1. Parallel Model Simplification of Very Large Polygonal Meshesby
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 Models are too large
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?
Reduce the number of polygons
Maintain shape
70,000 Polygons
5,000 Polygons

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

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 13

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 Access in model order
Start with a coarse approximation and refine by adding vertices
Access in model order

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

26. What do we do? Simplify in reverse - “R”-Simp Access in model order
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 Re-triangulate the new surface
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 Speedup
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 871,306 David 8,253,996 St. Matthews 6,755,412 Lucy
Dragon
871,306
David
8,253,996
St. Matthews
6,755,412
Lucy
28,045,920
Happy Buddha
1,087,474
Stanford Bunny
69,451
Blade
1,765,388

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

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

49. Sequential vs parallel quality5K
10K
20K
Sequential
Parallel

50. Quantitative results
Simplified a 30M polygon model

51. Quantitative results Simplified a 30M polygon model
No increase in surface error [Metro]

52. Quantitative results Simplified a 30M polygon model
No increase in surface error [Metro]
Obtained significant speedup for large models
Model
Speedup
# of Proc.
Bunny
4.70 12
Dragon
5.61
Buddha
8.09
Blade
8.90
St. Matthews
7.89
David
8.17
Lucy
6.40 16

53. Quantitative results Simplified a 30M polygon model
No increase in surface error [Metro]
Obtained significant speedup for large models
Output quality is mostly unaffected by the number of processors
Efficiency is approximately 59%

54. Conclusions
Large models can be simplified by using common desktop resources
The R-Simp algorithm is well suited for parallelization
Data can easily be partitioned
Quality does not significantly degrade as more processors are added
Use two step simplification if quality is very important

55. Thanks Questions?? Thanks to:
Mike Feeley, Norm Hutchinson, Alan Wagner, and the other characters in the DSG Lab.
Questions??

57. Quantitative Results Simplified a 30M polygon model
No increase in surface error [Metro]