Image Space Based Visualization of Unsteady Flow on Surfaces Robert S. Laramee1, Bruno Jobard2 Helwig Hauser1 1VRVis Research Center, Austria, www.VRVis.at, {Laramee,Hauser}@VRVis.at 2University of Pau, France, www.univ-pau.fr, bjobard@univ-pau.fr

Overview goals previous work image space based vis of unsteady flow on surfaces results conclusions, future work

Our Goals & Motivation application: vis of CFD simulation data dense rep. of unsteady flow on surfaces visualize flow on complex, adaptive resolution surfaces user-interaction fast vis flow on dynamic meshes no parameterization

Previous Work Lagrangian-Eulerian Advection by Jobard et al. path integration (Lagrangian) update of color pixels (Eulerian) Image Based Flow Visualization by Van Wijk advection of images

Method Overview Vector Field Projection Edge Detection Compute Advection Mesh Dynamic Case Image Advection Noise Blending Static Case Edge Blending Image Overlay Application

Vector Field Encoding Velocity Image Assign colors to the mesh vertices as a function of velocity Velocity Image Colored image used as the simplified (view dependent) 3D vector field 3D vectors are projected to image space transforming the computation from 3D to 2D No more computation time spent on occluded polyons

Advection Mesh Computation and Boundary Treatment Euler approximation of a pathline (like IBFV) pk+1 = pk + vp(pk;t) dt Advect Noise Backward integration (like LEA) Pk-1 = pk - vp(pk-1;t) dt

Edge Detection and Blending Discontinuity Condition |zk-1 - zk | > e |pk-1 - pk|

Edge Detection and Blending can also be used to prevent background color(s) from “leaking in” edge detection enabled

Noise Injection and Blending Why noise injection and blending? –for full coveratge both spatial and temporal characteristics: linearly interpolated sequence of random values Temporal characteristics: a black and white pulsing function

Image Overlay Application final stage computed once for each dynamic case applied last User controlled opacity

Putting Pieces Together Vector Field Projection Edge Detection Compute Advection Mesh Image Advection Noise Blending Edge Blending Image Overlay Application Dynamic Case Static Case

Texture Clipping Example is exaggerated for exposition Texture clipped along edges to reduce artifacts

Results, Large, Complex Data Sets

Results, Large, Complex Data Sets

Results, Zooming

Results, Medical Simulation Data

Results, Performance Times # mesh polygons % image space Advection mesh res. FPS static FPS dynamic 10K 75 32^2 64 40 64^2 35 128^2 18 256^2 32 8 512^2 15-16 2.3 48K 74 13 10-11 6 15 2 221K 84 5 4 63-64 2.9 1.5 Not the same as in paper! Nvidia 980XGL Quadro 2.8 GHz dual processor

Results, time-dependent mesh geometry and topology

Conclusions and Future Work We presented an algorithm with the following properties: dense representation of unsteady flow on surfaces vis flow on large surfaces, independent of surface’s complexity and resolution supports user-interaction fast vis flow on dynamic meshes does not rely on parameterization Future work extension to unsteady, 3D flow application of more specialized HW, e.g. programmable per-pixel operations

Acknowledgements Thanks to: Helmut Doleisch Tom Laramee Michael Mayer Jürgen Schneider Jarke van Wijk Austrian governmental research program, Kplus (www.kplus.at) AVL (www.avl.com) Many result animations available at: http://www.VRVis.at/ar3/pr2/vis03/