NCS 2009: Workshop on Image Processing, Computer Graphics, and Multimedia Technologies(ICM) Adaptive Continuous Collision Detection for Cloth Models using a Skipping Frame Session 黃 世強 ( Sai-Keung Wong ) Department of Computer Science National Chiao Tung University Email: cswingo@cs.nctu.edu.tw Paper ID: 16

Contents Introduction Background The pipeline of continuous collision detection Self-collision detection Analysis and discussion Experiments and results Conclusions

Introduction Continuous collision detection? - Perform linear (or higher order) interpolation for two discrete frames - Compute contact time of primitives, such as triangles - Triangular meshes: linear interpolation - solving cubic equations - computing shortest distances - six point-triangle and nine edge-edge pairs Frame 1 Frame 2

Introduction Applications: Deformable objects Cloth simulation A problem: A large set of potentially colliding pairs Slow performance An observation: Local coherence A large portion of colliding pairs remains the same

Introduction: Local coherence

Introduction BVH traversal contributes a significant amount of time Elementary test processing BVH traversal BVH update

Contributions A novel adaptive pipeline for continuous collision detection: BVH update BVH traversal A skipping frame session Elementary tests A partial traversal scheme Handling triangles with large movement Robustness: keep track of colliding pairs

Background: Cloth simulation D.E. Baraff and A. Witkin, “Large steps in cloth simulation”, SIGGRAPH, 1998. R. Bridson, R. Fedkiw, and J. Anderson, “Robust treatment of collisions, contact and friction for cloth simulation”, ACM ToG 2002. K.J. Choi and H.S. Ko, “Stable but responsive cloth”, SIGGRAPH, 2004 A. Selle, J. Su, G. Irving, and R. Fedkiw, “Robust high-resolution cloth using parallelism history-based collisions and accurate friction”, TVCG 2008. P. Volino and N. Magnenat-Thalmann, “Efficient self-collision detection on smoothly discretised surface and animation using geometrical shape regularity”, Computer graphics forum, 1994.

Background: Continuous collision detection M. Hutter and Fuhrmann, “Optimized continuous collision detection for deformable triangle meshes”, WSCG, 2007. T. Larsson and T. Akenine-Moller, “Efficient collision detection deformed by morphing”, Visual computer, 2003. M.Tang, S.E. Yoon and D. Manocha, “Adjacency-based culling for continuous collision detection ”, Visual Computer, 2008. M.Tang, S. Curtis, S.E. Yoon and D. Manocha, “ICCD: Interactive continuous collision detection between deformable models using connectivity-based culling”, TVCG, 2009. S.K. Wong and G. Baciu, “Dynamic interaction between deformable surfaces and nonsmooth objects”, TVCG, 2005. S.K. Wong and G. Baciu, “A randomized marking scheme for continuous collision detection in simulation of deformable surfaces”, ACM International Conference on Virtual Reality Continuum and Its Applications, 2006.

The Pipeline of CCD Preprocessing stage Runtime stage Construction of bounding volume hierarchies (BVHs) The primitive assignment Runtime stage BVH update with inflation, refitting each node BVH traversal, collecting potentially colliding pairs Adaptively apply a skipping frame session Front-end and back-end filtering stages

Preprocessing stage Construction of bounding volume hierarchies (BVHs) Build a hierarchy structure to bound each object

Preprocessing stage Primitive assignment q0 eB1 (a) (b) Assign each triangle to itself Assign each edge and each vertex to one of its incident triangles eA0 eB0 q0 Vertex assignment A B Edge assignment eB1 (a) (b)

Runtime stage: BVH update Purpose: refitting each node with inflation Estimated movement distance d(p) = ( a v (p) + b v ) D t+ g l Larger bounding volume

Runtime stage: BVH traversal Purpose: Collect potentially colliding pairs Bounding volumes overlap Problems: A large number of such pairs Too far away to collide within the current interval Further treatment A potentially colliding pair

Runtime stage: Front-end and back-end filtering stages Front-end: eliminate redundant triangle pairs Check estimated shortest distance de i (T0, T1) <= dei+1(T0) + dei+1(T1) + d dei+1(T0) Back-end: Perform continuous collision detection Solve coplanar times for each primitive pair Compute shortest distances for verification

Runtime stage: Skipping frame session Purpose: Adaptively apply a skipping frame session Advantages: Local movement of a triangle Lying inside its inflated bounding volume > no need BVH update > no need traversal

Handling dangling triangles Triangles with large movement Passing through their bounding volumes Two solutions: 1. Traversal individually 2. Partial traversal scheme Large movement

Self-collision detection Low curvatured surface partitioning Compute continuous normal cone for each triangle Perform bottom-up merging to obtain low curvature surfaces Collision detection between low curvatured surfaces

Analysis Consider a small box b lying inside another box B Free movement distance: d = d(b, B) Time step = D t Relative speed = v Number of skipping frames = d / ( v D t )

Experiments and Results Intel (R) Core (TM2) Quadcore CPU machine with 2.4GHz of 2GB memory One thread for computation Comparison with two methods and others: NoDup : S.K. Wong and G. Baciu, “A randomized marking scheme for continuous collision detection in simulation of deformable surfaces”, ACM International Conference on Virtual Reality Continuum and Its Applications, 2006. R-RTI : S. Curtis, R. Tamstorf, and D. Manocha, “Fast collision detection for deformable models using representative-triangles”, Proceedings of the 2008 symposium on Interactive 3D graphics and games, 2008

Experiment Set One: < 100k triangles

Average Collision Detection Time Per Time Step ( sec ) Experiment Set One: Average Collision Detection Time Per Time Step ( sec ) (including self-collision detection) NoDup R-TRI nSwD SwD ( % R-TRI ) Ani. One Spinning ball 0.23 0.18 0.15 0.13 ( 72%) Ani. Two Ball-cloth 0.12 0.10 0.082 0.074 ( 74%) Ani. Three Four cones 0.31 0.27 0.16 ( 59%) Ani. Four Garment 0.092 0.076 0.062 0.052 (68%)

Experiment Set Two: > 300k triangles

Experiment Set Two Labels: a x f a x : length of skipping frame session

Experiments and Results Experiment Set One: Model Complexities Rigid Objects ( #Tri ) Cloth Models ( #Tri ) Ani. One 5.2 k 97 k Ani. Two 10 k 45 k Ani. Three 0.5 k Ani. Four 34 k 20 k Experiment Set Two: Model Complexities 11 k 320 k 7 k 500 k 1 k 502 k 40 k

Comparison: Traditional approach vs our approach Traditonal Our Bounding volume size smaller larger BVH update yes sometimes BVH traversal Number of potentially colliding pairs fewer Memory storage less higher Robustness ok better Speed faster

Conclusions & future work Propose a novel adaptive framework for continuous collision detection using a skipping frame session Fast performance High memory requirement but increased robustness Apply to multilayered garments Reduce storage size

Thank you. Q & A.