Method ParameterizePolygon

Common/DataModel/vtkPolygon.cxx:630–703

------------------------------------------------------------------------------ Create a local s-t coordinate system for a polygon. The point p0 is the origin of the local system, p10 is s-axis vector, and p20 is the t-axis vector. (These are expressed in the modelling coordinate system and are vectors of dimension [3].) The values l20 and l20 are the lengths of the vectors p10 and p20, and n is th

// are vectors of dimension [3].) The values l20 and l20 are the lengths of
// the vectors p10 and p20, and n is the polygon normal.
int vtkPolygon::ParameterizePolygon(
  double* p0, double* p10, double& l10, double* p20, double& l20, double* n)
{
  int i, j;
  double s, t, p[3], p1[3], p2[3], sbounds[2], tbounds[2];
  int numPts = this->Points->GetNumberOfPoints();
  double x1[3], x2[3];

  if (numPts < 3)
  {
    return 0;
  }

  //  This is a two pass process: first create a p' coordinate system
  //  that is then adjusted to ensure that the polygon points are all in
  //  the range 0<=s,t<=1.  The p' system is defined by the polygon normal,
  //  first vertex and the first edge.
  //
  this->ComputeNormal(this->Points, n);
  this->Points->GetPoint(0, x1);
  this->Points->GetPoint(1, x2);
  for (i = 0; i < 3; i++)
  {
    p0[i] = x1[i];
    p10[i] = x2[i] - x1[i];
  }
  vtkMath::Cross(n, p10, p20);

  // Determine lengths of edges
  //
  if ((l10 = vtkMath::Dot(p10, p10)) == 0.0 || (l20 = vtkMath::Dot(p20, p20)) == 0.0)
  {
    return 0;
  }

  //  Now evaluate all polygon points to determine min/max parametric
  //  coordinate values.
  //
  // first vertex has (s,t) = (0,0)
  sbounds[0] = 0.0;
  sbounds[1] = 0.0;
  tbounds[0] = 0.0;
  tbounds[1] = 0.0;

  for (i = 1; i < numPts; i++)
  {
    this->Points->GetPoint(i, x1);
    for (j = 0; j < 3; j++)
    {
      p[j] = x1[j] - p0[j];
    }
    s = (p[0] * p10[0] + p[1] * p10[1] + p[2] * p10[2]) / l10;
    t = (p[0] * p20[0] + p[1] * p20[1] + p[2] * p20[2]) / l20;
    sbounds[0] = (s < sbounds[0] ? s : sbounds[0]);
    sbounds[1] = (s > sbounds[1] ? s : sbounds[1]);
    tbounds[0] = (t < tbounds[0] ? t : tbounds[0]);
    tbounds[1] = (t > tbounds[1] ? t : tbounds[1]);
  }