Hi David,<div><br></div><div>Yes indeed, it is a triangle mesh... However as I mentioned vtkDelaunay3D seems to work on all of the other vertices of my mesh, except on the one included the previous e-mail... This seems so odd!</div>
<div><br></div><div>The problem is that I need the 3-D convex hull, since I later want to know if current vertex is enclosed by its neighbors' convex hull... If I use delaunay2D (by projecting my mesh onto a flat surface) would still be possible to check if the point is contained in this convex hull.</div>
<div><br></div><div>Thanks,</div><div>Miguel<br><br><div class="gmail_quote">2011/7/26 David Gobbi <span dir="ltr"><<a href="mailto:david.gobbi@gmail.com">david.gobbi@gmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Hi Miguel,<br>
<br>
The vtkDelaunay3D filter is for tetrahedral meshes, but your mesh<br>
looks like a triangle mesh. So my guess is that you should be using<br>
vtkDelaunay2D instead. But since Delanay2D is a 2D filter, you might<br>
have to project your mesh onto a flat surface first.<br>
<br>
Also, Delaunay often performs worse on noiseless data. If you are<br>
working with synthetic data, you will get better results if you<br>
perturb each point with a small, random displacement. With noiseless<br>
data, it is often the case that three points will lie along a straight<br>
line, and the Delaunay algorithm will consider three such points as<br>
forming a degenerate triangle. Another problem with noiseless data,<br>
specifically for rectangular grids, is that they can result in<br>
situations where there is more than one valid Delaunay triangulation.<br>
These will cause the algorithm to go into deep recursion.<br>
<br>
- David<br>
<br>
<br>
2011/7/25 Miguel Sotaquirá <<a href="mailto:msotaquira@gmail.com">msotaquira@gmail.com</a>>:<br>
<div><div></div><div class="h5">> Hi,<br>
> I'm using vtkDelaunay3D to create the local (1-ring neighborhood) convex<br>
> hull for each point in a mesh. For now I'm using a synthetic, perfectly<br>
> regular, noiseless mesh, where each vertex has exactly 6 neighbors.<br>
> I'm having troubles creating this convex hull only on one of the vertices<br>
> (the others are computed correctly). In this particular case the convex hull<br>
> computed does NOT include one of the six neighbors, as seen on the image<br>
> below:<br>
> <a href="http://tinypic.com/r/2944hag/7" target="_blank">http://tinypic.com/r/2944hag/7</a><br>
> the purple point being the center of the neighborhood, the gray spheres its<br>
> neighbors and the gray lines the convex hull obtained from vtkDelaunay3D.<br>
> Here's the code I'm using (neighbors are introduced as a polydata named<br>
> "pointcloud"):<br>
> vtkSmartPointer<vtkDelaunay3D> delaunay3D =<br>
> vtkSmartPointer<vtkDelaunay3D>::New();<br>
> delaunay3D->SetInput(pointCloud);<br>
> delaunay3D->Update();<br>
> during execution I get this warning: "vtkDelaunay3D (0x10345a490): 1<br>
> degenerate triangles encountered, mesh quality suspect"<br>
> How come, since I'm using a synthetic and perfectly regular mesh? As I<br>
> mentioned before, for other points (which have the exact same<br>
> characteristics) the convex hull is computed correctly.... Also, I've tried<br>
> using the methods "SetTolerance" and "BoundingTriangulationOn" of<br>
> vtkDelaunay3D but with no success<br>
> Thanks!<br>
> Miguel<br>
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