Delaunay 2D (Delaunay2D)
Create 2D Delaunay triangulation of input points. It expects a vtkPointSet as input and produces vtkPolyData as output. The points are expected to be in a mostly planar distribution.
Delaunay2D is a filter that constructs a 2D 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 a
polygonal dataset containing a triangle mesh.
The 2D Delaunay triangulation is defined as the triangulation that
satisfies the Delaunay criterion for n-dimensional simplexes (in this
case n=2 and the simplexes are triangles). This criterion states that a
circumsphere of each simplex in a triangulation contains only the n+1
defining points of the simplex. In two dimensions, this translates into an
optimal triangulation. That is, the maximum interior angle of any
triangle is less than or equal to that of any possible triangulation.
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, even though the triangulation is 2D. Thus the
triangulation is constructed in the x-y plane, and the z coordinate is
ignored (although carried through to the output). You can use the option
ProjectionPlaneMode in order to compute the best-fitting plane to the
set of points, project the points and that plane and then perform the
triangulation using their projected positions and then use it as the
plane in which the triangulation is performed.
The Delaunay triangulation can be numerically sensitive in some cases.
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 three
points will form a triangle; other degenerate points will not break this
triangle.
Points that are coincident (or nearly so) may be discarded by the
algorithm. This is because the Delaunay triangulation requires unique
input points. The output of the Delaunay triangulation is supposedly a
convex hull. In certain cases this implementation may not generate the
convex hull.
Property | Description | Default Value(s) | Restrictions |
Alpha (Alpha) |
The value of this property controls the output of this filter. For a non-zero alpha value, only edges or triangles contained within a sphere centered at mesh vertices will be output. Otherwise, only triangles will be output.
|
0 |
The value must be greater than or equal to 0.
|
Bounding Triangulation (BoundingTriangulation) |
If this property is set to 1, 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 2D 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 is a multiplier to control the size of the initial, bounding Delaunay triangulation.
|
1 |
The value must be greater than or equal to 0.75.
|
Projection Plane Mode (ProjectionPlaneMode) |
This property determines type of projection plane to use in performing the triangulation.
|
0 |
The value must be one of the following: XY Plane (0), Best-Fitting Plane (2).
|
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.
|
1e-05 |
The value must be greater than or equal to 0 and less than or equal to 1.
|