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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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List of all members.

Public Methods

virtual const char * GetClassName ()
virtual int IsA (const char *type)
vtkCellMakeObject ()
vtkCellGetEdge (int edgeId)
int GetCellType ()
int GetCellDimension ()
int GetNumberOfEdges ()
int GetNumberOfFaces ()
vtkCellGetFace (int)
int CellBoundary (int subId, float pcoords[3], vtkIdList *pts)
void Contour (float value, vtkScalars *cellScalars, vtkPointLocator *locator, vtkCellArray *verts, vtkCellArray *lines, vtkCellArray *polys, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, int cellId, vtkCellData *outCd)
int EvaluatePosition (float x[3], float *closestPoint, int &subId, float pcoords[3], float &dist2, float *weights)
void EvaluateLocation (int &subId, float pcoords[3], float x[3], float *weights)
int Triangulate (int index, vtkIdList *ptIds, vtkPoints *pts)
void Derivatives (int subId, float pcoords[3], float *values, int dim, float *derivs)
void Clip (float value, vtkScalars *cellScalars, vtkPointLocator *locator, vtkCellArray *polys, vtkPointData *inPd, vtkPointData *outPd, vtkCellData *inCd, int cellId, vtkCellData *outCd, int insideOut)
int IntersectWithLine (float p1[3], float p2[3], float tol, float &t, float x[3], float pcoords[3], int &subId)
int GetParametricCenter (float pcoords[3])
int CellBoundary (int subId, float pcoords[3], vtkIdList &pts)
int Triangulate (int index, vtkIdList &ptIds, vtkPoints &pts)

Static Public Methods

vtkTriangle * New ()
int IsTypeOf (const char *type)
vtkTriangle * SafeDownCast (vtkObject *o)
void TriangleCenter (float p1[3], float p2[3], float p3[3], float center[3])
float TriangleArea (float p1[3], float p2[3], float p3[3])
double Circumcircle (double p1[2], double p2[2], double p3[2], double center[2])
int BarycentricCoords (double x[2], double x1[2], double x2[2], double x3[2], double bcoords[3])
int ProjectTo2D (double x1[3], double x2[3], double x3[3], double v1[2], double v2[2], double v3[2])
void ComputeNormal (vtkPoints *p, int numPts, int *pts, float n[3])
void ComputeNormal (float v1[3], float v2[3], float v3[3], float n[3])
void ComputeNormalDirection (float v1[3], float v2[3], float v3[3], float n[3])
void ComputeNormal (double v1[3], double v2[3], double v3[3], double n[3])
void ComputeNormalDirection (double v1[3], double v2[3], double v3[3], double n[3])
int PointInTriangle (float x[3], float x1[3], float x2[3], float x3[3], float tol2)
void ComputeQuadric (float x1[3], float x2[3], float x3[3], float quadric[4][4])
void ComputeQuadric (float x1[3], float x2[3], float x3[3], vtkQuadric *quadric)

Protected Methods

 vtkTriangle ()
 ~vtkTriangle ()
 vtkTriangle (const vtkTriangle &)
void operator= (const vtkTriangle &)

Protected Attributes

vtkLineLine

Detailed Description

a cell that represents a triangle.

Date:
2000/12/10 20:08:20
Revision:
1.63

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

Examples:
vtkTriangle (examples)


Member Function Documentation

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.

int vtkTriangle::CellBoundary int    subId,
float    pcoords[3],
vtkIdList   pts
[inline]
 

For legacy compatibility. Do not use.

int vtkTriangle::CellBoundary int    subId,
float    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.

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

Compute the circumcenter (center[3]) and radius (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.)

void vtkTriangle::Clip float    value,
vtkScalars   cellScalars,
vtkPointLocator   locator,
vtkCellArray   polys,
vtkPointData   inPd,
vtkPointData   outPd,
vtkCellData   inCd,
int    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.

void vtkTriangle::ComputeNormal double    v1[3],
double    v2[3],
double    v3[3],
double    n[3]
[inline, static]
 

Compute the triangle normal from three points (double-precision version).

void vtkTriangle::ComputeNormal float    v1[3],
float    v2[3],
float    v3[3],
float    n[3]
[inline, static]
 

Compute the triangle normal from three points.

void vtkTriangle::ComputeNormal vtkPoints   p,
int    numPts,
int *    pts,
float    n[3]
[static]
 

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

void vtkTriangle::ComputeNormalDirection double    v1[3],
double    v2[3],
double    v3[3],
double    n[3]
[inline, static]
 

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

void vtkTriangle::ComputeNormalDirection float    v1[3],
float    v2[3],
float    v3[3],
float    n[3]
[inline, static]
 

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

void vtkTriangle::ComputeQuadric float    x1[3],
float    x2[3],
float    x3[3],
float    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")

void vtkTriangle::Contour float    value,
vtkScalars   cellScalars,
vtkPointLocator   locator,
vtkCellArray   verts,
vtkCellArray   lines,
vtkCellArray   polys,
vtkPointData   inPd,
vtkPointData   outPd,
vtkCellData   inCd,
int    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.

void vtkTriangle::Derivatives int    subId,
float    pcoords[3],
float *    values,
int    dim,
float *    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.

void vtkTriangle::EvaluateLocation int &    subId,
float    pcoords[3],
float    x[3],
float *    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.

int vtkTriangle::EvaluatePosition float    x[3],
float *    closestPoint,
int &    subId,
float    pcoords[3],
float &    dist2,
float *    weights
[virtual]
 

Given a point x[3] return inside(=1) or outside(=0) cell; 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.

int vtkTriangle::GetCellDimension   [inline, virtual]
 

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

Implements vtkCell.

int vtkTriangle::GetCellType   [inline, virtual]
 

See the vtkCell API for descriptions of these methods.

Implements vtkCell.

virtual const char* vtkTriangle::GetClassName   [virtual]
 

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 vtkCell.

vtkCell* vtkTriangle::GetEdge int    edgeId [virtual]
 

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

Implements vtkCell.

vtkCell* vtkTriangle::GetFace int    [inline, virtual]
 

Return the face cell from the faceId of the cell.

Implements vtkCell.

int vtkTriangle::GetNumberOfEdges   [inline, virtual]
 

Return the number of edges in the cell.

Implements vtkCell.

int vtkTriangle::GetNumberOfFaces   [inline, virtual]
 

Return the number of faces in the cell.

Implements vtkCell.

int vtkTriangle::GetParametricCenter float    pcoords[3] [inline, virtual]
 

Return the center of the triangle in parametric coordinates.

Reimplemented from vtkCell.

int vtkTriangle::IntersectWithLine float    p1[3],
float    p2[3],
float    tol,
float &    t,
float    x[3],
float    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.

virtual int vtkTriangle::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 vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkCell.

int vtkTriangle::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 vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkCell.

vtkCell* vtkTriangle::MakeObject   [virtual]
 

Create a new cell and copy this triangle's information into the cell. Returns a pointer to the new cell created.

Implements vtkCell.

vtkTriangle* vtkTriangle::New   [static]
 

Create an object with Debug turned off, modified time initialized to zero, and reference counting on.

Reimplemented from vtkObject.

int vtkTriangle::PointInTriangle float    x[3],
float    x1[3],
float    x2[3],
float    x3[3],
float    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.

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.

vtkTriangle* vtkTriangle::SafeDownCast vtkObject   o [static]
 

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 vtkCell.

float vtkTriangle::TriangleArea float    p1[3],
float    p2[3],
float    p3[3]
[inline, static]
 

Compute the area of a triangle in 3D.

void vtkTriangle::TriangleCenter float    p1[3],
float    p2[3],
float    p3[3],
float    center[3]
[inline, static]
 

Compute the center of the triangle.

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.

Implements vtkCell.


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