Parallel Model Simplification of Very Large Polygonal Meshes

1. Parallel Model Simplification of Very Large Polygonal Meshes by Dmitry Brodsky and Jan Bækgaard Pedersen

2. What did we do? • Parallelized an existing mesh simplification algorithm • Show that R-Simp [Brodsky & Watson] is well suited for parallel environments • Able to simplify large models • Achieve good speedup • Retain good output quality 30M 20K

3. Computer graphics • Scenes are created from models I am the Stanford Bunny

4. Computer graphics • Scenes are created from models • Models are create from polygons • The more polygons the more realistic the model • Triangles are most often used • Consisting of 3 vertices specifying a face • Hardware is optimized for triangles

5. Why simplify? • Graphics hardware is too slow • Render ~10k polygons in real-time • Models are too large • 100k polygons or more • Highly detailed models are not always required • Trade quality for rendering speed

6. What is simplification? 70,000 Polygons 5,000 Polygons • Reduce the number of polygons • Maintain shape

7. What is simplification? 70,000 Polygons 5,000 Polygons • The desired number of polygons depends on the scene

8. So what’s the problem? • Models are becoming very large • Model acquisition is getting better • Simplification is time consuming • Trade-off time for quality • On the order of hours and days • Models do not fit into core memory • Algorithms require 10’s of gigabytes • 32 bits are not enough

9. What can we do? • Partition the simplification process into smaller tasks • Execute the tasks in parallel or sequentially • Reduce contention for core (page faults) • Not applicable to all algorithms

10. Surface simplification • Flat surface patches can be represented with a few polygons • Remove excess polygons by removing edges or vertices

11. Surface simplification • Flat surface patches can be represented with a few polygons • Remove excess polygons by removing edges or vertices

12. Surface simplification • Flat surface patches can be represented with a few polygons • Remove excess polygons by removing edges or vertices

13. Removing primitives • Remove the primitive that causes the least amount of distortion • Preserve significant features • E.g. corners

14. Removing primitives • Remove the primitive that causes the least amount of distortion • Preserve significant features • E.g. corners • Avoid primitives that form corners

15. Removing primitives • Remove the primitive that causes the least amount of distortion • Preserve significant features • E.g. corners • Avoid primitives that form corners • Choose primitives on flat patches

16. Conventional algorithms • Edge collapse • Iteratively remove edges [Garland & Heckbert, Hoppe, Lindstrom, Turk] • Decimation • Combine polygons, remove vertices to create large planar patches [Hanson, Schroeder] • Clustering • Spatially cluster vertices or faces • Poor quality output [Rossignac & Borrel]

17. Edge collapse • High quality output • Access is in distortion order

18. Edge collapse • High quality output • Access is in distortion order 4 2 1 3

19. Edge collapse • High quality output • Access is in distortion order • Edges are sorted by distortion • Can’t exploit access locality • Data can not be partitioned • O(n log n ), n is input size • Large models are problematic • Take long to simplify • Have to fit into core memory

20. Decimation • Good quality output • Access is in spatial order

21. Decimation • Good quality output • Access is in spatial order 1 2 3 4

22. Decimation • Good quality output • Access is in spatial order • Models are usually polygonal soups • Data reorganization is necessary to exploit access locality • Topology information is needed • Surface partitioning is unintuitive • Data has to be sorted first • Should not split planar regions

23. Memory efficient algorithms • Edge collapse [Lindstrom & Turk] • Cluster refinement [Garland] • Modified R-Simp • Re-organizes and clusters vertices and faces to improve memory access locality [Salamon et al.]

24. What do we do? • Simplify in reverse - “R”-Simp • Start with a coarse approximation and refine by adding vertices • Access in model order

25. What do we do? Vertices Faces x0, y0, z0 0: v1, v2, z3 x1, y1, z1 1:va, vb, vc xn, yn, zn m: vi, vj, vk • Simplify in reverse - “R”-Simp • Start with a coarse approximation and refine by adding vertices • Access in model order 1 2 3

26. What do we do? • Simplify in reverse - “R”-Simp • Start with a coarse approximation and refine by adding vertices • Access in model order • Can exploit access locality • Less reorganization necessary • Data intuitively partitions • Linear runtime for an output size • O(ni log no) • Produce good quality output

27. The algorithm • Partition the model

28. Initial clustering • Spatially partition into 8 clusters • Cluster: A vertex in the output model

29. The algorithm • Partition the model • Main loop • Choose a cluster to split

30. Choosing a cluster • Select the cluster with the largest surface variation (curvature).

31. Surface variation • Computed using face normals and face area

32. Surface variation • Computed using face normals and face area • curvedness = ∑normali* areai

33. The algorithm • Partition the model • Loop • Choose a cluster to split • Partition the cluster

34. Splitting a cluster • Split into 2,

35. Splitting a cluster • Split into 2, 4,

36. Splitting a cluster • Split into 2, 4, or 8 subclusters

37. How to split? • Split based on surface curvature • Compute the mean normal and directions of maximum and minimum curvature • Directions guide the partitioning Mean Normal Direction of Minimum Curvature Direction of Maximum Curvature

38. Surface types • Goal: create large planar patches • Cylindrical: partitioned into 2 • Hemispherical: partitioned into 4 • Everything else is partitioned into 8

39. The algorithm • Partition the model • Loop • Choose a cluster to split • Partition the cluster • Compute surface variation for subclusters • Repeat • Re-triangulate the new surface

40. Moving to PR-Simp • Clusters naturally partition data • Assign initial clusters to processors • Each processor refines to a specified limit • Results are reduced and the surfaces are stitched together

41. PR-Simp • Master - Slave configuration • The dataset is available to all processors • Current implementation uses MPI • Scales to any number of processors

42. Master: initialization • Determine bounding box of model • Determine initial clusters: • Axis aligned planes • # of Procs = fx x fy x fz • Slaves receive: • bounding box, fx x fy x fz, and output size • Processor ID corresponds to a unique cluster

43. Slave: simplification • Determine output size for cluster: Pout = Pin (Fullout / Fullin) • Read in the cluster • Store faces that span processor boundaries • Run standard R-Simp algorithm • Re-triangulate assigned portion of the simplified surface

44. Building the output model • Reduce the results • Slaves propagate: • The new triangulated surface • Faces that span processor boundaries • Surfaces are stitched together at each reduction step • Master outputs the simplified model

45. Evaluation • Ability to simplify • Some models needed more than 4GB of core • Speedup • Reduce page faulting (memory thrashing) • Little or no loss of output quality • Test bed: • 20 Pentium III 550Mhz with 512MB • Connected by 100Mbps network

46. Test subjects David St. Matthews Dragon 8,253,996 871,306 6,755,412 Happy Buddha Lucy Stanford Bunny Blade 1,765,388 28,045,920 69,451 1,087,474

47. Output quality at 20K David St. Matthews Dragon 8,253,996 871,306 6,755,412

48. Output quality at 20K Happy Buddha Lucy Stanford Bunny Blade 1,765,388 28,045,920 69,451 1,087,474

49. Sequential vs parallel quality 5K 10K 20K Sequential Parallel

50. Quantitative results • Simplified a 30M polygon model