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Data Visualization

Data Visualization. Lecture 10 Flow Visualization – Part 2 - Image-based Methods - Critical Point Methods. Flow Visualization - Texture Effects. A new class of image-based methods attempts to visualize flow as a texturing effect

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Data Visualization

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  1. Data Visualization Lecture 10 Flow Visualization – Part 2 - Image-based Methods - Critical Point Methods

  2. Flow Visualization - Texture Effects • A new class of image-based methods attempts to visualize flow as a texturing effect • Most successful for 2D flow - and also for flow over surfaces in 3D • Methods include: • spot noise • line integral convolution - lic

  3. one spot many spots spot texture Spot Noise for Flow Visualization • Spots of random size and intensity drawn in a plane give a texture effect Texture defined as an intensity function f: f( x ) =  ai h( x - xi ) where xi is random position, ai is random scale (zero mean), and h is the spot function - zero everywhere except for small area (here circular)

  4. Spot Noise for Flow Visualization • Different textures result from different spot shapes • Aligning the shape of the spot with the direction of flow gives a good visualization effect • In direction of flow, scale proportional to ( 1 + |v | ) , |v| = velocity magnitude • At 90 degrees to flow, scale proportional to 1 / ( 1 + | v | )

  5. Spot Noise Example

  6. Numerical simulation of flow, visualized using spot noise Wall friction displayed using oil and paint - wind evaporates oil and paint leaves white traces Flow Over a Surface

  7. Spot Noise Example

  8. Spot Noise Movie

  9. Learning More about Spot Noise • Spot noise has been developed by researchers in the Netherlands • van Wijk and de Leeuw • see http://www.cwi.nl/~wimc/spotnoise.html • Thanks to Wim de Leeuw for the images used in these slides • Thanks to Jack van Wijk for the movie • http://www.win.tue.nl/~vanwijk

  10. flow lines white noise LIC Line Integral Convolution (LIC) • Essence of method is: • consider a white noise texture, T(x,y) • for each pixel, set its intensity as a function (eg average) of values of T along a short streamline segment through the pixel • this has effect of correlating the resulting pixel values along streamlines, so a sense of the flow direction is obtained

  11. LIC Example Flow over surface of car - from CIRA, Italy Italian Aerospace Research Centre

  12. LIC Example Flow underneath car - from CIRA, Italy

  13. LIC Movie

  14. LIC Developments -Oriented LIC • Original LIC shows direction of flow but not orientation (ie -> or <- ) • Oriented LIC uses a sparse texture and a weighting of samples along streamline to give orientation effect

  15. Image-based Methods over Surfaces

  16. Learning More about LIC and Image-based Flow Vis • Original LIC • B Cabral and C Leedom, Imaging Vector Fields Using Line Integral Convolution, SIGGRAPH93, ACM Computer Graphics, pp263-270, 1993 • Oriented LIC • R Wegenkittl and E Groller • www.cg.tuwien.ac.at/research/vis/dynsys/frolic/ • Image-based flow visualization generally • Jack van Wijk – thanks to Jack for the surface based movies

  17. Vector Field Topology • This approach aims to visualize only the significant features of a flow field • It identifies critical points • points where velocity magnitude is zero • point of repulsion, attraction or a saddle point • streamlines from critical points divide space into regions of similar behaviour

  18. Characterising a Critical Point • Let u = velocity in x; v = velocity in y • Look at Jacobian matrix: partial derivatives du / dx du / dy dv / dx dv / dy The critical points are characterised by the eigenvalues of this matrix: a1 + i b1 a2 - i b2

  19. Characterising a Critical Point • Sign of real part indicates: • repulsion a1, a2 positive • attraction a1, a2 negative • saddle a1, a2 opposite signs • centre a1, a2 zero • Imaginary part indicates rotation of flow about critical point: • no rotation b1, b2 zero (node) • rotation b1,b2 non-zero (focus)

  20. Attachment and Detachment Points • There are also critical points along surfaces, where streamlines start (detachment points) or end (attachment points) • The flow field topology is produced by: • identifying critical points • drawing streamlines from detachment or attachment points and saddles (4 from saddles)... to repulsors and attractors • drawing streamlines to/from critical points that exit boundary

  21. Vector Field Topology • In 3D, similar analysis can be carried out - we get stream surfaces separating flow field into uniform regions • Reading: • J Helman and L Hesselink, Representation and Display of Vector Field Topology in Fluid Flow Data Sets, in Visualization in Scientific Computing, IEEE Press 1990 • http://science.nas.nasa.gov/Groups/VisTech/other/topology

  22. Flow Topology on Surface

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