vtkOrderedTriangulator Class Reference

#include <vtkOrderedTriangulator.h>

Inheritance diagram for vtkOrderedTriangulator:

[legend]Collaboration diagram for vtkOrderedTriangulator:

[legend]List of all members.

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Detailed Description

helper class to generate triangulations

This class is used to generate unique triangulations of points. The uniqueness of the triangulation is controlled by the id of the inserted points in combination with a Delaunay criterion. The class is designed to be as fast as possible (since the algorithm can be slow) and uses block memory allocations to support rapid triangulation generation. Also, the assumption behind the class is that a maximum of hundreds of points are to be triangulated. If you desire more robust triangulation methods use vtkPolygon::Triangulate(), vtkDelaunay2D, or vtkDelaunay3D.

Background:

This work is documented in the technical paper: W.J. Schroeder, B. Geveci, M. Malaterre. Compatible Triangulations of Spatial Decompositions. In Proceedings of Visualization 2004, IEEE Press October 2004.

Background:

Delaunay triangulations are unique assuming a random distribution of input points. The 3D Delaunay criterion is as follows: the circumsphere of each tetrahedron contains no other points of the triangulation except for the four points defining the tetrahedron. In application this property is hard to satisfy because objects like cubes are defined by eight points all sharing the same circumsphere (center and radius); hence the Delaunay triangulation is not unique. These so-called degenerate situations are typically resolved by arbitrary selecting a triangulation. This code does something different: it resolves degenerate triangulations by modifying the "InCircumsphere" method to use a slightly smaller radius. Hence, degenerate points are always considered "out" of the circumsphere. This, in combination with an ordering (based on id) of the input points, guarantees a unique triangulation.

Background:

There is another related characteristic of Delaunay triangulations. Given a N-dimensional Delaunay triangulation, points lying on a (N-1) dimensional plane also form a (N-1) Delaunay triangulation. This means for example, that if a 3D cell is defined by a set of (2D) planar faces, then the face triangulations are Delaunay. Combining this with the method to generate unique triangulations described previously, the triangulations on the face are guaranteed unique. This fact can be used to triangulate 3D objects in such a way to guarantee compatible face triangulations. This is a very useful fact for parallel processing, or performing operations like clipping that require compatible triangulations across 3D cell faces. (See vtkClipVolume for an example.)

Background:

A special feature of this class is that it can generate triangulation templates on the fly. If template triangulation is enabled, then the ordered triangulator will first triangulate the cell using the slower ordered Delaunay approach, and then store the result as a template. Later, if the same cell type and cell configuration is encountered, then the template is reused which greatly speeds the triangulation.

Warning:

Duplicate vertices will be ignored, i.e., if two points have the same coordinates the second one is discarded. The implications are that the user of this class must prevent duplicate points. Because the precision of this algorithm is double, it's also a good idea to merge points that are within some epsilon of one another.

The triangulation is performed using the parametric coordinates of the inserted points. Therefore the bounds (see InitTriangulation()) should represent the range of the parametric coordinates of the inserted points.

See also:

vtkDelaunay2D vtkDelaunay3D vtkPolygon

Tests:

vtkOrderedTriangulator (Tests)

Definition at line 115 of file vtkOrderedTriangulator.h.

void	InitTriangulation (double xmin, double xmax, double ymin, double ymax, double zmin, double zmax, int numPts)
void	InitTriangulation (double bounds[6], int numPts)
static vtkOrderedTriangulator *	New ()
Public Types
typedef vtkObject	Superclass
Public Member Functions
virtual const char *	GetClassName ()
virtual int	IsA (const char *type)
void	PrintSelf (ostream &os, vtkIndent indent)
void	UpdatePointType (vtkIdType internalId, int type)
double *	GetPointPosition (vtkIdType internalId)
double *	GetPointLocation (vtkIdType internalId)
vtkIdType	GetTetras (int classification, vtkUnstructuredGrid *ugrid)
vtkIdType	AddTetras (int classification, vtkUnstructuredGrid *ugrid)
vtkIdType	AddTetras (int classification, vtkIdList *ptIds, vtkPoints *pts)
vtkIdType	AddTriangles (vtkCellArray *connectivity)
vtkIdType	AddTriangles (vtkIdType id, vtkCellArray *connectivity)
vtkIdType	InsertPoint (vtkIdType id, double x[3], double p[3], int type)
vtkIdType	InsertPoint (vtkIdType id, vtkIdType sortid, double x[3], double p[3], int type)
vtkIdType	InsertPoint (vtkIdType id, vtkIdType sortid, vtkIdType sortid2, double x[3], double p[3], int type)
void	Triangulate ()
void	TemplateTriangulate (int cellType, int numPts, int numEdges)
vtkIdType	GetPointId (vtkIdType internalId)
virtual int	GetNumberOfPoints ()
virtual void	SetUseTemplates (int)
virtual int	GetUseTemplates ()
virtual void	UseTemplatesOn ()
virtual void	UseTemplatesOff ()
virtual void	SetPreSorted (int)
virtual int	GetPreSorted ()
virtual void	PreSortedOn ()
virtual void	PreSortedOff ()
virtual void	SetUseTwoSortIds (int)
virtual int	GetUseTwoSortIds ()
virtual void	UseTwoSortIdsOn ()
virtual void	UseTwoSortIdsOff ()
vtkIdType	AddTetras (int classification, vtkCellArray *connectivity)
vtkIdType	AddTetras (int classification, vtkPointLocator *locator, vtkCellArray *outConnectivity, vtkPointData *inPD, vtkPointData *outPD, vtkCellData *inCD, vtkIdType cellId, vtkCellData *outCD)
void	InitTetraTraversal ()
int	GetNextTetra (int classification, vtkTetra *tet, vtkDataArray *cellScalars, vtkDoubleArray *tetScalars)
Static Public Member Functions
static int	IsTypeOf (const char *type)
static vtkOrderedTriangulator *	SafeDownCast (vtkObject *o)
Protected Member Functions
	vtkOrderedTriangulator ()
	~vtkOrderedTriangulator ()

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Member Typedef Documentation

typedef vtkObject vtkOrderedTriangulator::Superclass

Reimplemented from vtkObject. Definition at line 118 of file vtkOrderedTriangulator.h.

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Constructor & Destructor Documentation

vtkOrderedTriangulator::vtkOrderedTriangulator (   )  [protected]

vtkOrderedTriangulator::~vtkOrderedTriangulator (   )  [protected]

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Member Function Documentation

virtual const char* vtkOrderedTriangulator::GetClassName (   )  [virtual]

Reimplemented from vtkObject.

static int vtkOrderedTriangulator::IsTypeOf (  const char *  type  )  [static]

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 vtkTypeRevisionMacro found in vtkSetGet.h. Reimplemented from vtkObject.

virtual int vtkOrderedTriangulator::IsA (  const char *  type  )  [virtual]

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 vtkTypeRevisionMacro found in vtkSetGet.h. Reimplemented from vtkObject.

static vtkOrderedTriangulator* vtkOrderedTriangulator::SafeDownCast (  vtkObject *  o  )  [static]

Reimplemented from vtkObject.

void vtkOrderedTriangulator::PrintSelf (  ostream &  os, vtkIndent  indent )  [virtual]

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 vtkObject.

static vtkOrderedTriangulator* vtkOrderedTriangulator::New (   )  [static]

Construct object. Reimplemented from vtkObject.

void vtkOrderedTriangulator::InitTriangulation (  double  xmin, double  xmax, double  ymin, double  ymax, double  zmin, double  zmax, int  numPts )

Initialize the triangulation process. Provide a bounding box and the maximum number of points to be inserted. Note that since the triangulation is performed using parametric coordinates (see InsertPoint()) the bounds should be represent the range of the parametric coordinates inserted. Postcondition: no_point_inserted: GetNumberOfPoints()==0

void vtkOrderedTriangulator::InitTriangulation (  double  bounds[6], int  numPts )

Initialize the triangulation process. Provide a bounding box and the maximum number of points to be inserted. Note that since the triangulation is performed using parametric coordinates (see InsertPoint()) the bounds should be represent the range of the parametric coordinates inserted. Postcondition: no_point_inserted: GetNumberOfPoints()==0

vtkIdType vtkOrderedTriangulator::InsertPoint (  vtkIdType  id, double  x[3], double  p[3], int  type )

For each point to be inserted, provide an id, a position x, parametric coordinate p, and whether the point is inside (type=0), outside (type=1), or on the boundary (type=2). You must call InitTriangulation() prior to invoking this method. Make sure that the number of points inserted does not exceed the numPts specified in InitTriangulation(). Also note that the "id" can be any integer and can be greater than numPts. It is used to create tetras (in AddTetras()) with the appropriate connectivity ids. The method returns an internal id that can be used prior to the Triangulate() method to update the type of the point with UpdatePointType(). (Note: the algorithm triangulated with the parametric coordinate p[3] and creates tetras with the global coordinate x[3]. The parametric coordinates and global coordinates may be the same.)

vtkIdType vtkOrderedTriangulator::InsertPoint (  vtkIdType  id, vtkIdType  sortid, double  x[3], double  p[3], int  type )

For each point to be inserted, provide an id, a position x, parametric coordinate p, and whether the point is inside (type=0), outside (type=1), or on the boundary (type=2). You must call InitTriangulation() prior to invoking this method. Make sure that the number of points inserted does not exceed the numPts specified in InitTriangulation(). Also note that the "id" can be any integer and can be greater than numPts. It is used to create tetras (in AddTetras()) with the appropriate connectivity ids. The method returns an internal id that can be used prior to the Triangulate() method to update the type of the point with UpdatePointType(). (Note: the algorithm triangulated with the parametric coordinate p[3] and creates tetras with the global coordinate x[3]. The parametric coordinates and global coordinates may be the same.)

vtkIdType vtkOrderedTriangulator::InsertPoint (  vtkIdType  id, vtkIdType  sortid, vtkIdType  sortid2, double  x[3], double  p[3], int  type )

For each point to be inserted, provide an id, a position x, parametric coordinate p, and whether the point is inside (type=0), outside (type=1), or on the boundary (type=2). You must call InitTriangulation() prior to invoking this method. Make sure that the number of points inserted does not exceed the numPts specified in InitTriangulation(). Also note that the "id" can be any integer and can be greater than numPts. It is used to create tetras (in AddTetras()) with the appropriate connectivity ids. The method returns an internal id that can be used prior to the Triangulate() method to update the type of the point with UpdatePointType(). (Note: the algorithm triangulated with the parametric coordinate p[3] and creates tetras with the global coordinate x[3]. The parametric coordinates and global coordinates may be the same.)

void vtkOrderedTriangulator::Triangulate (   )

Perform the triangulation. (Complete all calls to InsertPoint() prior to invoking this method.) A special version is available when templates should be used.

void vtkOrderedTriangulator::TemplateTriangulate (  int  cellType, int  numPts, int  numEdges )

Perform the triangulation. (Complete all calls to InsertPoint() prior to invoking this method.) A special version is available when templates should be used.

void vtkOrderedTriangulator::UpdatePointType (  vtkIdType  internalId, int  type )

Update the point type. This is useful when the merging of nearly coincident points is performed. The id is the internal id returned from InsertPoint(). The method should be invoked prior to the Triangulate method. The type is specified as inside (type=0), outside (type=1), or on the boundary (type=2). Precondition: valid_range: internalId>=0 && internalId<this->GetNumberOfPoints()

double* vtkOrderedTriangulator::GetPointPosition (  vtkIdType  internalId  )

Return the parametric coordinates of point `internalId'. It assumes that the point has already been inserted. The method should be invoked prior to the Triangulate method. Precondition: valid_range: internalId>=0 && internalId<this->GetNumberOfPoints()

double* vtkOrderedTriangulator::GetPointLocation (  vtkIdType  internalId  )

Return the global coordinates of point `internalId'. It assumes that the point has already been inserted. The method should be invoked prior to the Triangulate method. Precondition: valid_range: internalId>=0 && internalId<this->GetNumberOfPoints()

vtkIdType vtkOrderedTriangulator::GetPointId (  vtkIdType  internalId  )

Return the Id of point `internalId'. This id is the one passed in argument of InsertPoint. It assumes that the point has already been inserted. The method should be invoked prior to the Triangulate method. Precondition: valid_range: internalId>=0 && internalId<this->GetNumberOfPoints()

virtual int vtkOrderedTriangulator::GetNumberOfPoints (   )  [virtual]

Return the number of inserted points.

virtual void vtkOrderedTriangulator::SetUseTemplates (  int   )  [virtual]

If this flag is set, then the ordered triangulator will create and use templates for the triangulation. To use templates, the TemplateTriangulate() method should be called when appropriate. (Note: the TemplateTriangulate() method works for complete (interior) cells without extra points due to intersection, etc.)

virtual int vtkOrderedTriangulator::GetUseTemplates (   )  [virtual]

If this flag is set, then the ordered triangulator will create and use templates for the triangulation. To use templates, the TemplateTriangulate() method should be called when appropriate. (Note: the TemplateTriangulate() method works for complete (interior) cells without extra points due to intersection, etc.)

virtual void vtkOrderedTriangulator::UseTemplatesOn (   )  [virtual]

If this flag is set, then the ordered triangulator will create and use templates for the triangulation. To use templates, the TemplateTriangulate() method should be called when appropriate. (Note: the TemplateTriangulate() method works for complete (interior) cells without extra points due to intersection, etc.)

virtual void vtkOrderedTriangulator::UseTemplatesOff (   )  [virtual]

If this flag is set, then the ordered triangulator will create and use templates for the triangulation. To use templates, the TemplateTriangulate() method should be called when appropriate. (Note: the TemplateTriangulate() method works for complete (interior) cells without extra points due to intersection, etc.)

virtual void vtkOrderedTriangulator::SetPreSorted (  int   )  [virtual]

Boolean indicates whether the points have been pre-sorted. If pre-sorted is enabled, the points are not sorted on point id. By default, presorted is off. (The point id is defined in InsertPoint().)

virtual int vtkOrderedTriangulator::GetPreSorted (   )  [virtual]

Boolean indicates whether the points have been pre-sorted. If pre-sorted is enabled, the points are not sorted on point id. By default, presorted is off. (The point id is defined in InsertPoint().)

virtual void vtkOrderedTriangulator::PreSortedOn (   )  [virtual]

Boolean indicates whether the points have been pre-sorted. If pre-sorted is enabled, the points are not sorted on point id. By default, presorted is off. (The point id is defined in InsertPoint().)

virtual void vtkOrderedTriangulator::PreSortedOff (   )  [virtual]

Boolean indicates whether the points have been pre-sorted. If pre-sorted is enabled, the points are not sorted on point id. By default, presorted is off. (The point id is defined in InsertPoint().)

virtual void vtkOrderedTriangulator::SetUseTwoSortIds (  int   )  [virtual]

Tells the triangulator that a second sort id is provided for each point and should also be considered when sorting.

virtual int vtkOrderedTriangulator::GetUseTwoSortIds (   )  [virtual]

Tells the triangulator that a second sort id is provided for each point and should also be considered when sorting.

virtual void vtkOrderedTriangulator::UseTwoSortIdsOn (   )  [virtual]

Tells the triangulator that a second sort id is provided for each point and should also be considered when sorting.

virtual void vtkOrderedTriangulator::UseTwoSortIdsOff (   )  [virtual]

Tells the triangulator that a second sort id is provided for each point and should also be considered when sorting.

vtkIdType vtkOrderedTriangulator::GetTetras (  int  classification, vtkUnstructuredGrid *  ugrid )

Initialize and add the tetras and points from the triangulation to the unstructured grid provided. New points are created and the mesh is allocated. (This method differs from AddTetras() in that it inserts points and cells; AddTetras only adds the tetra cells.) The tetrahdera added are of the type specified (0=inside,1=outside,2=all). Inside tetrahedron are those whose points are classified "inside" or on the "boundary." Outside tetrahedron have at least one point classified "outside." The method returns the number of tetrahedrahedron of the type requested.

vtkIdType vtkOrderedTriangulator::AddTetras (  int  classification, vtkUnstructuredGrid *  ugrid )

Add the tetras to the unstructured grid provided. The unstructured grid is assumed to have been initialized (with Allocate()) and points set (with SetPoints()). The tetrahdera added are of the type specified (0=inside,1=outside,2=all). Inside tetrahedron are those whose points are classified "inside" or on the "boundary." Outside tetrahedron have at least one point classified "outside." The method returns the number of tetrahedrahedron of the type requested.

vtkIdType vtkOrderedTriangulator::AddTetras (  int  classification, vtkCellArray *  connectivity )

Add the tetrahedra classified (0=inside,1=outside) to the connectivity list provided. Inside tetrahedron are those whose points are all classified "inside." Outside tetrahedron have at least one point classified "outside." The method returns the number of tetrahedron of the type requested.

vtkIdType vtkOrderedTriangulator::AddTetras (  int  classification, vtkPointLocator *  locator, vtkCellArray *  outConnectivity, vtkPointData *  inPD, vtkPointData *  outPD, vtkCellData *  inCD, vtkIdType  cellId, vtkCellData *  outCD )

Assuming that all the inserted points come from a cell `cellId' to triangulate, get the tetrahedra in outConnectivity, the points in locator and copy point data and cell data. Return the number of added tetras. Precondition: locator_exists: locator!=0 outConnectivity: outConnectivity!=0 inPD_exists: inPD!=0 outPD_exists: outPD!=0 inCD_exists: inCD!=0 outCD_exists: outCD!=0

vtkIdType vtkOrderedTriangulator::AddTetras (  int  classification, vtkIdList *  ptIds, vtkPoints *  pts )

Add the tetrahedra classified (0=inside,1=outside) to the list of ids and coordinates provided. These assume that the first four points form a tetrahedron, the next four the next, and so on.

vtkIdType vtkOrderedTriangulator::AddTriangles (  vtkCellArray *  connectivity  )

Add the triangle faces classified (2=boundary) to the connectivity list provided. The method returns the number of triangles.

vtkIdType vtkOrderedTriangulator::AddTriangles (  vtkIdType  id, vtkCellArray *  connectivity )

Add the triangle faces classified (2=boundary) and attached to the specified point id to the connectivity list provided. (The id is the same as that specified in InsertPoint().)

void vtkOrderedTriangulator::InitTetraTraversal (   )

Methods to get one tetra at a time. Start with InitTetraTraversal() and then invoke GetNextTetra() until the method returns 0.

int vtkOrderedTriangulator::GetNextTetra (  int  classification, vtkTetra *  tet, vtkDataArray *  cellScalars, vtkDoubleArray *  tetScalars )

Methods to get one tetra at a time. Start with InitTetraTraversal() and then invoke GetNextTetra() until the method returns 0. cellScalars are point-centered scalars on the original cell. tetScalars are point-centered scalars on the tetra: the values will be copied from cellScalars. Precondition: tet_exists: tet!=0 cellScalars_exists: cellScalars!=0 tetScalars_exists: tetScalars!=0 tetScalars_valid_size: tetScalars->GetNumberOfTuples()==4

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The documentation for this class was generated from the following file:

• dox/Filtering/vtkOrderedTriangulator.h

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