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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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]

Edge collapse High quality output Access is in distortion order

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

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

Decimation Good quality output Access is in spatial order

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

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

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.]

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

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

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

The algorithm Partition the model

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

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

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

Surface variation Computed using face normals and face area

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

The algorithm Partition the model Loop Choose a cluster to split Partition the cluster

Splitting a cluster Split into 2,

Splitting a cluster Split into 2, 4,

Splitting a cluster Split into 2, 4, or 8 subclusters

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

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

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

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

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

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

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

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

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

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

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

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

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

Quantitative results Simplified a 30M polygon model

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

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

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%

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

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

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