a cell that represents a triangle More...

#include <vtkTriangle.h>

Inheritance diagram for vtkTriangle:

Collaboration diagram for vtkTriangle:

Public Types
typedef vtkCell	Superclass

Public Types inherited from vtkCell
typedef vtkObject	Superclass

Public Types inherited from vtkObject
typedef vtkObjectBase	Superclass

Public Member Functions
virtual int	IsA (const char *type)

vtkTriangle *	NewInstance () const

void	PrintSelf (ostream &os, vtkIndent indent)

vtkCell *	GetEdge (int edgeId)

int	GetCellType ()

int	GetCellDimension ()

int	GetNumberOfEdges ()

int	GetNumberOfFaces ()

vtkCell *	GetFace (int)

int	CellBoundary (int subId, double pcoords[3], vtkIdList *pts)

void	Contour (double value, vtkDataArray cellScalars, vtkIncrementalPointLocator locator, vtkCellArray verts, vtkCellArray lines, vtkCellArray polys, vtkPointData inPd, vtkPointData outPd, vtkCellData inCd, vtkIdType cellId, vtkCellData *outCd)

int	EvaluatePosition (double x[3], double closestPoint, int &subId, double pcoords[3], double &dist2, double weights)

void	EvaluateLocation (int &subId, double pcoords[3], double x[3], double *weights)

int	Triangulate (int index, vtkIdList ptIds, vtkPoints pts)

void	Derivatives (int subId, double pcoords[3], double values, int dim, double derivs)

virtual double *	GetParametricCoords ()

double	ComputeArea ()

void	Clip (double value, vtkDataArray cellScalars, vtkIncrementalPointLocator locator, vtkCellArray polys, vtkPointData inPd, vtkPointData outPd, vtkCellData inCd, vtkIdType cellId, vtkCellData *outCd, int insideOut)

virtual void	InterpolateFunctions (double pcoords[3], double sf[3])

virtual void	InterpolateDerivs (double pcoords[3], double derivs[6])

int *	GetEdgeArray (int edgeId)

int	IntersectWithLine (double p1[3], double p2[3], double tol, double &t, double x[3], double pcoords[3], int &subId)

int	GetParametricCenter (double pcoords[3])

double	GetParametricDistance (double pcoords[3])

Public Member Functions inherited from vtkCell
vtkCell *	NewInstance () const

void	Initialize (int npts, vtkIdType pts, vtkPoints p)

virtual void	ShallowCopy (vtkCell *c)

virtual void	DeepCopy (vtkCell *c)

virtual int	IsLinear ()

virtual int	RequiresInitialization ()

virtual void	Initialize ()

virtual int	IsExplicitCell ()

virtual int	RequiresExplicitFaceRepresentation ()

virtual void	SetFaces (vtkIdType *vtkNotUsed(faces))

virtual vtkIdType *	GetFaces ()

vtkPoints *	GetPoints ()

vtkIdType	GetNumberOfPoints ()

vtkIdList *	GetPointIds ()

vtkIdType	GetPointId (int ptId)

void	GetBounds (double bounds[6])

double *	GetBounds ()

double	GetLength2 ()

virtual int	IsPrimaryCell ()

virtual void	InterpolateFunctions (double vtkNotUsed(pcoords)[3], double *vtkNotUsed(weight))

virtual void	InterpolateDerivs (double vtkNotUsed(pcoords)[3], double *vtkNotUsed(derivs))

Public Member Functions inherited from vtkObject
vtkObject *	NewInstance () const

virtual void	DebugOn ()

virtual void	DebugOff ()

bool	GetDebug ()

void	SetDebug (bool debugFlag)

virtual void	Modified ()

virtual unsigned long	GetMTime ()

unsigned long	AddObserver (unsigned long event, vtkCommand *, float priority=0.0f)

unsigned long	AddObserver (const char event, vtkCommand , float priority=0.0f)

vtkCommand *	GetCommand (unsigned long tag)

void	RemoveObserver (vtkCommand *)

void	RemoveObservers (unsigned long event, vtkCommand *)

void	RemoveObservers (const char event, vtkCommand )

int	HasObserver (unsigned long event, vtkCommand *)

int	HasObserver (const char event, vtkCommand )

void	RemoveObserver (unsigned long tag)

void	RemoveObservers (unsigned long event)

void	RemoveObservers (const char *event)

void	RemoveAllObservers ()

int	HasObserver (unsigned long event)

int	HasObserver (const char *event)

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, void(T::*callback)(), float priority=0.0f)

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, void(T::callback)(vtkObject , unsigned long, void *), float priority=0.0f)

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, bool(T::callback)(vtkObject , unsigned long, void *), float priority=0.0f)

int	InvokeEvent (unsigned long event, void *callData)

int	InvokeEvent (const char event, void callData)

int	InvokeEvent (unsigned long event)

int	InvokeEvent (const char *event)

Public Member Functions inherited from vtkObjectBase
const char *	GetClassName () const

virtual void	Delete ()

virtual void	FastDelete ()

void	Print (ostream &os)

virtual void	PrintHeader (ostream &os, vtkIndent indent)

virtual void	PrintTrailer (ostream &os, vtkIndent indent)

virtual void	Register (vtkObjectBase *o)

virtual void	UnRegister (vtkObjectBase *o)

int	GetReferenceCount ()

void	SetReferenceCount (int)

void	PrintRevisions (ostream &)

Static Public Member Functions
static vtkTriangle *	New ()

static int	IsTypeOf (const char *type)

static vtkTriangle *	SafeDownCast (vtkObjectBase *o)

static void	InterpolationFunctions (double pcoords[3], double sf[3])

static void	InterpolationDerivs (double pcoords[3], double derivs[6])

static void	TriangleCenter (double p1[3], double p2[3], double p3[3], double center[3])

static double	TriangleArea (double p1[3], double p2[3], double p3[3])

static double	Circumcircle (double p1[2], double p2[2], double p3[2], double center[2])

static int	BarycentricCoords (double x[2], double x1[2], double x2[2], double x3[2], double bcoords[3])

static int	ProjectTo2D (double x1[3], double x2[3], double x3[3], double v1[2], double v2[2], double v3[2])

static void	ComputeNormal (vtkPoints p, int numPts, vtkIdType pts, double n[3])

static void	ComputeNormal (double v1[3], double v2[3], double v3[3], double n[3])

static void	ComputeNormalDirection (double v1[3], double v2[3], double v3[3], double n[3])

static int	PointInTriangle (double x[3], double x1[3], double x2[3], double x3[3], double tol2)

static void	ComputeQuadric (double x1[3], double x2[3], double x3[3], double quadric[4][4])

static void	ComputeQuadric (double x1[3], double x2[3], double x3[3], vtkQuadric *quadric)

Static Public Member Functions inherited from vtkCell
static int	IsTypeOf (const char *type)

static vtkCell *	SafeDownCast (vtkObjectBase *o)

Static Public Member Functions inherited from vtkObject
static int	IsTypeOf (const char *type)

static vtkObject *	SafeDownCast (vtkObjectBase *o)

static vtkObject *	New ()

static void	BreakOnError ()

static void	SetGlobalWarningDisplay (int val)

static void	GlobalWarningDisplayOn ()

static void	GlobalWarningDisplayOff ()

static int	GetGlobalWarningDisplay ()

Static Public Member Functions inherited from vtkObjectBase
static int	IsTypeOf (const char *name)

static vtkObjectBase *	New ()

Protected Member Functions
virtual vtkObjectBase *	NewInstanceInternal () const

	vtkTriangle ()

	~vtkTriangle ()

Protected Member Functions inherited from vtkCell
	vtkCell ()

	~vtkCell ()

Protected Member Functions inherited from vtkObject
	vtkObject ()

virtual	~vtkObject ()

virtual void	RegisterInternal (vtkObjectBase *, int check)

virtual void	UnRegisterInternal (vtkObjectBase *, int check)

void	InternalGrabFocus (vtkCommand mouseEvents, vtkCommand keypressEvents=NULL)

void	InternalReleaseFocus ()

Protected Member Functions inherited from vtkObjectBase
	vtkObjectBase ()

virtual	~vtkObjectBase ()

virtual void	CollectRevisions (ostream &)

virtual void	ReportReferences (vtkGarbageCollector *)

	vtkObjectBase (const vtkObjectBase &)

void	operator= (const vtkObjectBase &)

Protected Attributes
vtkLine *	Line

Protected Attributes inherited from vtkCell
double	Bounds [6]

Protected Attributes inherited from vtkObject
bool	Debug

vtkTimeStamp	MTime

vtkSubjectHelper *	SubjectHelper

Protected Attributes inherited from vtkObjectBase
vtkAtomicInt32	ReferenceCount

vtkWeakPointerBase **	WeakPointers

Additional Inherited Members
Public Attributes inherited from vtkCell
vtkPoints *	Points

vtkIdList *	PointIds

Detailed Description

a cell that represents a triangle

vtkTriangle is a concrete implementation of vtkCell to represent a triangle located in 3-space.

Examples:: vtkTriangle (Examples)

Tests:: vtkTriangle (Tests)

Definition at line 40 of file vtkTriangle.h.

Member Typedef Documentation

◆ Superclass

typedef vtkCell vtkTriangle::Superclass

Definition at line 44 of file vtkTriangle.h.

Constructor & Destructor Documentation

◆ vtkTriangle()

vtkTriangle::vtkTriangle ( )

protected

◆ ~vtkTriangle()

vtkTriangle::~vtkTriangle ( )

protected

Member Function Documentation

◆ New()

static vtkTriangle* vtkTriangle::New ( )

static

◆ IsTypeOf()

static int vtkTriangle::IsTypeOf ( const char * type )

static

◆ IsA()

virtual int vtkTriangle::IsA ( const char * name )

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 vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkCell.

◆ SafeDownCast()

static vtkTriangle* vtkTriangle::SafeDownCast ( vtkObjectBase * o )

static

◆ NewInstanceInternal()

virtual vtkObjectBase* vtkTriangle::NewInstanceInternal ( ) const

protectedvirtual

Reimplemented from vtkCell.

◆ NewInstance()

vtkTriangle* vtkTriangle::NewInstance ( ) const

◆ PrintSelf()

void vtkTriangle::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 vtkCell.

int vtkTriangle::CellBoundary	(	int	subId,
		double	pcoords[3],
		vtkIdList *	pts
	)

virtual

Given parametric coordinates of a point, return the closest cell boundary, and whether the point is inside or outside of the cell. The cell boundary is defined by a list of points (pts) that specify a face (3D cell), edge (2D cell), or vertex (1D cell). If the return value of the method is != 0, then the point is inside the cell.

Implements vtkCell.

◆ Contour()

void vtkTriangle::Contour	(	double	value,
		vtkDataArray *	cellScalars,
		vtkIncrementalPointLocator *	locator,
		vtkCellArray *	verts,
		vtkCellArray *	lines,
		vtkCellArray *	polys,
		vtkPointData *	inPd,
		vtkPointData *	outPd,
		vtkCellData *	inCd,
		vtkIdType	cellId,
		vtkCellData *	outCd
	)

virtual

Generate contouring primitives. The scalar list cellScalars are scalar values at each cell point. The point locator is essentially a points list that merges points as they are inserted (i.e., prevents duplicates). Contouring primitives can be vertices, lines, or polygons. It is possible to interpolate point data along the edge by providing input and output point data - if outPd is NULL, then no interpolation is performed. Also, if the output cell data is non-NULL, the cell data from the contoured cell is passed to the generated contouring primitives. (Note: the CopyAllocate() method must be invoked on both the output cell and point data. The cellId refers to the cell from which the cell data is copied.)

Implements vtkCell.

◆ EvaluatePosition()

int vtkTriangle::EvaluatePosition	(	double	x[3],
		double *	closestPoint,
		int &	subId,
		double	pcoords[3],
		double &	dist2,
		double *	weights
	)

virtual

Given a point x[3] return inside(=1), outside(=0) cell, or (-1) computational problem encountered; evaluate parametric coordinates, sub-cell id (!=0 only if cell is composite), distance squared of point x[3] to cell (in particular, the sub-cell indicated), closest point on cell to x[3] (unless closestPoint is null, in which case, the closest point and dist2 are not found), and interpolation weights in cell. (The number of weights is equal to the number of points defining the cell). Note: on rare occasions a -1 is returned from the method. This means that numerical error has occurred and all data returned from this method should be ignored. Also, inside/outside is determine parametrically. That is, a point is inside if it satisfies parametric limits. This can cause problems for cells of topological dimension 2 or less, since a point in 3D can project onto the cell within parametric limits but be "far" from the cell. Thus the value dist2 may be checked to determine true in/out.

Implements vtkCell.

◆ EvaluateLocation()

void vtkTriangle::EvaluateLocation	(	int &	subId,
		double	pcoords[3],
		double	x[3],
		double *	weights
	)

virtual

Determine global coordinate (x[3]) from subId and parametric coordinates. Also returns interpolation weights. (The number of weights is equal to the number of points in the cell.)

Implements vtkCell.

◆ Triangulate()

int vtkTriangle::Triangulate	(	int	index,
		vtkIdList *	ptIds,
		vtkPoints *	pts
	)

virtual

Generate simplices of proper dimension. If cell is 3D, tetrahedron are generated; if 2D triangles; if 1D lines; if 0D points. The form of the output is a sequence of points, each n+1 points (where n is topological cell dimension) defining a simplex. The index is a parameter that controls which triangulation to use (if more than one is possible). If numerical degeneracy encountered, 0 is returned, otherwise 1 is returned. This method does not insert new points: all the points that define the simplices are the points that define the cell.

Implements vtkCell.

◆ Derivatives()

void vtkTriangle::Derivatives	(	int	subId,
		double	pcoords[3],
		double *	values,
		int	dim,
		double *	derivs
	)

virtual

Compute derivatives given cell subId and parametric coordinates. The values array is a series of data value(s) at the cell points. There is a one-to-one correspondence between cell point and data value(s). Dim is the number of data values per cell point. Derivs are derivatives in the x-y-z coordinate directions for each data value. Thus, if computing derivatives for a scalar function in a hexahedron, dim=1, 8 values are supplied, and 3 deriv values are returned (i.e., derivatives in x-y-z directions). On the other hand, if computing derivatives of velocity (vx,vy,vz) dim=3, 24 values are supplied ((vx,vy,vz)1, (vx,vy,vz)2, ....()8), and 9 deriv values are returned ((d(vx)/dx),(d(vx)/dy),(d(vx)/dz), (d(vy)/dx),(d(vy)/dy), (d(vy)/dz), (d(vz)/dx),(d(vz)/dy),(d(vz)/dz)).

Implements vtkCell.

◆ GetParametricCoords()

virtual double* vtkTriangle::GetParametricCoords ( )

virtual

Return a contiguous array of parametric coordinates of the points defining this cell. In other words, (px,py,pz, px,py,pz, etc..) The coordinates are ordered consistent with the definition of the point ordering for the cell. This method returns a non-NULL pointer when the cell is a primary type (i.e., IsPrimaryCell() is true). Note that 3D parametric coordinates are returned no matter what the topological dimension of the cell.

Reimplemented from vtkCell.

◆ ComputeArea()

double vtkTriangle::ComputeArea ( )

A convenience function to compute the area of a vtkTriangle.

◆ Clip()

void vtkTriangle::Clip	(	double	value,
		vtkDataArray *	cellScalars,
		vtkIncrementalPointLocator *	locator,
		vtkCellArray *	polys,
		vtkPointData *	inPd,
		vtkPointData *	outPd,
		vtkCellData *	inCd,
		vtkIdType	cellId,
		vtkCellData *	outCd,
		int	insideOut
	)

virtual

Clip this triangle using scalar value provided. Like contouring, except that it cuts the triangle to produce other triangles.

Implements vtkCell.

◆ InterpolationFunctions()

static void vtkTriangle::InterpolationFunctions	(	double	pcoords[3],
		double	sf[3]
	)

static

Deprecated:: Replaced by vtkTriangle::InterpolateFunctions as of VTK 5.2

◆ InterpolationDerivs()

static void vtkTriangle::InterpolationDerivs	(	double	pcoords[3],
		double	derivs[6]
	)

static

Deprecated:: Replaced by vtkTriangle::InterpolateDerivs as of VTK 5.2

◆ InterpolateFunctions()

virtual void vtkTriangle::InterpolateFunctions	(	double	pcoords[3],
		double	sf[3]
	)

inlinevirtual

Compute the interpolation functions/derivatives (aka shape functions/derivatives)

Definition at line 96 of file vtkTriangle.h.

◆ InterpolateDerivs()

virtual void vtkTriangle::InterpolateDerivs	(	double	pcoords[3],
		double	derivs[6]
	)

inlinevirtual

Definition at line 100 of file vtkTriangle.h.

◆ GetEdgeArray()

int* vtkTriangle::GetEdgeArray ( int edgeId )

Return the ids of the vertices defining edge (edgeId). Ids are related to the cell, not to the dataset.

◆ IntersectWithLine()

int vtkTriangle::IntersectWithLine	(	double	p1[3],
		double	p2[3],
		double	tol,
		double &	t,
		double	x[3],
		double	pcoords[3],
		int &	subId
	)

virtual

Plane intersection plus in/out test on triangle. The in/out test is performed using tol as the tolerance.

Implements vtkCell.

◆ GetParametricCenter()

int vtkTriangle::GetParametricCenter ( double pcoords[3] )

inlinevirtual

Return the center of the triangle in parametric coordinates.

Reimplemented from vtkCell.

Definition at line 218 of file vtkTriangle.h.

◆ GetParametricDistance()

double vtkTriangle::GetParametricDistance ( double pcoords[3] )

virtual

Return the distance of the parametric coordinate provided to the cell. If inside the cell, a distance of zero is returned.

Reimplemented from vtkCell.

◆ TriangleCenter()

void vtkTriangle::TriangleCenter	(	double	p1[3],
		double	p2[3],
		double	p3[3],
		double	center[3]
	)

inlinestatic

Compute the center of the triangle.

Definition at line 256 of file vtkTriangle.h.

◆ TriangleArea()

double vtkTriangle::TriangleArea	(	double	p1[3],
		double	p2[3],
		double	p3[3]
	)

inlinestatic

Compute the area of a triangle in 3D. See also vtkTriangle::ComputeArea()

Definition at line 265 of file vtkTriangle.h.

◆ Circumcircle()

static double vtkTriangle::Circumcircle	(	double	p1[2],
		double	p2[2],
		double	p3[2],
		double	center[2]
	)

static

Compute the circumcenter (center[3]) and radius squared (method return value) of a triangle defined by the three points x1, x2, and x3. (Note that the coordinates are 2D. 3D points can be used but the z-component will be ignored.)

◆ BarycentricCoords()

static int vtkTriangle::BarycentricCoords	(	double	x[2],
		double	x1[2],
		double	x2[2],
		double	x3[2],
		double	bcoords[3]
	)

static

Given a 2D point x[2], determine the barycentric coordinates of the point. Barycentric coordinates are a natural coordinate system for simplices that express a position as a linear combination of the vertices. For a triangle, there are three barycentric coordinates (because there are three vertices), and the sum of the coordinates must equal 1. If a point x is inside a simplex, then all three coordinates will be strictly positive. If two coordinates are zero (so the third =1), then the point x is on a vertex. If one coordinates are zero, the point x is on an edge. In this method, you must specify the vertex coordinates x1->x3. Returns 0 if triangle is degenerate.

◆ ProjectTo2D()

static int vtkTriangle::ProjectTo2D	(	double	x1[3],
		double	x2[3],
		double	x3[3],
		double	v1[2],
		double	v2[2],
		double	v3[2]
	)

static

Project triangle defined in 3D to 2D coordinates. Returns 0 if degenerate triangle; non-zero value otherwise. Input points are x1->x3; output 2D points are v1->v3.

◆ ComputeNormal() [1/2]

static void vtkTriangle::ComputeNormal	(	vtkPoints *	p,
		int	numPts,
		vtkIdType *	pts,
		double	n[3]
	)

static

Compute the triangle normal from a points list, and a list of point ids that index into the points list.

◆ ComputeNormal() [2/2]

void vtkTriangle::ComputeNormal	(	double	v1[3],
		double	v2[3],
		double	v3[3],
		double	n[3]
	)

inlinestatic

Compute the triangle normal from three points.

Definition at line 240 of file vtkTriangle.h.

◆ ComputeNormalDirection()

void vtkTriangle::ComputeNormalDirection	(	double	v1[3],
		double	v2[3],
		double	v3[3],
		double	n[3]
	)

inlinestatic

Compute the (unnormalized) triangle normal direction from three points.

Definition at line 225 of file vtkTriangle.h.

◆ PointInTriangle()

static int vtkTriangle::PointInTriangle	(	double	x[3],
		double	x1[3],
		double	x2[3],
		double	x3[3],
		double	tol2
	)

static

Given a point x, determine whether it is inside (within the tolerance squared, tol2) the triangle defined by the three coordinate values p1, p2, p3. Method is via comparing dot products. (Note: in current implementation the tolerance only works in the neighborhood of the three vertices of the triangle.

◆ ComputeQuadric() [1/2]

static void vtkTriangle::ComputeQuadric	(	double	x1[3],
		double	x2[3],
		double	x3[3],
		double	quadric[4][4]
	)

static

Calculate the error quadric for this triangle. Return the quadric as a 4x4 matrix or a vtkQuadric. (from Peter Lindstrom's Siggraph 2000 paper, "Out-of-Core Simplification of Large Polygonal Models")

◆ ComputeQuadric() [2/2]

static void vtkTriangle::ComputeQuadric	(	double	x1[3],
		double	x2[3],
		double	x3[3],
		vtkQuadric *	quadric
	)

static

Member Data Documentation

◆ Line

vtkLine* vtkTriangle::Line

protected

Definition at line 210 of file vtkTriangle.h.

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

dox/opt/build/vtk6-6.3.0+dfsg2/Common/DataModel/vtkTriangle.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Superclass

Constructor & Destructor Documentation

◆ vtkTriangle()

◆ ~vtkTriangle()

Member Function Documentation

◆ New()

◆ IsTypeOf()

◆ IsA()

◆ SafeDownCast()

◆ NewInstanceInternal()

◆ NewInstance()

◆ PrintSelf()

◆ GetEdge()

◆ GetCellType()

◆ GetCellDimension()

◆ GetNumberOfEdges()

◆ GetNumberOfFaces()

◆ GetFace()

◆ CellBoundary()

◆ Contour()

◆ EvaluatePosition()

◆ EvaluateLocation()

◆ Triangulate()

◆ Derivatives()

◆ GetParametricCoords()

◆ ComputeArea()

◆ Clip()

◆ InterpolationFunctions()

◆ InterpolationDerivs()

◆ InterpolateFunctions()

◆ InterpolateDerivs()

◆ GetEdgeArray()

◆ IntersectWithLine()

◆ GetParametricCenter()

◆ GetParametricDistance()

◆ TriangleCenter()

◆ TriangleArea()

◆ Circumcircle()

◆ BarycentricCoords()

◆ ProjectTo2D()

◆ ComputeNormal() [1/2]

◆ ComputeNormal() [2/2]

◆ ComputeNormalDirection()

◆ PointInTriangle()

◆ ComputeQuadric() [1/2]

◆ ComputeQuadric() [2/2]

Member Data Documentation

◆ Line