[Paraview-developers] normalizing vector field during integration

[burlen]

I've modified the LIC code so that vector field is not normalized. The 
result is much better, relationships between flow features are 
preserved. Are there objections to making the normalization optional in LIC?

without normalization:
http://www.hpcvis.com/downloads/lic-ui-not-normalized-200.png

with normalization:
http://www.hpcvis.com/downloads/lic-ui-mag-200-anno.png

On 10/03/2012 06:25 PM, burlen wrote:
> Hi,
>
> I'm doubting the following claim made in vtkStreamTracer documentation 
> about increased numerical accuracy when using a normalized velocity 
> field. It's not true when |V|<<1, even when using adaptive step size 
> methods. It's also not immediately clear how the normalization impacts 
> the error estimation algorithm employed in the adaptive step methods. 
> The field normalization technique is also being employed in pv's 
> surface LIC  implementation.
>
> I can see how normalizing the field makes the stream tracer/surface 
> lic easy to use, narrowing the range of input parameters one needs to 
> adjust to make it work on a wide variety of datasets and making it 
> easy to get streamlines that travel consistently through the dataset. 
> Unfortunately, normalizing the vector field changes the relationships 
> between flow features which are defined by variations in the flow. 
> These changes give one a false sense of the flow behavior during 
> visualization, feature detection, and analysis. I think that field 
> normalization during integration should be optional, and should 
> probably be disabled by default.
>
> A few illustrative examples follow.
>
> Burlen
>
> from the vtkStreamTracer documentation:
>
> > Note that normalized vectors are adopted in streamline integration,
> > which achieves high numerical accuracy/smoothness of flow lines that is
> > particularly guaranteed for Runge-Kutta45 with adaptive step size and
> > error control).
>
> What happens when you normalize the velocity field during streamline 
> integration? For the sake of discussion consider a concrete example of 
> a shear flow (like a strong wind over the surface of the ocean), with:
>
> > V(y>0)=1000.0,2000.0
> > V(Y<0)=0.001,0.002
> >
> > let W=V/|V| then
> >
> > W(y>0)=0.4472,0.8944
> > W(y<0)=0.4472,0.8944
>
> The defining characteristic of the flow, namely sharp velocity 
> differential across an interface, is lost.
>
> Here's example from a real dataset where normalizing the vector field 
> "amplifies" an insignificant feature (|V|~1e-5) in the flow. The 
> relative differences between features in the visualization are 
> completely lost.
> http://www.hpcvis.com/downloads/lic-ui-mag-200-anno.png
> lic-ui-200
>
> glyphing reveals true relationships:
> http://www.hpcvis.com/downloads/glyph-ui-scale-by-2000-200.png
> glyph-ui-200
>
>
> The claim that normalizing the field during integration increases 
> numerical accuracy is false. when |V|<<1 exactly the opposite occurs. 
> the effect of normalization is similar to computing the streamline 
> with an increased step size, although the "growth factor" is dependent 
> on the direction. The amount of harm done by this increase will depend 
> on how much smaller |V| is compared to 1. Because of variations in the 
> field across a dataset, the accuracy of the computed streamlines 
> varies in a way that's not easily identified and accounted for. For 
> the sake of discussion consider the following simple example using the 
> Euler method which, although exaggerates the error, shares properties 
> with other RK methods.
>
> > dt=0.1
> > x_0=0,0
> > V(x_0)=0.001,0.002
> > W(x_0)=V(x_0)/|V(x_0)|=0.4472,0.8944
> > x_1 = x_0 + V(x_0)dt = 0.0001,0.0002
> > x_1 = x_0 + W(x_0)dt = 0.0447,0.0894
>
> The effective step size taken when normalizing the field is orders of 
> magnitude larger. Note, using an adaptive method doesn't prevent the 
> overstep, and it's not clear how normalizing the field changes the 
> behavior of the error estimator.
>
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