Delaunay 3D (Delaunay3D)
Create a 3D Delaunay triangulation of input points. It expects a vtkPointSet as input and produces vtkUnstructuredGrid as output.
Delaunay3D is a filter that constructs a 3D Delaunay triangulation
from a list of input points. These points may be represented by any
dataset of type vtkPointSet and subclasses. The output of the filter
is an unstructured grid dataset. Usually the output is a tetrahedral
mesh, but if a non-zero alpha distance value is specified (called
the "alpha" value), then only tetrahedra, triangles, edges, and
vertices lying within the alpha radius are output. In other words,
non-zero alpha values may result in arbitrary combinations of
tetrahedra, triangles, lines, and vertices. (The notion of alpha
value is derived from Edelsbrunner's work on "alpha shapes".)


The 3D Delaunay triangulation is defined as the triangulation that
satisfies the Delaunay criterion for n-dimensional simplexes (in
this case n=3 and the simplexes are tetrahedra). This criterion
states that a circumsphere of each simplex in a triangulation
contains only the n+1 defining points of the simplex. (See text for
more information.) While in two dimensions this translates into an
"optimal" triangulation, this is not true in 3D, since a measurement
for optimality in 3D is not agreed on.


Delaunay triangulations are used to build topological structures
from unorganized (or unstructured) points. The input to this filter
is a list of points specified in 3D. (If you wish to create 2D
triangulations see Delaunay2D.) The output is an unstructured
grid.


The Delaunay triangulation can be numerically sensitive. To prevent
problems, try to avoid injecting points that will result in
triangles with bad aspect ratios (1000:1 or greater). In practice
this means inserting points that are "widely dispersed", and enables
smooth transition of triangle sizes throughout the mesh. (You may
even want to add extra points to create a better point
distribution.) If numerical problems are present, you will see a
warning message to this effect at the end of the triangulation
process.


Warning:
Points arranged on a regular lattice (termed degenerate cases) can
be triangulated in more than one way (at least according to the
Delaunay criterion). The choice of triangulation (as implemented by
this algorithm) depends on the order of the input points. The first
four points will form a tetrahedron; other degenerate points
(relative to this initial tetrahedron) will not break it.


Points that are coincident (or nearly so) may be discarded by the
algorithm. This is because the Delaunay triangulation requires
unique input points. You can control the definition of coincidence
with the "Tolerance" instance variable.


The output of the Delaunay triangulation is supposedly a convex
hull. In certain cases this implementation may not generate the
convex hull. This behavior can be controlled by the Offset instance
variable. Offset is a multiplier used to control the size of the
initial triangulation. The larger the offset value, the more likely
you will generate a convex hull; and the more likely you are to see
numerical problems.


The implementation of this algorithm varies from the 2D Delaunay
algorithm (i.e., Delaunay2D) in an important way. When points are
injected into the triangulation, the search for the enclosing
tetrahedron is quite different. In the 3D case, the closest
previously inserted point point is found, and then the connected
tetrahedra are searched to find the containing one. (In 2D, a "walk"
towards the enclosing triangle is performed.) If the triangulation
is Delaunay, then an enclosing tetrahedron will be found. However,
in degenerate cases an enclosing tetrahedron may not be found and
the point will be rejected.
PropertyDescriptionDefault Value(s)Restrictions
Alpha
(Alpha)
This property specifies the alpha (or distance) value to control the output of this filter. For a non-zero alpha value, only edges, faces, or tetra contained within the circumsphere (of radius alpha) will be output. Otherwise, only tetrahedra will be output. 0

The value must be greater than or equal to 0.

 
Bounding Triangulation
(BoundingTriangulation)
This boolean controls whether bounding triangulation points (and associated triangles) are included in the output. (These are introduced as an initial triangulation to begin the triangulation process. This feature is nice for debugging output.) 0

Only the values 0 and 1 are accepted.

 
Input
(Input)
This property specifies the input dataset to the Delaunay 3D filter.  

The selected object must be the result of the following: sources (includes readers), filters.

The selected dataset must be one of the following types (or a subclass of one of them): vtkPointSet.

 
Offset
(Offset)
This property specifies a multiplier to control the size of the initial, bounding Delaunay triangulation. 2.5

The value must be greater than or equal to 2.5.

 
Tolerance
(Tolerance)
This property specifies a tolerance to control discarding of closely spaced points. This tolerance is specified as a fraction of the diagonal length of the bounding box of the points. 0.001

The value must be greater than or equal to 0 and less than or equal to 1.