

• Complete– R-Tris will find all collisions, guaranteed.

R-Tris Properties

• Compact– R-Tris need no additional memory. (However,

O(|E|) data can be cached to potentially boost performance.)

R-Tris Properties

• Connectivity-based– Representation is a function of topology. For

meshes which only undergo deformation, assignment is a pre-processing step.

Computing R-Tris Assignment Schema

• How are features assigned to R-Tris?

• Does it matter?

• How many elementary tests are performed per contact?

Assignment Schema

• Optimal assignment– One elementary test per contact.

Assignment Schema

• Optimal assignment– One elementary test per contact.– Dependent on triangle-pair culling efficiency.

Assignment Schema

• Optimal assignment– One elementary test per contact.– Dependent on triangle-pair culling efficiency.– Assignment schema offer limited freedom.

Assignment Schema

• Example

Assignment Schema

• Example • Tests– 2 VF, 0 EE

• Total– 2 VF, 0 EE

Assignment Schema



Assignment Schema



Assignment Schema



Assignment Schema



Assignment Schema



Assignment Schema

• Example

Assignment Schema



Assignment Schema



Assignment Schema



Assignment Schema



Assignment Schema



Assignment Schema



Global Optimality

• A single assignment scheme which provides optimal performance for all cases.

Global Optimality


• Unfeasible in general

Global Optimality


• Unfeasible in general– No a priori knowledge of

deformations.

Global Optimality


• Unfeasible in general– No a priori knowledge of

deformations.– Representation is localized.

• The probability that neighboring triangles are included by the triangle-pair culling algorithm are high.

Global Assignment Schema

• Maximal Scheme [Wong and Baciu 2005]

• Total Tests– 3 VF

Empty Tri


• Maximal Scheme [Wong and Baciu 2005]

• Total Tests– 9 VF– 27 EE

• Average– 19.5 tests

Full Tri


• Uniform Scheme

• Total Tests– 9 VF

– 9 EE

V-E Tri


• Uniform Scheme• Total Tests

– 9 VF– 9 EE

• Average– 18 tests

E-E Tri


• Efficacy of a scheme depends on:– Actual mesh deformation, and– Triangle-pair culling efficiency.


• Efficacy of a scheme depends on:– Actual mesh deformation, and– Triangle-pair culling efficiency.

• The assignment scheme doesn’t really matter.


• Simple greedy scheme– Visit each triangle

• For each incident feature that hasn’t already been assigned, assign it to this triangle.


• Simple greedy scheme– Visit each triangle

• For each incident feature that hasn’t already been assigned, assign it to this triangle

• Very simple.

• Very fast.

BenchmarksFlamenco Dancer

Tris: 50 K

Verts: 26 K

Edges: 75 K

Frames: 352

Princess

Tris: 92 K

Verts: 47 K

Edges: 139 K

Frames: 1045

N-Body Balls

Tris: 34 K

Verts: 18 K

Edges: 51 K

Frames: 375

Cloth-Ball

Tris: 40 K

Verts: 20 K

Edges: 60 K

Frames: 465

Results

• System Characteristics– Binary BVH.– AABB BVs.– For self-collision, adjacent features are never

tested.

Results

• System Characteristics– Binary BVH.– AABB BVs.– For self-collision, adjacent features are never

tested.

• Hardware– Intel Xeon 3 GHz with 3 GBytes RAM– 32-bit Windows XP

Results

• Comparison Algorithms– R-Tri (RTRI)

* In the paper DB is ADJ and MARK is NO-DUPL.

Results

• Comparison Algorithms– R-Tri (RTRI)– Database (DB)*

• Run-time database to eliminate duplicate queries.

• Feature BVs for improved culling.


Results




– Mark-up (MARK)*

• Uses representation without feature BVs.


Results




– Mark-up (MARK)*

• Uses representation without feature BVs.

– Baseline (BASIC)• No duplicate culling and no feature BVs.


ResultsAverage Number of Elementary Tests (× 106) /

Average Frame Time for CCD (sec)

Speed-up of R-TRI

R-TRI DB MARK BASIC R-TRI DB MARK BASIC

0.23 /

0.09

0.23 /

0.13

0.74 /

0.13

2.0 /

0.461.0 X 1.5 X 1.5 X 5.3 X

0.27 /

0.23

0.27 /

0.39

1.7 /

0.36

7.6 /

1.151.0 X 1.7 X 1.6 X 5.1 X

0.45 /

0.15

0.45 /

0.43

1.2 /

0.22

5.5 /

0.751.0 X 2.9 X 1.4 X 5.0 X

0.46 /

0.19

0.46 /

0.63

1.5 /

0.28

6.8 /

0.921.0 X 3.3 X 1.5 X 4.9 X

Limitations

• Subservient to the choice of BV-type – even with feature BVs (AABB) false positives > 90%.

Limitations


• Benefit decreases as the meshes become triangle soups – every triangle represents all of its own features.

Limitations


• Benefit decreases as the meshes become triangle soups – every triangle represents all of its own features.

• It may take a performance hit in memory-strapped systems.

Conclusions

• A simple mechanism for accelerating collision detection.

Conclusions

• A simple mechanism for accelerating collision detection.– Eliminates duplicate queries without expensive

run-time data structures.

Conclusions


run-time data structures.– Easy to implement.

Conclusions


run-time data structures.– Easy to implement.– Complementary to most existing CD systems.

Conclusions


run-time data structures.– Easy to implement.– Complementary to most existing CD systems.– Orthogonal to culling algorithm and BV type.

Acknowledgments

• ARO

• NSF

• DARPA/RDECOM

• Intel

• Walt Disney Animation Studios

Questions

References

• BRADSHAW, G., AND O’SULLIVAN, C. 2004. Adaptive medial-axis approximation for sphere-tree construction. ACM Trans. on Graphics 23, 1.

• EHMANN, S., AND LIN, M. C. 2001. Accurate and fast proximity queries between polyhedra using convex surface decomposition. Computer Graphics Forum (Proc. of Eurographics’2001) 20, 3, 500–510.

• ERICSON, C. 2004. Real-Time Collision Detection. Morgan Kaufmann.

• GOTTSCHALK, S., LIN, M., AND MANOCHA, D. 1996. OBBTree: A hierarchical structure for rapid interference detection. Proc. of ACM Siggraph’96, 171–180.

References

• GOVINDARAJU, N., KNOTT, D., JAIN, N., KABAL, I., TAMSTORF, R., GAYLE, R., LIN, M., AND MANOCHA, D. 2005. Collision detection between deformable models using chromatic decomposition. ACM Trans. on Graphics (Proc. of ACM SIGGRAPH) 24, 3, 991–999.

• HUBBARD, P. M. 1993. Interactive collision detection. In Proceedings of IEEE Symposium on Research Frontiers in Virtual Reality.

• HUTTER, M., AND FUHRMANN, A. 2007. Optimized continuous collision detection for deformable triangle meshes. In Proc. WSCG ’07, 25–32.

• KLOSOWSKI, J., HELD, M., MITCHELL, J., SOWIZRAL, H., AND ZIKAN, K. 1998. Efficient collision detection using bounding volume hierarchies of k-dops. IEEE Trans. on Visualization and Computer Graphics 4, 1, 21–37.

References

• LARSSON, T., AND AKENINE-MÖLLER, T. 2006. A dynamic bounding volume hierarchy for generalized collision detection. Computers and Graphics 30, 3, 451–460.

• LIN, M., AND CANNY, J. F. 1991. Efficient algorithms for incremental distance computation. In IEEE Conference on Robotics and Automation, 1008–1014.

• LIN, M., AND MANOCHA, D. 2003. Collision and Proximity Queries. In Handbook of Discrete and Computational Geometry: Collision detection

• MIRTICH, B. 1998. V-Clip: Fast and robust polyhedral collision detection. ACM Transactions on Graphics 17, 3 (July), 177–208.

References

• MOLLER, T. 1997. A fast triangle-triangle intersection test. Journal of Graphics Tools 2, 2.

• OTADUY, M., CHASSOT, O., STEINEMANN, D., AND GROSS, M. 2007. Balanced hierarchies for collision detection between fracturing objects. In IEEE Virtual Reality.

• PROVOT, X. 1997. Collision and self-collision handling in cloth model dedicated to design garment. Graphics Interface, 177–189.

• TANG, M., YOON, S., CURTIS, S., AND MANOCHA, D. 2007. Interactive continuous collision detection between deformable models using connectivity-based culling. UNC Chapel Hill, Technical Report.

References

• TESCHNER, M., KIMMERLE, S., HEIDELBERGER, B., ZACHMANN, G., RAGHUPATHI, L., FUHRMANN, A., CANI, M.- P., FAURE, F., MAGNENAT-THALMANN, N., STRASSER, W., AND VOLINO, P. 2005. Collision detection for deformable objects. Computer Graphics Forum 19, 1, 61–81.

• TROPP, O., TAL, A., SHIMSHONI, I. 2006. A fast triangle to triangle intersection test for collision detection. Computer Animation and Virtual Worlds 17, 5, 527–535.

• VAN DEN BERGEN, G. 1997. Efficient collision detection of complex deformable models using AABB trees. Journal of Graphics Tools 2, 4, 1–14.

References

• WONG, W. S.-K., AND BACIU, G. 2006. A randomized marking scheme for continuous collision detection in simulation of deformable surfaces. Proc. of ACM VRCIA.

• YOON, S., CURTIS, S., AND MANOCHA, D. 2007. Ray tracing dynamic scenes using selective restructuring. Proc. of Eurographics Symposium on Rendering.

• ZACHMANN, G., AND WELLER, R. 2006. Kinetic bounding volume hierarchies for deforming objects. In ACM Int’l Conf. on Virtual Reality Continuum and its Applications.

Feature-based Hierarchies

• Memory– There are 2 * N nodes in a BVH with N nodes.– Typically, |E| + |V| = 2 * F. – There are 3 * F total leaves yielding 6 * F total

nodes. – In a triangle soup, |E| + |V| = 6 * F giving 14 *

F total nodes.

Representative Triangles The Strengths

• Preliminary results – VF culling:

Benchmark Total non-adjacent

pairs

Implied VF tests

VF_BV Overlaps

VF_BV Cull rate

V-Line Intersections

V-Line Cull rate

balls 4.7 x 107 2.82 x 108 7.81 x 107 72.3% 6.23 x 107 77.9%

cloth-ball 9.98 x 107 5.99 x 108 1.36 x 108 77.4% 7.22 x 107 87.9%

princess 2.33 x 108 1.4 x 109 7.12 x 108 49.1% 4.78 x 108 65.8%

dragon-bunny

2.66 x 108 1.6 x 109 1.04 x 109 34.9% 7.49 x 108 53.1%

Representative Triangles The Strengths

• Preliminary results – EE culling:

Benchmark Total non-adjacent

pairs

Implied EE tests

EE_BV Overlaps

EE_BV Cull rate

balls 4.7 x 107 4.23 x 108 1.78 x 108 58.0%

cloth-ball 9.98 x 107 8.98 x 108 3.3 x 108 63.2%

princess 2.33 x 108 2.1 x 109 1.33 x 109 36.7%

dragon-bunny

2.66 x 108 2.4 x 109 1.8 x 109 24.9%

Last Thoughts

• Zero additional memory– Swept vertices need no BV.– Edge BVs can be computed on the fly.– Assignment encoded in triangle ID.

• Adaptive reassignment– Might be possible to adaptively change

assignments to accommodate actual collisions.– Move non-colliding feature assignments to

incident tris not involved in collisions.

Documents

Fast Collision Detection for Deformable Models using Representative-Triangles