Method PointInTriangle

Common/DataModel/vtkTriangle.cxx:1567–1613

------------------------------------------------------------------------------ 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.

// (Note: in current implementation the tolerance only works in the
// neighborhood of the three vertices of the triangle.
int vtkTriangle::PointInTriangle(
  const double x[3], const double p1[3], const double p2[3], const double p3[3], double tol2)
{
  double x1[3], x2[3], x3[3], v13[3], v21[3], v32[3];
  double n1[3], n2[3], n3[3];

  //  Compute appropriate vectors
  //
  for (int i = 0; i < 3; i++)
  {
    x1[i] = x[i] - p1[i];
    x2[i] = x[i] - p2[i];
    x3[i] = x[i] - p3[i];
    v13[i] = p1[i] - p3[i];
    v21[i] = p2[i] - p1[i];
    v32[i] = p3[i] - p2[i];
  }

  //  See whether intersection point is within tolerance of a vertex.
  //
  if ((x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]) <= tol2 ||
    (x2[0] * x2[0] + x2[1] * x2[1] + x2[2] * x2[2]) <= tol2 ||
    (x3[0] * x3[0] + x3[1] * x3[1] + x3[2] * x3[2]) <= tol2)
  {
    return 1;
  }

  //  If not near a vertex, check whether point is inside of triangular face.
  //
  //  Obtain normal off of triangular face
  //
  vtkMath::Cross(x1, v13, n1);
  vtkMath::Cross(x2, v21, n2);
  vtkMath::Cross(x3, v32, n3);

  //  Check whether ALL the three normals go in same direction
  //
  if ((vtkMath::Dot(n1, n2) >= 0.0) && (vtkMath::Dot(n2, n3) >= 0.0) &&
    (vtkMath::Dot(n1, n3) >= 0.0))
  {
    return 1;
  }
  else
  {
    return 0;
  }
}

//------------------------------------------------------------------------------
double vtkTriangle::GetParametricDistance(const double pcoords[3])