[vtk-developers] VTK classes useful for meshless methods visualization

[Michel Audette]

Hi Arnaud,

thanks for your kind reply.

On Thu, Mar 24, 2011 at 3:37 PM, Gelas, Arnaud Joel Florent <
Arnaud_Gelas at hms.harvard.edu> wrote:

> Dear Michel,
>
> If I understood what you meant is that you work in 3D and you want to
> represent the interface of an implicit function represented by CSRBF where
> coefficients evolve based on some PDE ?
>
>
yes, that's an apt description. I had not thought it through in these terms,
but I think that we can formulate the "resectedness" (or rather tissue
destruction) implicitly. That's actually cooler than what I first had in
mind. :-)


> "The most effective way" is then to sample your implicit function on a grid
> (size of the grid should depends on the separation and fill distance; make
> sure to use a kd-tree for the evaluation of the implicit function it really
> speeds up the process), and then use the Marching Cubes to generate the
> mesh. Note that you could also use this for moving least squares technique.
>
>
sounds reasonable. I wonder if there is an example in VTK for this kind of
meshing.


> If your point remains next to the interface, and the sampling is not too
> bad you can consider some approximation that are not (to my knowledge) yet
> in vtk.
>
>
I'd be open to other suggestions, particularly if these could be added to
VTK readily.


> I can give you some more tips/advices but it fairly depends on the problem
> you have and the way you want to solve it.
>
>
Feel free to email me offline with these. I'll tell you a bit more about the
project.

Cheers,

Michel

> HTH,
> Arnaud
>
>
> ________________________________________
> From: vtk-developers-bounces at vtk.org [vtk-developers-bounces at vtk.org] On
> Behalf Of Michel Audette [michel.audette at kitware.com]
> Sent: Thursday, March 24, 2011 6:04 PM
> To: vtk-developers at vtk.org
> Subject: [vtk-developers] VTK classes useful for meshless methods
> visualization
>
> Dear VTK developers,
>
> I'm interested in the development of a visualization technique for meshless
> methods, which is a fairly hot topic in continuum mechanics these days, in
> the course of a proposal that I am writing.
>
> The basic idea is that the meshless formalism does away with an assemblage
> of elements, which in 3D would normally be tetrahedra, and replaces finite
> elements with functions of local support (eg radial basis functions)
> centered at each point, within a cloud of points, in discretizing partial
> differential equations. It turns out that the expressions in finite elements
> that relate deformation, stress and strain and that normally would be solved
> in their weak form on a system of equations based on elemental shape
> functions instead can be restated in terms of radial shape functions defined
> about one point, or node. In short, the computation is done on a cloud of
> points, not on a mesh of triangles or tetrahedra.
>
> The main attraction for this type of formalism, is that if the tissue
> undergoes a topological change, such as cutting or resection in an
> interactive surgery simulator, there is no need to re-mesh dynamically,
> which is a complex problem, especially if high-quality tetrahedra are needed
> in the re-meshed result to ensure computational stability.
>
> Moreover, visualization of what goes on tends to involve surfels (surface
> elements), or boundary points of the point-cloud, as well as an estimate of
> the surface normal at each boundary point.
>
> My question then is, what classes exist in VTK for handling surface
> rendering of a set of surfels, as well as updating the visualization
> efficiently to account for possibly resected points, while exploiting the
> temporal stability of unresected points?
>
> Thanks for your consideration.
>
> Cheers,
>
> Michel
>
> --
> Michel Audette, Ph.D.
> R & D Engineer,
> Kitware Inc.,
> Chapel Hill, N.C.
>
>


-- 
Michel Audette, Ph.D.
R & D Engineer,
Kitware Inc.,
Chapel Hill, N.C.
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