[vtkusers] vtkDelaunay3D: wrong convex hull

[Miguel Sotaquirá]

Hi David,

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!

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.

Thanks,
Miguel

2011/7/26 David Gobbi <david.gobbi at gmail.com>

> Hi Miguel,
>
> The vtkDelaunay3D filter is for tetrahedral meshes, but your mesh
> looks like a triangle mesh.  So my guess is that you should be using
> vtkDelaunay2D instead.  But since Delanay2D is a 2D filter, you might
> have to project your mesh onto a flat surface first.
>
> Also, Delaunay often performs worse on noiseless data.  If you are
> working with synthetic data, you will get better results if you
> perturb each point with a small, random displacement.  With noiseless
> data, it is often the case that three points will lie along a straight
> line, and the Delaunay algorithm will consider three such points as
> forming a degenerate triangle.  Another problem with noiseless data,
> specifically for rectangular grids, is that they can result in
> situations where there is more than one valid Delaunay triangulation.
> These will cause the algorithm to go into deep recursion.
>
>  - David
>
>
> 2011/7/25 Miguel Sotaquirá <msotaquira at gmail.com>:
> > Hi,
> > I'm using vtkDelaunay3D to create the local (1-ring neighborhood) convex
> > hull for each point in a mesh. For now I'm using a synthetic, perfectly
> > regular, noiseless mesh, where each vertex has exactly 6 neighbors.
> > I'm having troubles creating this convex hull only on one of the vertices
> > (the others are computed correctly). In this particular case the convex
> hull
> > computed does NOT include one of the six neighbors, as seen on the image
> > below:
> > http://tinypic.com/r/2944hag/7
> > the purple point being the center of the neighborhood, the gray spheres
> its
> > neighbors and the gray lines the convex hull obtained from vtkDelaunay3D.
> > Here's the code I'm using (neighbors are introduced as a polydata named
> > "pointcloud"):
> > vtkSmartPointer<vtkDelaunay3D> delaunay3D =
> > vtkSmartPointer<vtkDelaunay3D>::New();
> > delaunay3D->SetInput(pointCloud);
> > delaunay3D->Update();
> > during execution I get this warning: "vtkDelaunay3D (0x10345a490): 1
> > degenerate triangles encountered, mesh quality suspect"
> > How come, since I'm using a synthetic and perfectly regular mesh? As I
> > mentioned before, for other points (which have the exact same
> > characteristics) the convex hull is computed correctly.... Also, I've
> tried
> > using the methods "SetTolerance" and "BoundingTriangulationOn" of
> > vtkDelaunay3D but with no success
> > Thanks!
> > Miguel
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