Download presentation

Presentation is loading. Please wait.

Published byWyatt Daly Modified over 4 years ago

1
10.1 Vis_04 Data Visualization Lecture 10 Flow Visualization – Part 2 - Image-based Methods - Critical Point Methods

2
10.2 Vis_04 Flow Visualization - Texture Effects n A new class of image-based methods attempts to visualize flow as a texturing effect n Most successful for 2D flow - and also for flow over surfaces in 3D n Methods include: – spot noise – line integral convolution - lic

3
10.3 Vis_04 Spot Noise for Flow Visualization n Spots of random size and intensity drawn in a plane give a texture effect Texture defined as an intensity function f: f( x ) = a i h( x - x i ) where x i is random position, a i is random scale (zero mean), and h is the spot function - zero everywhere except for small area (here circular) one spotmany spotsspot texture

4
10.4 Vis_04 Spot Noise for Flow Visualization n Different textures result from different spot shapes n Aligning the shape of the spot with the direction of flow gives a good visualization effect n In direction of flow, scale proportional to ( 1 + |v | ), |v| = velocity magnitude n At 90 degrees to flow, scale proportional to 1 / ( 1 + | v | )

5
10.5 Vis_04 Spot Noise Example

6
10.6 Vis_04 Flow Over a Surface Wall friction displayed using oil and paint - wind evaporates oil and paint leaves white traces Numerical simulation of flow, visualized using spot noise

7
10.7 Vis_04 Spot Noise Example

8
10.8 Vis_04 Spot Noise Movie

9
10.9 Vis_04 Learning More about Spot Noise n 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
10.10 Vis_04 Line Integral Convolution (LIC) n 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 white noise flow lines LIC

11
10.11 Vis_04 LIC Example Flow over surface of car - from CIRA, Italy Italian Aerospace Research Centre

12
10.12 Vis_04 LIC Example Flow underneath car - from CIRA, Italy

13
10.13 Vis_04 LIC Movie

14
10.14 Vis_04 LIC Developments - Oriented LIC n Original LIC shows direction of flow but not orientation (ie -> or <- ) n Oriented LIC uses a sparse texture and a weighting of samples along streamline to give orientation effect

15
10.15 Vis_04 Image-based Methods over Surfaces

16
10.16 Vis_04 Learning More about LIC and Image-based Flow Vis n Original LIC – B Cabral and C Leedom, Imaging Vector Fields Using Line Integral Convolution, SIGGRAPH93, ACM Computer Graphics, pp263-270, 1993 n Oriented LIC – R Wegenkittl and E Groller – www.cg.tuwien.ac.at/research/vis/dynsys/frolic/ www.cg.tuwien.ac.at/research/vis/dynsys/frolic/ n Image-based flow visualization generally – Jack van Wijk – thanks to Jack for the surface based movies

17
10.17 Vis_04 Vector Field Topology n This approach aims to visualize only the significant features of a flow field n 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
10.18 Vis_04 Characterising a Critical Point n Let u = velocity in x; v = velocity in y n Look at Jacobian matrix: du / dx du / dy dv / dx dv / dy The critical points are characterised by the eigenvalues of this matrix: a 1 + i b 1 a 2 - i b 2 partial derivatives

19
10.19 Vis_04 Characterising a Critical Point n Sign of real part indicates: – repulsiona 1, a 2 positive – attractiona 1, a 2 negative – saddlea 1, a 2 opposite signs – centrea 1, a 2 zero n Imaginary part indicates rotation of flow about critical point: – no rotationb 1, b 2 zero(node) – rotationb 1,b 2 non-zero (focus)

20
10.20 Vis_04 Attachment and Detachment Points n There are also critical points along surfaces, where streamlines start ( detachment points) or end ( attachment points) n 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
10.21 Vis_04 Vector Field Topology n In 3D, similar analysis can be carried out - we get stream surfaces separating flow field into uniform regions n 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
10.22 Vis_04 Flow Topology on Surface

23
10.23 Vis_04

Similar presentations

Presentation is loading. Please wait....

OK

Group Meeting Presented by Wyman 10/14/2006

Group Meeting Presented by Wyman 10/14/2006

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google