Efficient Raytracing of Deforming Point-Sampled Surfaces

1. Mark Pauly Leonidas J. Guibas Bart Adams Philip Dutré Richard Keiser Markus Gross Efficient Raytracing of Deforming Point-Sampled Surfaces

2. Contributions • dynamic bounding sphere hierarchy • lazy updates • from deformation field only • various caching optimizations • handling of sharp features • Efficient algorithm for raytracing of deforming point-sampled surfaces

3. Related Work • Adamson & Alexa [SGP ‘03] • ray-surface intersection algorithm • James & Pai [SIG ‘04] • BD-tree • dynamic update principle • Wald & Seidel [PBG ‘05] • accelerated raytracing for static point clouds

4. Talk Overview • Part 1: Static Surfaces • surface representation • ray-surface intersection algorithm • bounding sphere hierarchy • extension: sharp edges & corners • Part 2: Deforming Surfaces • physics framework • surface deformation • dynamic bounding sphere update • caching optimizations

5. Talk Overview • Part 1: Static Surfaces • surface representation • ray-surface intersection algorithm • bounding sphere hierarchy • extension: sharp edges & corners • Part 2: Deforming Surfaces • physics framework • surface deformation • dynamic bounding sphere update • caching optimizations

6. Surface Representation • Surface defined by elliptical splats • position x • tangent axes u and v • normal n from uxv • (material properties) • Should be hole-free • splats should overlap sufficiently • but not too much!1 u v x 1 Wu & Kobbelt: Optimized Sub-Sampling of Point Sets for Surface Splatting, EG 2004

7. x1 x2 Ray-Surface Intersection • Intersect ray with surfel ellipse: point x1 • From x1 compute • weighted average normal n • weighted average position a  plane • Intersect plane: point x2 • Repeat until convergence

8. Bounding Sphere Hierarchy • To speed up ray-surface intersection test • Built top-down similar to QSplat

9. Bounding Sphere Hierarchy • To speed up ray-surface intersection test • Built top-down similar to QSplat

10. Bounding Sphere Hierarchy • To speed up ray-surface intersection test • Built top-down similar to QSplat

11. Bounding Sphere Hierarchy • To speed up ray-surface intersection test • Built top-down similar to QSplat

12. Bounding Sphere Hierarchy • Use bounding sphere hierarchy to efficiently locate ellipse intersection

13. Bounding Sphere Hierarchy • Use bounding sphere hierarchy to efficiently locate ellipse intersection

14. Bounding Sphere Hierarchy • Use bounding sphere hierarchy to efficiently locate ellipse intersection

15. Bounding Sphere Hierarchy • Use bounding sphere hierarchy to efficiently locate ellipse intersection

16. Bounding Sphere Hierarchy • Use bounding sphere hierarchy to efficiently locate ellipse intersection

17. boolean operations fracture animation Sharp Edges & Corners • Inherent smoothing in intersection algorithm • average normal, position, … • Sometimes sharp edges & corners wanted

18. S1 S1 x S2 S2 Sharp Edges & Corners • One solution: detect sharp features1 • But often: features known a priori (e.g. csg) • define feature by surface-surface clipping relations • S1 clips S2 and vice versa  x rejected 1 Fleishman et al.: Robust Moving Least-squares Fitting with Sharp Features, SIG 2005

19. boolean operations fracture animation Sharp Edges & Corners

20. Talk Overview • Part 1: Static Surfaces • surface representation • ray-surface intersection algorithm • bounding sphere hierarchy • extension: sharp edges & corners • Part 2: Deforming Surfaces • physics framework • surface deformation • dynamic bounding sphere update • caching optimizations

21. Surface Animation • Point-based approach for physically-based simulation1 • point-based volume (physics) • point-based surface (visualization) • Decoupling! • low-res physics (~100) • high-res surface (~100000) simulation nodes {pj} surfels {si} 1 Müller et al.: Point Based Animation of Elastic, Plastic and Melting Objects, SCA 2004

22. Surface Animation • Simulation nodes define a displacement field u x x+u displacement field u

23. gradient of displacement vector summation over neighboring nodes j displacement vector of node j smooth normalized weight function Surface Animation Deformation of surfels is computed from neighboring simulation nodes: simulation nodes {pj} surfels {si}

24. Dynamic Sphere Update • Key Idea: • sphere bounds surfels • deformation of surfels is defined by subset of simulation nodes • update sphere by looking at deformation of these nodes only Recall: ~100 nodes vs. ~100000 surfels!

25. Dynamic Sphere Update • Center update • similar to surfel update  linear in the number of simulation nodes

26. can be pre-computed once remain constant under deformation Dynamic Sphere Update • Radius update • radius defined by maximal distance between deformed surfels and sphere center • find R’’  R’ (see paper for details)  linear in the number of simulation nodes

27. Dynamic Sphere Update • Radius update • Observations • R’’  R even if object shrinks • less nodes is better • R’’ smaller if displacements smaller • rigidly transform sphere hierarchy before update to align as good as possible

28. rigid transform (rotation + translation) smaller displacements Optimal Rigid Transformation

29. surfel neighbors (for intersection algorithm) Caching Optimizations • Use static neighborhood information • neighbors of each surfel computed once • in undeformed reference system • no need for k-NN queries simulation node neighbors (for deformation)

30. Caching Optimizations • Remember per-ray sphere node intersections • test cached sphere node first in next frame • good upper bound on t-value • less sphere/surface intersection tests same sphere frame n frame n+1

31. Algorithm Summary • For each ray: • start from cached sphere node first • next, descend hierarchy from root • if node visited for first time: • update node’s center and radius • if ray hits leaf node: • update surfel and its neighbors • intersect ellipse • perform iterative intersection algorithm • trim if necessary

32. Elastic Balls 6k surfels, 88 simulation nodes (one ball, 40 balls total)  3.0x speedup

33. Cannon Ball Armadillo 170k surfels, 453 simulation nodes Time (sec)  2.1x speedup

34. Gymnastic Goblin 100k surfels, 502 simulation nodes  2.1x speedup

35. Bouncing CSG Heads 91k surfels, 253 simulation nodes (one head)  2.2x speedup

36. Discussion & Future Work • There is a trade-off: • fast lazy updates • suboptimal spheres •  speedup not guaranteed • Future work: • dynamic update vs. (local) rebuild • handle dynamic objects with changing topology • e.g. by fracturing

37. Thank you! • Acknowledgements • reviewers • NSF grants CARGO-0138456, ITR-0205671 • ARO grant DAAD19-03-1-033 • NIH Simbios Center grant 1091129-1-PABAE • F.W.O.-Vlaanderen • Contact information • Bart Adams barta@cs.kuleuven.ac.be • Richard Keiser keiser@inf.ethz.ch • Mark Pauly pauly@inf.ethz.ch • Leonidas J. Guibasguibas@cs.stanford.edu • Markus Grossgrossm@inf.ethz.ch • Phil Dutréphil@cs.kuleuven.ac.be

39. Tighter Sphere Fitting • If parent and child spheres already updated • Tighter bound might be possible: C C2 C1