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vtkDelaunay2D Class Reference
create 2D Delaunay triangulation of input points.
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#include <vtkDelaunay2D.h>
Inheritance diagram for vtkDelaunay2D:
[legend]Collaboration diagram for vtkDelaunay2D:
[legend]List of all members.
Detailed Description
create 2D Delaunay triangulation of input points.
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Date:
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2001/12/13 20:46:39
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Revision:
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1.34.2.1
vtkDelaunay2D 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. Usually the output is a triangle mesh, but if a non-zero alpha distance value is specified (called the "alpha" value), then only triangles, edges, and vertices lying within the alpha radius are output. In other words, non-zero alpha values may result in arbitrary combinations of triangles, lines, and vertices. (The notion of alpha value is derived from Edelsbrunner's work on "alpha shapes".) Also, it is possible to generate "constrained triangulations" using this filter. A constrained triangulation is one where edges and loops (i.e., polygons) can be defined and the triangulation will preserve them (read on for more information).
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. (See "The Visualization Toolkit" text for more information.) 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). If you desire to triangulate in a different plane, you can use the vtkTransformFilter to transform the points into and out of the x-y plane or you can specify a transform to the Delaunay2D directly. In the latter case, the input points are transformed, the transformed points are triangulated, and the output will use the triangulated topology for the original (non-transformed) points. This avoids transforming the data back as would be required when using the vtkTransformFilter method. Specifying a transform directly also allows any transform to be used: rigid, non-rigid, non-invertible, etc.
If an input transform is used, then alpha values are applied (for the most part) in the original data space. The exception is when BoundingTriangulation is on. In this case, alpha values are applied in the original data space unless a cell uses a bounding vertex.
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.
To create constrained meshes, you must define an additional input. This input is an instance of vtkPolyData which contains lines, polylines, and/or polygons that define constrained edges and loops. Only the topology of (lines and polygones) from this second input are used. The topology is assumed to reference points in the input point set (the one to be triangulated). In other words, the lines and polygons use point ids from the first input point set. Lines and polylines found in the input will be mesh edges in the output. Polygons define a loop with inside and outside regions. The inside of the polygon is determined by using the right-hand-rule, i.e., looking down the z-axis a polygon should be ordered counter-clockwise. Holes in a polygon should be ordered clockwise. If you choose to create a constrained triangulation, the final mesh may not satisfy the Delaunay criterion. (Noted: the lines/polygon edges must not intersect when projected onto the 2D plane. It may not be possible to recover all edges due to not enough points in the triangulation, or poorly defined edges (coincident or excessively long). The form of the lines or polygons is a list of point ids that correspond to the input point ids used to generate the triangulation.)
If an input transform is used, constraints are defined in the "transformed" space. So when the right hand rule is used for a polygon constraint, that operation is applied using the transformed points. Since the input transform can be any transformation (rigid or non-rigid), care must be taken in constructing constraints when an input transform is used.
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Warning:
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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.
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Warning:
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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.
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Warning:
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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; but the more likely you are to see numerical problems.
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See also:
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vtkDelaunay3D vtkTransformFilter vtkGaussianSplatter
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Examples:
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vtkDelaunay2D (Examples)
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Tests:
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vtkDelaunay2D (Tests)
Definition at line 167 of file vtkDelaunay2D.h.
Constructor & Destructor Documentation
| vtkDelaunay2D::vtkDelaunay2D |
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| vtkDelaunay2D::~vtkDelaunay2D |
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Member Function Documentation
| virtual const char* vtkDelaunay2D::GetClassName |
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| int vtkDelaunay2D::IsTypeOf |
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const char * |
type |
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Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.
Reimplemented from vtkPolyDataSource. |
| virtual int vtkDelaunay2D::IsA |
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const char * |
type |
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Return 1 if this class is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.
Reimplemented from vtkPolyDataSource. |
| vtkDelaunay2D* vtkDelaunay2D::SafeDownCast |
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vtkObject * |
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Will cast the supplied object to vtkObject* is this is a safe operation (i.e., a safe downcast); otherwise NULL is returned. This method is defined in all subclasses of vtkObject with the vtkTypeMacro found in vtkSetGet.h.
Reimplemented from vtkPolyDataSource. |
| void vtkDelaunay2D::PrintSelf |
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ostream & |
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vtkIndent |
indent |
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Methods invoked by print to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.
Reimplemented from vtkSource. |
| vtkDelaunay2D* vtkDelaunay2D::New |
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Construct object with Alpha = 0.0; Tolerance = 0.001; Offset = 1.25; BoundingTriangulation turned off.
Reimplemented from vtkPolyDataSource. |
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Specify the source object used to specify constrained edges and loops. (This is optional.) If set, and lines/polygons are defined, a constrained triangulation is created. The lines/polygons are assumed to reference points in the input point set (i.e. point ids are identical in the input and source). |
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Specify the source object used to specify constrained edges and loops. (This is optional.) If set, and lines/polygons are defined, a constrained triangulation is created. The lines/polygons are assumed to reference points in the input point set (i.e. point ids are identical in the input and source). |
| virtual void vtkDelaunay2D::SetAlpha |
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double |
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Specify alpha (or distance) value to control 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. |
| virtual double vtkDelaunay2D::GetAlpha |
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Specify alpha (or distance) value to control 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. |
| virtual void vtkDelaunay2D::SetTolerance |
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double |
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Specify 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. |
| virtual double vtkDelaunay2D::GetTolerance |
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Specify 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. |
| virtual void vtkDelaunay2D::SetOffset |
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double |
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Specify a multiplier to control the size of the initial, bounding Delaunay triangulation. |
| virtual double vtkDelaunay2D::GetOffset |
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Specify a multiplier to control the size of the initial, bounding Delaunay triangulation. |
| virtual void vtkDelaunay2D::SetBoundingTriangulation |
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int |
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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.) |
| virtual int vtkDelaunay2D::GetBoundingTriangulation |
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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.) |
| virtual void vtkDelaunay2D::BoundingTriangulationOn |
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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.) |
| virtual void vtkDelaunay2D::BoundingTriangulationOff |
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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.) |
| virtual void vtkDelaunay2D::SetInput |
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vtkPointSet * |
input |
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Set / get the input data or filter. |
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Set / get the input data or filter. |
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Set / get the transform which is applied to points to generate a 2D problem. This maps a 3D dataset into a 2D dataset where triangulation can be done on the XY plane. The points are transformed and triangulated. The topology of triangulated points is used as the output topology. The output points are the original (untransformed) points. The transform can be any subclass of vtkAbstractTransform (thus it does not need to be a linear or invertible transform). |
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Set / get the transform which is applied to points to generate a 2D problem. This maps a 3D dataset into a 2D dataset where triangulation can be done on the XY plane. The points are transformed and triangulated. The topology of triangulated points is used as the output topology. The output points are the original (untransformed) points. The transform can be any subclass of vtkAbstractTransform (thus it does not need to be a linear or invertible transform). |
| void vtkDelaunay2D::Execute |
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This method is the old style execute method
Reimplemented from vtkSource. |
Member Data Documentation
double vtkDelaunay2D::Alpha [protected]
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double vtkDelaunay2D::Tolerance [protected]
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int vtkDelaunay2D::BoundingTriangulation [protected]
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double vtkDelaunay2D::Offset [protected]
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The documentation for this class was generated from the following file:
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