1. Interactive Volume Visualization of General Polyhedral Grids Philipp Muigg 1,3, Markus Hadwiger 2, Helmut Doleisch 3, M. Eduard Gröller 1 1, Vienna University of Technology, Austria 2, King Abdullah University of Science and Technology, Saudi Arabia 3, SimVis GmbH, Vienna, Austria

2. Motivation Computational Fluid Dynamics (CFD) simulations Increase in size Meshes become more complex

3. Motivation Many unstructured grid volume visualization techniques limited to tetrahedral grids Tetrahedralization required 1.4M poly cells (~89M tets)82K poly cells (~4M tets)

4. Motivation Direct volume rendering for grids composed of general polyhedral cells Data structure to represent polyhedral grids Low memory footprint Support traversal operations required by ray casting

5. Data Structure Requirements for ray casting Query all faces of a cell Query neighouring cell across a face Query vertices of a face

6. Data Structure 2D illustration 3D Faces  2D Edges 3D Cells  2D Faces Example contains 6 „faces“ 3 „cells“

7. Common grid representations cell centered Data Structure 6 links

8. Data Structure Common grid representations cell centered Cell to cell traversal for ray casting requires (redundant) face connectivity

9. Data Structure Redundancy Cell to face data derivable from face to cell data Face to cell data derivable from cell to face data 21 links

10. Data Structure: TSFL Two sided face lists (TSFL) Face based (comparable to winged/half edge) Cells represented via linked lists Two links per face (front and back link)

11. Data Structure: TSFL Additional bit flag per link (front and back flag) Blue  facing towards cell Green  facing away from cell

12. Data Structure: TSFL Visit all faces of a cell via links Select link at face based on previous flag Step from one cell to neighbour by selecting other link 12 links

13. Data Structure: TSFSL Two sided face sequence lists (TSFSL) Group faces facing towards same cell Discard front links (retain last in sequence)

14. Data Structure: TSFSL Two sided face sequence lists (TSFSL) Group faces facing towards same cell Discard front links (retain last in sequence) 9 links

15. Data Structure: TSFSL Requirements for ray casting Query all faces of a cell Query neighouring cell across a face Query vertices of a face

16. Data Structure: TSFSL TSFSL storage Interleave mesh connectivity and face geometry Back links stored in front of face geometry Terminating front link stored at end of sequence (sequence terminator) Entire mesh stored in single 1D array f bl c d e f fl Sequence [cde] f bl a f f fl Sequence [af] f bl b f fl Sequence [b]

17. Data Structure: TSFSL Requirements for ray casting Query all faces of a cell Query neighouring cell across a face Query vertices of a face

18. GPU based Ray Casting TSFSL traversal for ray casting blc d efl Sequence [cde] bla ffl Sequence [af] blbfl Sequence [b]

19. bla ffl GPU based Ray Casting TSFSL traversal for ray casting blc d efl Sequence [cde] Sequence [af] blbfl Sequence [b]

20. GPU based Ray Casting Spatial subdivision based on kD-tree Bricks rasterized independently Depth peeling for non-convex meshes Mean-value interpolation within cells Ray casting performed in view space See paper for additional details

21. Application Examples Hardware: Core 2 Quad @ 2.8GHz Geforce GTX480 1GB RAM HAVS [Callahan 2005]: ~7-9 byte/tet GPU and 118-149 byte/tet CPU Tet Strips [Weiler 2004]: ~15 byte/tet Cells/Faces1.5M/4.7M1.3M/8.9M Tetrahedra17M89M Byte/Tetrahedra8.5 byte/tet7.5 byte/tet Bricks/Overhead4/1.7%10/8.6% Render Time (preview)222ms (81ms)2.9s (742ms)

22. Summary/Future Work TSFSL data structure Face based Low memory footprint GPU-based ray-casting on polyhedral meshes Works directly on TSFSL Domain decomposition for culling/depth peeling Future Work Utilize CUDA/OpenCL shared memory during ray-casting Parallelize across multiple GPUs

23. Questions? Thank you for your attention! Acknowledgements: Polyhedral datasets courtesy of CD-Adapco Cooling jacket and Diesel Particulate Filter datasets courtesy of AVL List GmbH, Graz, Austria Parts of this project have been funded by the Austrian Research Funding Agency (FFG) in the scope of the project AutARG (No. 819352) and the ScaleVS (WWTF) project