1. Afrigraph 2004 Interactive Ray-Tracing of Free-Form Surfaces Carsten Benthin Ingo Wald Philipp Slusallek Computer Graphics Lab Saarland University, Germany http://graphics.cs.uni-sb.de

2. Motivation Why ray-tracing of free-form surfaces ? Tessellating surfaces has disadvantages: Scene size complexity Accuracy Time complexity (preprocessing step) Workflow (Animation Tools, CAD) Want directly ray-trace Splines, NURBS, Subdivision Surfaces,...

3. Previous Approaches Splines and NURBS Bezier Clipping –Nishita, Campagna, Wang Newton Iteration –Wang, Martin Subdivision Surfaces Adaptive refinement –Kobbelt, Mueller  Too slow for interactive use

4. Interactive Ray-Tracing (IRT) OpenRT Wald, Benthin, Dietrich Interactive performance even on a commodity PC Limited to triangles Utah RTRT Shirley, Parker Supports even spline surfaces Need large parallel supercomputer for interactive performance

5. Outline Analysis of existing approaches (ray/primitive test) Our simple and generic approach Implementation: Bicubic Bezier, Loop Subdivision Complex Scenes Results Conclusion & Future Work

6. Analysis I Performance „killers“ of current CPU architectures Memory latency  cache misses Long pipelines  branch mispredictions Complex control flow  low instruction level parallelism Code Optimization Ensure data locality & memory access pattern Simple code control flow (streamline) Data level parallelism (SIMD), e.g. Intel‘s SSE Instructions

7. Analysis II Analytical/Iterative algorithms Algorithmic complexity Numerical problems Handling many special cases Complex control flow Adaptive refinement algorithms Test for required refinement is costly Crack prevention  additional book-keeping data structures Complex control flow

8. Our Approach I Simple and generic „divide and conquer“ Fixed number of refinement steps

9. Our Approach II Few core operations –Refinement –Pruning –Final Intersection No refinement test No crack handling Constant memory costs

10. 4x4 control points, suited for 4-way-SIMD Optimized data layout for maximize SIMD performance –SOA instead AOS Pruning: Ray as intersection of two planes (half-space criteria) Refinement: deCasteljau algorithm (alternate direction) Final Intersection: Triangulation + Ray/Triangle-Tests Implementation for Bicubic Bezier Surfaces

11. Implementation for Loop Subdivision Surfaces AOS data layout Regular/Irregular Triangles –One refinement step  max one irregular vertex Pruning: Two planes critera (1-neighborhood) Refinement: Loop subdivision  four new triangles Final Intersection: Triangle test

12. Core Performance ( Cycles) Bicubic BezierLoop Subdivision Pruning86172/222 Refinement168/244405/600 Final Intersection 294-366169 Subdivision core operations more complex  higher cost

13. Free-Form Objects Reduce tested primitives/ray Use spatial acceleration structure (KD-Tree) –Construct KD-Tree out of AABBs –Use fast traversal from IRT Surface Area Heuristics  better KD-Tree Mailboxing Reduction: up to 92% (78%) Dynamic Objects Less primtives  KD-Tree reconstruction every frame

14. Results (Bezier Surfaces) P4 CPU 2.2 GHz, 640x480, #tris = #primitives * 2^steps * 18

15. Results (Subdivision Surfaces) P4 CPU 2.2 GHz, 640x480, 640x480, #tris = #primitives * 4^steps

16. Video

17. Conclusion Pros Simple and robust approach Interactive performance on single CPU Memory efficient, compute bounded ray/primitive test Support for trimming curves Half the speed compared to triangle approach Can easily integrated into existing ray-tracers (OpenRT) Cons Over-refinement Subdivision Surface implementation not optimal

18. Current & Future Work Key to performance: tracing ray bundles (e.g. 16 rays) –Amortize core operation costs over rays Different variants for final intersection step –Plücker triangle test –Bilinear Patch Very fast KD-Tree reconstruction code –Multithreading Higher order bezier patches or even direct NURBS support Improve implementation for Subdivision Surfaces

19. Questions ?