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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 • 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 • Start with a coarse approximation and refine by adding vertices Access in model order What do we do? Simplify in reverse - “R”-Simp • Start with a coarse approximation and refine by adding vertices Access in model order Vertices Faces x0, y0, z0 0: v1, v2, z3 1 x1, y1, z1 1:va, vb, vc 2 3 xn, yn, zn m: vi, vj, vk 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 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 • • • • 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 • 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 Dragon David St. Matthews 871,306 8,253,996 6,755,412 Blade Stanford Bunny Happy Buddha Lucy 1,765,388 69,451 1,087,474 28,045,920 Output quality at 20K Dragon David St. Matthews 871,306 8,253,996 6,755,412 Output quality at 20K Blade Stanford Bunny Happy Buddha Lucy 1,765,388 69,451 1,087,474 28,045,920 Sequential vs parallel quality Parallel Sequential 5K 10K 20K Quantitative results Simplified a 30M polygon model Quantitative results Simplified a 30M polygon model No increase in surface error [Metro] 0.08 Total mean error 0.07 0.06 0.05 Bunny R-Simp Bunny PR-Simp Dragon R-Simp Dragon PR-Simp 0.04 0.03 0.02 0.01 0 5000 10000 Number of polygons 20000 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 12 Buddha 8.09 12 Blade 8.90 12 St. Matthews 7.89 12 David 8.17 12 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 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]