#include <vtkDelaunay2D.h>
Inheritance diagram for vtkDelaunay2D:
Public Methods | |
virtual const char * | GetClassName () |
virtual int | IsA (const char *type) |
void | PrintSelf (ostream &os, vtkIndent indent) |
void | SetSource (vtkPolyData *) |
vtkPolyData * | GetSource () |
virtual void | SetAlpha (double) |
virtual double | GetAlpha () |
virtual void | SetTolerance (double) |
virtual double | GetTolerance () |
virtual void | SetOffset (double) |
virtual double | GetOffset () |
virtual void | SetBoundingTriangulation (int) |
virtual int | GetBoundingTriangulation () |
virtual void | BoundingTriangulationOn () |
virtual void | BoundingTriangulationOff () |
virtual void | SetInput (vtkPointSet *input) |
vtkPointSet * | GetInput () |
Static Public Methods | |
int | IsTypeOf (const char *type) |
vtkDelaunay2D * | SafeDownCast (vtkObject *o) |
vtkDelaunay2D * | New () |
Protected Methods | |
vtkDelaunay2D () | |
~vtkDelaunay2D () | |
vtkDelaunay2D (const vtkDelaunay2D &) | |
void | operator= (const vtkDelaunay2D &) |
void | Execute () |
Protected Attributes | |
double | Alpha |
double | Tolerance |
int | BoundingTriangulation |
double | Offset |
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'll have to use the vtkTransformFilter to transform the points into and out of the x-y plane.)
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. 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.)
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Return the class name as a string. This method is defined in all subclasses of vtkObject with the vtkTypeMacro found in vtkSetGet.h. Reimplemented from vtkPolyDataSource. |
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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. |
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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. |
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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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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. |
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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. |
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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. |
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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.) |
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Set / get the input data or filter. |
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Specify a multiplier to control the size of the initial, bounding Delaunay triangulation. |
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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. |
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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. |