Face Cluster Radiosity

1. Face Cluster Radiosity Eurographics Workshop on Rendering, 1999 Andrew Willmott Paul Heckbert Michael Garland Carnegie Mellon University

2. The Claim • The Domain • Radiosity on scenes with detailed models • By using face cluster hierarchies we can • Get sub-linear or constant complexity • Better approximate detailed model surfaces

3. State of the Art • Hierarchical Radiosity with Volume Clustering • Constructs a complete scene hierarchy • Adds volume clusters above input polygons (preprocessing) • Subdivides below input polygons (during solution) • Algorithm is O(k logk + n) • k is the number of input polygons • n is the number of elements used by the solution

4. Problems • Slow for complex scenes (k >> n) • Must push irradiance down to leaves when gathering, pull radiosity up when shooting • All input polygons must be touched on each iteration • Approximation • Volume clusters approximate a cloud of unconnected polygons • Can do better for connected, largely smooth surfaces

5. Background • Experimenting with large scanned models • Large enough to make klogk a problem • Observation • Most polygons are for high resolution detail • Don’t affect radiosity computations much • and with Multiresolution Models • Allow you to adjust the resolution of the model at different places on the model

6. Intuition Instead of running radiosity on detailed model Run radiosity on simplified model Apply results to original model

7. A Better Solution • Combine simplification & radiosity algorithms • Use multiresolution hierarchies of the models directly • Adjust resolution on the fly to match that needed by the radiosity algorithm

8. Refinement in the Hierarchy Root: entire scene Input polygons Refinements High Resolution

9. Simplification Root Simplifications Input polygons High Resolution

10. Advantages • No manual selection of simplification level • Don’t access each of the k input polygons during each iteration • Don’t store radiosity for each input polygon • Multiresolution models are precalculated • Once for each new model acquired • Amortized over many scenes and renders

11. Multiresolution Models • Initially used edge-collapse models directly • These contain vertex hierarchies • Switched to using dual of vertex hierarchy algorithm: face cluster hierarchies • It’s easier to deal with face hierarchies

12. Face Clusters • Group faces rather than vertices • Don’t change geometry of the model

13. Hierarchical Radiosity Used refinements Input polygons Leaf elements Unused refinements

14. Add Volume Clustering Volume clusters Used refinements Input polygons Leaf elements Unused refinements

15. Add Face Clustering Volume clusters Face clusters Used refinements Unusedface clusters Input polygons Leaf elements Unused refinements

16. Face Cluster Hierarchies • Iteratively merge face clusters • Initial clusters each contain a single polygon • Create links between two child clusters and their union • Repeat until only root cluster left

17. A Face Cluster • An approximately planar region on the mesh • Container for a set of connected faces • Oriented bounding box • Aggregate area-weighted normal • Pointers to the two child clusters that partition it

18. Building the Hierarchy • We use Garland’s Quadric method • Dual of edge-collapse simplification • Quadric error term measures distance to best-fit plane of face vertices, rather than distance to face planes of best-fit vertex. • Most important properties • Produces clusters that are approximately planar • Tight oriented bounding box calculated via PCA • Add well-shaped term to get compact clusters

19. Face Clustered Venus Planar term only With ‘well-shaped’ term

20. Vector Radiosity • Standard radiosity equation is scalar • Applied to face clusters it incorrectly ignores variation in local normals • No obvious way of combining radiosities of two elements with different normals • Solution • Recast radiosity equation in terms of irradiance vector and power vector

21. Why Vector Radiosity? Leaf Elements Haar Basis Vector Radiosity

22. Vector Radiosity Approx. P E E = -mmTP m

23. Justification • Simplest representation that captures the appropriate behaviour • Minimises storage for each face cluster node • We combine vectors hierarchically to represent complex radiosity distributions

24. Algorithm Overview • Construct face cluster hierarchy file for each new model. Super-linear in k • Create scene from models • Read in scene description, add root face cluster nodes to a volume cluster hierarchy • Run gather/push-pull/refinesolver. Sub-linear in k • Propagate radiosity solution to leaves of all models, write to disk. Linear in k Dominant

25. Results • Tested on a million polygon scene. • Medium-high illumination complexity (sun, sky, three spotlights, much reflection) • 6 scanned models, implicit surface podium, displacement-mapped floor • Also tested at several resolutions of that scene, along with progressive and HRVC radiosity algorithms

26. Museum Scene 2,700,000 triangles Time: 109 secsMemory: 100 MB Progressive and HRVC would not fit in 1GB

27. Venus Close-up

28. Results: Solution Time Same scene, progressively fewer polygons

29. Results: Resident Set Size Same scene, progressively fewer polygons

30. Conclusions • Face cluster hierarchies proved highly effective for use with radiosity • Sub-linear performance in the number of input polygons, as opposed to ‘previous best’ of O(klogk) • Low memory usage • Extremely detailed scenes

31. Future Work • Better visibility sampling in final pass • Conservative bounds on radiosity transfer • Comparison to radiance and other radiosity code bases • Project page at • http://www.cs.cmu.edu/~radiosity/mrr/

32. EXTRAS

33. Virtual Memory • Face cluster files are written in breadth-first order, so get good memory locality • Usually only small first section of the face cluster file used, so it’s memory mapped • Progressive Radiosity has good total memory use, but very poor locality

34. Radiance: Medium Quality

35. Radiance: High Quality

36. Radiance: Memory Use

37. Details • m and its error estimated by sampling • Error term doesn’t depend on normals, but penalizes side-on clusters • Visibility by ray casting, nested grids • Use bounding boxes • Fractional visibility used during simulation, visibility resampled at higher resolution for final illumination

38. Complexity • O(slogs), not O(klogk), where s is the number of face cluster hierarchies. • s << k • Almost always, s << n • Each face cluster hierarchy represents a separate polygon mesh

39. Vector Radiosity Equations E P

40. A Dual Edge Contraction

41. Iterative Face Clustering

42. FCR Pedestal: Clusters

43. Transfer Examples

44. HRVC Pedestal Final

45. FCR Pedestal Final