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vtkTriangle Class Reference

a cell that represents a triangle More...

#include <vtkTriangle.h>

Inheritance diagram for vtkTriangle:
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Collaboration diagram for vtkTriangle:
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Public Types

typedef vtkCell Superclass
 
- Public Types inherited from vtkCell
typedef vtkObject Superclass
 

Public Member Functions

virtual vtkTypeBool IsA (const char *type)
 Return 1 if this class is the same type of (or a subclass of) the named class. More...
 
vtkTriangleNewInstance () const
 
void PrintSelf (ostream &os, vtkIndent indent) override
 Methods invoked by print to print information about the object including superclasses. More...
 
vtkCellGetEdge (int edgeId) override
 Get the edge specified by edgeId (range 0 to 2) and return that edge's coordinates. More...
 
int GetCellType () override
 See the vtkCell API for descriptions of these methods. More...
 
int GetCellDimension () override
 Return the topological dimensional of the cell (0,1,2, or 3). More...
 
int GetNumberOfEdges () override
 Return the number of edges in the cell. More...
 
int GetNumberOfFaces () override
 Return the number of faces in the cell. More...
 
vtkCellGetFace (int) override
 Return the face cell from the faceId of the cell. More...
 
int CellBoundary (int subId, const double pcoords[3], vtkIdList *pts) override
 Given parametric coordinates of a point, return the closest cell boundary, and whether the point is inside or outside of the cell. More...
 
void Contour (double value, vtkDataArray *cellScalars, vtkIncrementalPointLocator *locator, vtkCellArray *verts, vtkCellArray *lines, vtkCellArray *polys, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd) override
 Generate contouring primitives. More...
 
int EvaluatePosition (const double x[3], double closestPoint[3], int &subId, double pcoords[3], double &dist2, double weights[]) override
 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. More...
 
void EvaluateLocation (int &subId, const double pcoords[3], double x[3], double *weights) override
 Determine global coordinate (x[3]) from subId and parametric coordinates. More...
 
int Triangulate (int index, vtkIdList *ptIds, vtkPoints *pts) override
 Generate simplices of proper dimension. More...
 
void Derivatives (int subId, const double pcoords[3], const double *values, int dim, double *derivs) override
 Compute derivatives given cell subId and parametric coordinates. More...
 
double * GetParametricCoords () override
 Return a contiguous array of parametric coordinates of the points defining this cell. More...
 
double ComputeArea ()
 A convenience function to compute the area of a vtkTriangle. More...
 
void Clip (double value, vtkDataArray *cellScalars, vtkIncrementalPointLocator *locator, vtkCellArray *polys, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd, int insideOut) override
 Clip this triangle using scalar value provided. More...
 
void InterpolateFunctions (const double pcoords[3], double sf[3]) override
 Compute the interpolation functions/derivatives (aka shape functions/derivatives) More...
 
void InterpolateDerivs (const double pcoords[3], double derivs[6]) override
 
int * GetEdgeArray (int edgeId)
 Return the ids of the vertices defining edge (edgeId). More...
 
int IntersectWithLine (const double p1[3], const double p2[3], double tol, double &t, double x[3], double pcoords[3], int &subId) override
 Plane intersection plus in/out test on triangle. More...
 
int GetParametricCenter (double pcoords[3]) override
 Return the center of the triangle in parametric coordinates. More...
 
double GetParametricDistance (const double pcoords[3]) override
 Return the distance of the parametric coordinate provided to the cell. More...
 
- Public Member Functions inherited from vtkCell
vtkCellNewInstance () const
 
void Initialize (int npts, const vtkIdType *pts, vtkPoints *p)
 Initialize cell from outside with point ids and point coordinates specified. More...
 
void Initialize (int npts, vtkPoints *p)
 Initialize the cell with point coordinates specified. More...
 
virtual void ShallowCopy (vtkCell *c)
 Copy this cell by reference counting the internal data structures. More...
 
virtual void DeepCopy (vtkCell *c)
 Copy this cell by completely copying internal data structures. More...
 
virtual int IsLinear ()
 Non-linear cells require special treatment beyond the usual cell type and connectivity list information. More...
 
virtual int RequiresInitialization ()
 Some cells require initialization prior to access. More...
 
virtual void Initialize ()
 
virtual int IsExplicitCell ()
 Explicit cells require additional representational information beyond the usual cell type and connectivity list information. More...
 
virtual int RequiresExplicitFaceRepresentation ()
 Determine whether the cell requires explicit face representation, and methods for setting and getting the faces (see vtkPolyhedron for example usage of these methods). More...
 
virtual void SetFaces (vtkIdType *vtkNotUsed(faces))
 
virtual vtkIdTypeGetFaces ()
 
vtkPointsGetPoints ()
 Get the point coordinates for the cell. More...
 
vtkIdType GetNumberOfPoints ()
 Return the number of points in the cell. More...
 
vtkIdListGetPointIds ()
 Return the list of point ids defining the cell. More...
 
vtkIdType GetPointId (int ptId)
 For cell point i, return the actual point id. More...
 
void GetBounds (double bounds[6])
 Compute cell bounding box (xmin,xmax,ymin,ymax,zmin,zmax). More...
 
double * GetBounds ()
 Compute cell bounding box (xmin,xmax,ymin,ymax,zmin,zmax). More...
 
double GetLength2 ()
 Compute Length squared of cell (i.e., bounding box diagonal squared). More...
 
virtual int IsPrimaryCell ()
 Return whether this cell type has a fixed topology or whether the topology varies depending on the data (e.g., vtkConvexPointSet). More...
 
virtual void InterpolateFunctions (const double vtkNotUsed(pcoords)[3], double *vtkNotUsed(weight))
 Compute the interpolation functions/derivatives (aka shape functions/derivatives) No-ops at this level. More...
 
virtual void InterpolateDerivs (const double vtkNotUsed(pcoords)[3], double *vtkNotUsed(derivs))
 
- Public Member Functions inherited from vtkObject
 vtkBaseTypeMacro (vtkObject, vtkObjectBase)
 
virtual void DebugOn ()
 Turn debugging output on. More...
 
virtual void DebugOff ()
 Turn debugging output off. More...
 
bool GetDebug ()
 Get the value of the debug flag. More...
 
void SetDebug (bool debugFlag)
 Set the value of the debug flag. More...
 
virtual void Modified ()
 Update the modification time for this object. More...
 
virtual vtkMTimeType GetMTime ()
 Return this object's modified time. More...
 
unsigned long AddObserver (unsigned long event, vtkCommand *, float priority=0.0f)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
unsigned long AddObserver (const char *event, vtkCommand *, float priority=0.0f)
 
vtkCommandGetCommand (unsigned long tag)
 
void RemoveObserver (vtkCommand *)
 
void RemoveObservers (unsigned long event, vtkCommand *)
 
void RemoveObservers (const char *event, vtkCommand *)
 
vtkTypeBool HasObserver (unsigned long event, vtkCommand *)
 
vtkTypeBool HasObserver (const char *event, vtkCommand *)
 
void RemoveObserver (unsigned long tag)
 
void RemoveObservers (unsigned long event)
 
void RemoveObservers (const char *event)
 
void RemoveAllObservers ()
 
vtkTypeBool HasObserver (unsigned long event)
 
vtkTypeBool HasObserver (const char *event)
 
template<class U , class T >
unsigned long AddObserver (unsigned long event, U observer, void(T::*callback)(), float priority=0.0f)
 Overloads to AddObserver that allow developers to add class member functions as callbacks for events. More...
 
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)
 Allow user to set the AbortFlagOn() with the return value of the callback method. More...
 
int InvokeEvent (unsigned long event, void *callData)
 This method invokes an event and return whether the event was aborted or not. More...
 
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
 Return the class name as a string. More...
 
virtual void Delete ()
 Delete a VTK object. More...
 
virtual void FastDelete ()
 Delete a reference to this object. More...
 
void InitializeObjectBase ()
 
void Print (ostream &os)
 Print an object to an ostream. More...
 
virtual void PrintHeader (ostream &os, vtkIndent indent)
 
virtual void PrintTrailer (ostream &os, vtkIndent indent)
 
virtual void Register (vtkObjectBase *o)
 Increase the reference count (mark as used by another object). More...
 
virtual void UnRegister (vtkObjectBase *o)
 Decrease the reference count (release by another object). More...
 
int GetReferenceCount ()
 Return the current reference count of this object. More...
 
void SetReferenceCount (int)
 Sets the reference count. More...
 
void PrintRevisions (ostream &)
 Legacy. More...
 

Static Public Member Functions

static vtkTriangleNew ()
 
static vtkTypeBool IsTypeOf (const char *type)
 
static vtkTriangleSafeDownCast (vtkObjectBase *o)
 
static void InterpolationFunctions (const double pcoords[3], double sf[3])
 
static void InterpolationDerivs (const double pcoords[3], double derivs[6])
 
static void TriangleCenter (const double p1[3], const double p2[3], const double p3[3], double center[3])
 Compute the center of the triangle. More...
 
static double TriangleArea (const double p1[3], const double p2[3], const double p3[3])
 Compute the area of a triangle in 3D. More...
 
static double Circumcircle (const double p1[2], const double p2[2], const double p3[2], double center[2])
 Compute the circumcenter (center[3]) and radius squared (method return value) of a triangle defined by the three points x1, x2, and x3. More...
 
static int BarycentricCoords (const double x[2], const double x1[2], const double x2[2], const double x3[2], double bcoords[3])
 Given a 2D point x[2], determine the barycentric coordinates of the point. More...
 
static int ProjectTo2D (const double x1[3], const double x2[3], const double x3[3], double v1[2], double v2[2], double v3[2])
 Project triangle defined in 3D to 2D coordinates. More...
 
static void ComputeNormal (vtkPoints *p, int numPts, const vtkIdType *pts, double n[3])
 Compute the triangle normal from a points list, and a list of point ids that index into the points list. More...
 
static void ComputeNormal (const double v1[3], const double v2[3], const double v3[3], double n[3])
 Compute the triangle normal from three points. More...
 
static void ComputeNormalDirection (const double v1[3], const double v2[3], const double v3[3], double n[3])
 Compute the (unnormalized) triangle normal direction from three points. More...
 
static int TrianglesIntersect (const double p1[3], const double q1[3], const double r1[3], const double p2[3], const double q2[3], const double r2[3])
 
static int PointInTriangle (const double x[3], const double x1[3], const double x2[3], const double x3[3], const double tol2)
 
static void ComputeQuadric (const double x1[3], const double x2[3], const double x3[3], double quadric[4][4])
 Calculate the error quadric for this triangle. More...
 
static void ComputeQuadric (const double x1[3], const double x2[3], const double x3[3], vtkQuadric *quadric)
 
- Static Public Member Functions inherited from vtkCell
static vtkTypeBool IsTypeOf (const char *type)
 
static vtkCellSafeDownCast (vtkObjectBase *o)
 
- Static Public Member Functions inherited from vtkObject
static vtkObjectNew ()
 Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More...
 
static void BreakOnError ()
 This method is called when vtkErrorMacro executes. More...
 
static void SetGlobalWarningDisplay (int val)
 This is a global flag that controls whether any debug, warning or error messages are displayed. More...
 
static void GlobalWarningDisplayOn ()
 
static void GlobalWarningDisplayOff ()
 
static int GetGlobalWarningDisplay ()
 
- Static Public Member Functions inherited from vtkObjectBase
static vtkTypeBool IsTypeOf (const char *name)
 Return 1 if this class type is the same type of (or a subclass of) the named class. More...
 
static vtkObjectBaseNew ()
 Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More...
 

Protected Member Functions

virtual vtkObjectBaseNewInstanceInternal () const
 
 vtkTriangle ()
 
 ~vtkTriangle () override
 
- Protected Member Functions inherited from vtkCell
 vtkCell ()
 
 ~vtkCell () override
 
- Protected Member Functions inherited from vtkObject
 vtkObject ()
 
 ~vtkObject () override
 
void RegisterInternal (vtkObjectBase *, vtkTypeBool check) override
 
void UnRegisterInternal (vtkObjectBase *, vtkTypeBool check) override
 
void InternalGrabFocus (vtkCommand *mouseEvents, vtkCommand *keypressEvents=nullptr)
 These methods allow a command to exclusively grab all events. More...
 
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

vtkLineLine
 
- Protected Attributes inherited from vtkCell
double Bounds [6]
 
- Protected Attributes inherited from vtkObject
bool Debug
 
vtkTimeStamp MTime
 
vtkSubjectHelper * SubjectHelper
 
- Protected Attributes inherited from vtkObjectBase
std::atomic< int32_t > ReferenceCount
 
vtkWeakPointerBase ** WeakPointers
 

Additional Inherited Members

- Public Attributes inherited from vtkCell
vtkPointsPoints
 
vtkIdListPointIds
 

Detailed Description

a cell that represents a triangle

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

Definition at line 35 of file vtkTriangle.h.

Member Typedef Documentation

◆ Superclass

Definition at line 39 of file vtkTriangle.h.

Constructor & Destructor Documentation

◆ vtkTriangle()

vtkTriangle::vtkTriangle ( )
protected

◆ ~vtkTriangle()

vtkTriangle::~vtkTriangle ( )
overrideprotected

Member Function Documentation

◆ New()

static vtkTriangle* vtkTriangle::New ( )
static

◆ IsTypeOf()

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

◆ IsA()

virtual vtkTypeBool 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 
)
overridevirtual

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.

◆ GetEdge()

vtkCell* vtkTriangle::GetEdge ( int  edgeId)
overridevirtual

Get the edge specified by edgeId (range 0 to 2) and return that edge's coordinates.

Implements vtkCell.

◆ GetCellType()

int vtkTriangle::GetCellType ( )
inlineoverridevirtual

See the vtkCell API for descriptions of these methods.

Implements vtkCell.

Definition at line 52 of file vtkTriangle.h.

◆ GetCellDimension()

int vtkTriangle::GetCellDimension ( )
inlineoverridevirtual

Return the topological dimensional of the cell (0,1,2, or 3).

Implements vtkCell.

Definition at line 53 of file vtkTriangle.h.

◆ GetNumberOfEdges()

int vtkTriangle::GetNumberOfEdges ( )
inlineoverridevirtual

Return the number of edges in the cell.

Implements vtkCell.

Definition at line 54 of file vtkTriangle.h.

◆ GetNumberOfFaces()

int vtkTriangle::GetNumberOfFaces ( )
inlineoverridevirtual

Return the number of faces in the cell.

Implements vtkCell.

Definition at line 55 of file vtkTriangle.h.

◆ GetFace()

vtkCell* vtkTriangle::GetFace ( int  faceId)
inlineoverridevirtual

Return the face cell from the faceId of the cell.

Implements vtkCell.

Definition at line 56 of file vtkTriangle.h.

◆ CellBoundary()

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

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 
)
overridevirtual

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 nullptr, then no interpolation is performed. Also, if the output cell data is non-nullptr, 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 ( const double  x[3],
double  closestPoint[3],
int &  subId,
double  pcoords[3],
double &  dist2,
double  weights[] 
)
overridevirtual

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,
const double  pcoords[3],
double  x[3],
double *  weights 
)
overridevirtual

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 
)
overridevirtual

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,
const double  pcoords[3],
const double *  values,
int  dim,
double *  derivs 
)
overridevirtual

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()

double* vtkTriangle::GetParametricCoords ( )
overridevirtual

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-nullptr 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 
)
overridevirtual

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 ( const double  pcoords[3],
double  sf[3] 
)
static

◆ InterpolationDerivs()

static void vtkTriangle::InterpolationDerivs ( const double  pcoords[3],
double  derivs[6] 
)
static
Deprecated:
Replaced by vtkTriangle::InterpolateDerivs as of VTK 5.2

◆ InterpolateFunctions()

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

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

Definition at line 96 of file vtkTriangle.h.

◆ InterpolateDerivs()

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

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

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])
inlineoverridevirtual

Return the center of the triangle in parametric coordinates.

Reimplemented from vtkCell.

Definition at line 233 of file vtkTriangle.h.

◆ GetParametricDistance()

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

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 ( const double  p1[3],
const double  p2[3],
const double  p3[3],
double  center[3] 
)
inlinestatic

Compute the center of the triangle.

Definition at line 276 of file vtkTriangle.h.

◆ TriangleArea()

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

Compute the area of a triangle in 3D.

See also vtkTriangle::ComputeArea()

Definition at line 285 of file vtkTriangle.h.

◆ Circumcircle()

static double vtkTriangle::Circumcircle ( const double  p1[2],
const double  p2[2],
const 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 ( const double  x[2],
const double  x1[2],
const double  x2[2],
const 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 ( const double  x1[3],
const double  x2[3],
const 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,
const 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 ( const double  v1[3],
const double  v2[3],
const double  v3[3],
double  n[3] 
)
inlinestatic

Compute the triangle normal from three points.

Definition at line 260 of file vtkTriangle.h.

◆ ComputeNormalDirection()

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

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

Definition at line 241 of file vtkTriangle.h.

◆ TrianglesIntersect()

static int vtkTriangle::TrianglesIntersect ( const double  p1[3],
const double  q1[3],
const double  r1[3],
const double  p2[3],
const double  q2[3],
const double  r2[3] 
)
static

◆ PointInTriangle()

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

◆ ComputeQuadric() [1/2]

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

Member Data Documentation

◆ Line

vtkLine* vtkTriangle::Line
protected

Definition at line 225 of file vtkTriangle.h.


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