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

[Gelas, Arnaud Joel Florent]

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 ?

"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.

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 can give you some more tips/advices but it fairly depends on the problem you have and the way you want to solve it.

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.