Interactive Volume Visualization of General Polyhedral Grids

Philipp Muigg1,3, Markus Hadwiger2, Helmut Doleisch3, M. Eduard Gröller1

1, Vienna University of Technology, Austria

2, King Abdullah University of Science and Technology, Saudi Arabia

3, SimVis GmbH, Vienna, Austria

Motivation

• Computational Fluid Dynamics (CFD) simulations• Increase in size• Meshes become more complex

Motivation

• Many unstructured grid volume visualization techniques limited to tetrahedral grids

• Tetrahedralization required

1.4M poly cells (~89M tets)82K poly cells (~4M tets)

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

Data Structure

• Requirements for ray casting• Query all faces of a cell• Query neighouring cell across a face• Query vertices of a face

Data Structure

• 2D illustration• 3D Faces 2D Edges• 3D Cells 2D Faces

• Example contains• 6 „faces“• 3 „cells“

• Common grid representations cell centered

Data Structure

6 links

Data Structure

• Common grid representations cell centered• Cell to cell traversal for ray casting requires

(redundant) face connectivity

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

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)

Data Structure: TSFL

• Additional bit flag per link (front and back flag)• Blue facing towards cell• Green facing away from cell

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

Data Structure: TSFSL

• Two sided face sequence lists (TSFSL)• Group faces facing towards same cell• Discard front links

(retain last in sequence)

Data Structure: TSFSL

• Two sided face sequence lists (TSFSL)• Group faces facing towards same cell• Discard front links

(retain last in sequence)

9 links

Data Structure: TSFSL

• Requirements for ray casting

Query all faces of a cell

Query neighouring cell across a face• Query vertices of a face

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

fbl c fbl d fbl e ffl

Sequence [cde]

fbl a fbl f ffl

Sequence [af]

fbl b ffl

Sequence [b]

Data Structure: TSFSL

• Requirements for ray casting

Query all faces of a cell

Query neighouring cell across a face

Query vertices of a face

GPU based Ray Casting

• TSFSL traversal for ray casting

bl c bl d bl e flSequence [cde]

bl a bl f flSequence [af]

bl b flSequence [b]

bl a bl f fl

GPU based Ray Casting

• TSFSL traversal for ray casting

bl c bl d bl e flSequence [cde]

Sequence [af]

bl b flSequence [b]

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

Application Examples

Hardware:Core 2 Quad @ 2.8GHzGeforce 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/Faces 1.5M/4.7M 1.3M/8.9M

Tetrahedra 17M 89M

Byte/Tetrahedra 8.5 byte/tet 7.5 byte/tet

Bricks/Overhead 4/1.7% 10/8.6%

Render Time (preview) 222ms (81ms) 2.9s (742ms)

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

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