1. Ray Tracing Animated Scenes using Motion Decomposition Johannes Günther, Heiko Friedrich, Ingo Wald, Hans-Peter Seidel, and Philipp Slusallek

2. September 7, 2006Eurographics, Vienna2 Introduction  Nowadays realtime ray tracing on single PC –Packet tracing [Wald PhD04, Reshetov SIG05 ] –Clever acceleration structures (SAH [McDonald GI89 ] )  Best known method: kd-trees [Havran PhD01 ]  BUT, so far only static scenes –Walkthrough –Rigid-body animations [Wald PVG03 ]  Reason: high kd-tree build time  preprocessing

3. September 7, 2006Eurographics, Vienna3 Related Work – Dynamic Scenes Three approaches:  Alternative acceleration structures –BVHs [Wald TOG06, Lauterbach RT06] –Grids [Wald SIG06] –Hybrid data structures [Woop GH06, Havran RT06, Wächter EGSR06]  Faster construction of kd-trees –[Popov RT06, Hunt RT06]  Avoid the (re)construction of kd-trees

4. September 7, 2006Eurographics, Vienna4 Avoid Updating the KD-Tree  IDEA: “make dynamic scenes static”  Assumptions: –Deformation of a base mesh (constant connectivity) –All frames of animation known in advance –Local coherent motion

5. September 7, 2006Eurographics, Vienna5 Method Overview  Motion decomposition –Affine transformations + residual motion  Fuzzy kd-tree –Handles residual motion  Clustering –Exploit local coherent motion

6. September 7, 2006Eurographics, Vienna6 Motion Decomposition  Dynamic scene: ball thrown onto floor

7. September 7, 2006Eurographics, Vienna7 Motion Decomposition  Affine transformations –Approximate deformations –Include shearing (3 rd frame)

8. September 7, 2006Eurographics, Vienna8 Motion Decomposition residual motion

9. September 7, 2006Eurographics, Vienna9 Motion Decomposition fuzzy boxes

10. September 7, 2006Eurographics, Vienna10 Fuzzy KD-Tree  Handles residual motion  KD-Tree over the fuzzy boxes of triangles  Valid over complete animation

11. September 7, 2006Eurographics, Vienna11 Illustration transformation

12. September 7, 2006Eurographics, Vienna12 Illustration affine transformations onlyadding residual motion

13. September 7, 2006Eurographics, Vienna13 Details: Clustering  Efficient ray tracing: –Small fuzzy boxes  Minimize residual motion  Cluster coherently moving triangles  Many clustering algorithms –But mostly for static meshes –Not designed for ray tracing  Develop new one –based on Lloyd relaxation

14. September 7, 2006Eurographics, Vienna14 Clustering Algorithm  Start with one cluster (all triangles)  Lloyd relaxation: –Find transformations for clusters  Linear least squares problem –Recluster triangles –Until convergence  Insert new cluster –Seeded by triangle with highest residual motion  Until improvement below threshold

15. September 7, 2006Eurographics, Vienna15 Ray Tracing: Two-level Approach  Build top-level kd-tree over current cluster bounds  Transform rays into local coordinate system –Inverse affine transformation of cluster from motion decomposition  Traverse fuzzy kd-tree of cluster

16. September 7, 2006Eurographics, Vienna16 Results

17. September 7, 2006Eurographics, Vienna17 Video

18. September 7, 2006Eurographics, Vienna18 Ray Tracing Performance Single CPU (Opteron 2.8 GHz) 1024×1024 px Incl. shading

19. September 7, 2006Eurographics, Vienna19 More Complex Shading  With texturing, lighting, shadows: 2.2 fps (static kd-tree: 4.1 fps)

20. September 7, 2006Eurographics, Vienna20 Comparison to Static KD-Tree  Baseline: separate static kd-tree per frame  Traversal steps –Factor 1.5 - 2  Intersections –Factor 1.2 – 2, Cow 4, Chicken 6  Average fps –Factor 1.2 – 2.6, alone two-level kd-tree costs ca. 30%  Memory –only one fuzzy kd-tree (+ transformation matrices) –vs. #frames static kd-trees

21. September 7, 2006Eurographics, Vienna21 Clustering Process Residual Motion

22. September 7, 2006Eurographics, Vienna22  Clustering also in time domain –Better adaptation to separated animation sequences –E.g. with the chicken: walking, being scared, flying  Handle interpolation between key frames –By interpolation of the computed transformations?  Interaction with dynamic scenes –So far all poses known in advance  Harnessing more information from application –Skinning operators, skeleton, joint angles with limits –See also [TVC/PG06] Future Work

23. September 7, 2006Eurographics, Vienna23 Summary  Animated scenes at interactive frame rates –Motion decomposition and fuzzy kd-trees  Automatic clustering into coherently moving sub-meshes  Integrates nicely into existing ray tracing systems

24. September 7, 2006Eurographics, Vienna24 Questions? Thank You

25. September 7, 2006Eurographics, Vienna25

26. September 7, 2006Eurographics, Vienna26  Transformation X of vertex v  Solve linear least squares problem Finding “Good” Transformations

27. September 7, 2006Eurographics, Vienna27 Clustering Process Residual MotionSurface Area