135 #ifndef vtkTriangle_h
136 #define vtkTriangle_h
139 #include "vtkCommonDataModelModule.h"
173 int EvaluatePosition(
const double x[3],
double closestPoint[3],
int& subId,
double pcoords[3],
174 double& dist2,
double weights[])
override;
175 void EvaluateLocation(
int& subId,
const double pcoords[3],
double x[3],
double* weights)
override;
178 int subId,
const double pcoords[3],
const double* values,
int dim,
double* derivs)
override;
227 int IntersectWithLine(
const double p1[3],
const double p2[3],
double tol,
double& t,
double x[3],
228 double pcoords[3],
int& subId)
override;
244 static void TriangleCenter(
245 const double p1[3],
const double p2[3],
const double p3[3],
double center[3]);
251 static double TriangleArea(
const double p1[3],
const double p2[3],
const double p3[3]);
260 const double p1[2],
const double p2[2],
const double p3[2],
double center[2]);
275 const double x3[2],
double bcoords[3]);
282 static int ProjectTo2D(
const double x1[3],
const double x2[3],
const double x3[3],
double v1[2],
283 double v2[2],
double v3[2]);
294 static void ComputeNormal(
295 const double v1[3],
const double v2[3],
const double v3[3],
double n[3]);
300 static void ComputeNormalDirection(
301 const double v1[3],
const double v2[3],
const double v3[3],
double n[3]);
309 const double p2[3],
const double q2[3],
const double r2[3]);
318 const double x3[3],
const double tol2);
328 const double x1[3],
const double x2[3],
const double x3[3],
double quadric[4][4]);
330 const double x1[3],
const double x2[3],
const double x3[3],
vtkQuadric* quadric);
353 pcoords[0] = pcoords[1] = 1. / 3;
360 const double v1[3],
const double v2[3],
const double v3[3],
double n[3])
362 double ax, ay, az, bx, by, bz;
372 n[0] = (ay * bz - az * by);
373 n[1] = (az * bx - ax * bz);
374 n[2] = (ax * by - ay * bx);
379 const double v1[3],
const double v2[3],
const double v3[3],
double n[3])
385 if ((
length = sqrt((n[0] * n[0] + n[1] * n[1] + n[2] * n[2]))) != 0.0)
395 const double p1[3],
const double p2[3],
const double p3[3],
double center[3])
397 center[0] = (p1[0] + p2[0] + p3[0]) / 3.0;
398 center[1] = (p1[1] + p2[1] + p3[1]) / 3.0;
399 center[2] = (p1[2] + p2[2] + p3[2]) / 3.0;
object to represent cell connectivity
represent and manipulate cell attribute data
abstract class to specify cell behavior
virtual int GetParametricCenter(double pcoords[3])
Return center of the cell in parametric coordinates.
abstract superclass for arrays of numeric data
list of point or cell ids
Abstract class in support of both point location and point insertion.
a simple class to control print indentation
cell represents a 1D line
static float Norm(const float *x, int n)
Compute the norm of n-vector.
represent and manipulate point attribute data
represent and manipulate 3D points
evaluate implicit quadric function
a cell that represents a triangle
static int PointInTriangle(const double x[3], const double x1[3], const double x2[3], const double x3[3], const double tol2)
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.
vtkCell * GetFace(int) override
See the vtkCell API for descriptions of these methods.
void EvaluateLocation(int &subId, const double pcoords[3], double x[3], double *weights) override
See the vtkCell API for descriptions of these methods.
const vtkIdType * GetEdgeArray(vtkIdType edgeId)
Return the ids of the vertices defining edge (edgeId).
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 void ComputeQuadric(const double x1[3], const double x2[3], const double x3[3], vtkQuadric *quadric)
Calculate the error quadric for this triangle.
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 li...
int EvaluatePosition(const double x[3], double closestPoint[3], int &subId, double pcoords[3], double &dist2, double weights[]) override
See the vtkCell API for descriptions of these methods.
int GetParametricCenter(double pcoords[3]) override
Return the center of the triangle in parametric coordinates.
vtkCell * GetEdge(int edgeId) override
Get the edge specified by edgeId (range 0 to 2) and return that edge's coordinates.
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
See the vtkCell API for descriptions of these methods.
int GetNumberOfFaces() override
See the vtkCell API for descriptions of these methods.
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.
int CellBoundary(int subId, const double pcoords[3], vtkIdList *pts) override
See the vtkCell API for descriptions of these methods.
void InterpolateFunctions(const double pcoords[3], double sf[3]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
static double TriangleArea(const double p1[3], const double p2[3], const double p3[3])
Compute the area of a triangle in 3D.
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.
static bool ComputeCentroid(vtkPoints *points, const vtkIdType *pointIds, double centroid[3])
Get the centroid of the triangle.
static vtkTriangle * New()
double GetParametricDistance(const double pcoords[3]) override
Return the distance of the parametric coordinate provided to the cell.
int IntersectWithLine(const double p1[3], const double p2[3], double tol, double &t, double x[3], double pcoords[3], int &subId) override
Given a line defined by two points p1 and p2, determine whether it intersects the triangle.
int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) override
See the vtkCell API for descriptions of these methods.
void InterpolateDerivs(const double pcoords[3], double derivs[6]) override
Compute the interpolation functions/derivatives (aka shape functions/derivatives)
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
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 b...
static void InterpolationDerivs(const double pcoords[3], double derivs[6])
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.
int GetCellDimension() override
See the vtkCell API for descriptions of these methods.
double * GetParametricCoords() override
See the vtkCell API for descriptions of these methods.
double ComputeArea()
A convenience function to compute the area of a vtkTriangle.
static void TriangleCenter(const double p1[3], const double p2[3], const double p3[3], double center[3])
Compute the center of the triangle.
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.
int GetNumberOfEdges() override
See the vtkCell API for descriptions of these methods.
void Derivatives(int subId, const double pcoords[3], const double *values, int dim, double *derivs) override
See the vtkCell API for descriptions of these methods.
static void InterpolationFunctions(const double pcoords[3], double sf[3])
int GetCellType() override
See the vtkCell API for descriptions of these methods.