[Paraview] Stream Tracer in eigenvector field

Sat Aug 24 19:58:31 EDT 2013

Paul,

Sorry to have given such an off target answer! Your idea about checking 
the dot product as you progress makes sense. That's how VTK's a hyper 
stream tracer handles the issue. I wonder if you can make use of it? 
Bringing VTK classes into PV isn't too hard but parallelizing them can 
be challenging.

Burlen

On 08/24/2013 12:27 PM, Burlen Loring wrote:
> in the case of the glyphing algorithm it's the surface normals of the 
> transformed glyph that have the relation to the sign determinant of 
> the transform matrix. this transformation matrix is constructed from 
> the eigenvectors directly. at any rate, good luck.
>
> On 08/23/2013 06:35 PM, pwhiteho wrote:
>> Burlen, you had me hoping, but alas ... there is no direct 
>> correlation between the determinant ( a.k.a. the 3rd tensor invariant 
>> ) and the orientation of the computed eigenvectors. You did get me 
>> thinking there may be other possibilities. I'm sure I can use the dot 
>> product in a marching cube scheme to enforce a consistent orientation 
>> progression and generate a "vector" field ParaView will handle well. 
>> It'll just have to be robust enough to handle a true change near some 
>> sharp topological feature.
>>
>> Thanks,
>> Paul
>>
>> ------------------------------------------------------------------------
>> *From:* Burlen Loring [bloring at lbl.gov]
>> *Sent:* Friday, August 23, 2013 4:31 PM
>> *To:* Andy Bauer; pwhiteho
>> *Cc:* paraview at paraview.org
>> *Subject:* Re: [Paraview] Stream Tracer in eigenvector field
>>
>> Eigenvectors are unique up to a constantso if you took any 
>> eigenvector and multiplied it by -1 it's still an eigenvector. You 
>> could see it in the definition,
>>
>> M x=\lambda x
>>
>> eigenvector x appears in both sides of the eqn.
>>
>> I had a similar problem with tensor glyphs in ParaView. In that case 
>> I was able to solve by looking at the sign of the determinant of the 
>> transformation matrix (see bug report, patch and mail list posts 
>> below). I wonder if you could adapt/build on this solution there to 
>> solve your issue here?
>>
>> http://vtk.org/Bug/view.php?id=12179
>> http://vtk.1045678.n5.nabble.com/tensor-glyph-inward-pointing-surface-normals-td4388361.html
>>
>> Burlen
>>
>>
>> On 08/23/2013 01:10 PM, Andy Bauer wrote:
>>> Hi Paul,
>>>
>>> Apologies as my math is a bit rusty but isn't the sign of the 
>>> eigenvector related to the sign of its corresponding eigenvalue? In 
>>> that case if you make sure that all of the eigenvalues are positive 
>>> then all of their corresponding eigenvectors should be aligned 
>>> properly. If that's the case and you have access to the eigenvalues 
>>> of the eigenvectors you could use the calculator or python 
>>> calculator to properly orient the eigenvectors.
>>>
>>> In any case, if you can come up with an algorithm that properly 
>>> orients the eigenvectors you should be able to do that in the python 
>>> calculator or calculator filters. If not, then things could get a 
>>> bit hairy as far as computationally figuring out which is the 
>>> "proper" direction your eigenvalues should have.
>>>
>>> Regards,
>>> Andy
>>>
>>>
>>> On Fri, Aug 23, 2013 at 3:38 PM, pwhiteho 
>>> <pwhiteho at masonlive.gmu.edu <mailto:pwhiteho at masonlive.gmu.edu>> wrote:
>>>
>>>     The term "eigenvector", used to describe the principal
>>>     directions of a tensor, is a bit of a misnomer since it's not a
>>>     "vector" as interpreted by the Stream Tracer filter - it's more
>>>     accurately bi-directional like tension/compression and could be
>>>     termed "eigenaxis/eigenaxes". When interpreted as a vector,
>>>     there is an inherent sign ambiguity in each eigenvector - the
>>>     sign is indeterminate and one is free to choose + or -, and that
>>>     is exactly what Mathematica does ( likely true for other
>>>     routines also ).
>>>
>>>     I've been using Mathematica to prototype computations for the
>>>     investigation of tensor topology which I then visualize in
>>>     ParaView. Eigen-decomposition of a tensor field at each grid
>>>     point returns an orthonormal set of eigenvectors, uncorrelated
>>>     with any neighbors. Taken separately, each eigenvector field
>>>     exhibits large regions of smoothly varying orientation, but
>>>     there are systematic and random reversals of orientation that
>>>     confound the Stream Tracer filter, sending streamlines wandering
>>>     around the field. What is needed is a true tangent curve (
>>>     tensor line ) integrator that would avoid "doubling back" as the
>>>     "streamline" propagates, similar to the scheme of Weinstein, et.
>>>     al., ( IEEE VIS'99 ) which computes the dot product of the
>>>     incoming propagation vector with the eigenvector; and if near
>>>     -1, negate the outgoing propagation vector. This can also be
>>>     fancied-up to accommodate noisy initial tensor data as in Weinstein.
>>>
>>>     I think I would be taking on too much at this point in learning
>>>     to write my own filter so have been exploring ways to
>>>     pre-process the eigenvector fields before visualizing in
>>>     Paraview, but I ask:
>>>     1. Have I missed something in existing filters that would handle
>>>     this?
>>>     2. Can the existing Stream Tracer be modified?
>>>     3. Does the eigenvector routine in ParaView yield the same sign
>>>     ambiguity among uncorrelated computations?
>>>
>>>     Thanks,
>>>     Paul W
>>>
>>>
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