Method GetCentroid

Common/DataModel/vtkPolyhedron.cxx:1198–1250

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bool vtkPolyhedron::GetCentroid(double centroid[3]) const
{
  assert(this->Faces != nullptr && "Faces must be set before calling GetCentroid.");
  const vtkIdType numPts = this->Points->GetNumberOfPoints();
  // compute apex center as the centroid of all points
  double apexCentroid[3] = { 0.0, 0.0, 0.0 }, x[3];
  for (vtkIdType i = 0; i < numPts; i++)
  {
    this->Points->GetPoint(i, x);
    vtkMath::Add(apexCentroid, x, apexCentroid);
  }
  vtkMath::MultiplyScalar(apexCentroid, 1.0 / numPts);

  // computer the weighted barycenter of the pyramids formed by the apex and each face
  const vtkIdType numFaces = this->Faces->GetNumberOfCells();
  std::fill_n(centroid, 3, 0.0);
  double totalVolume = 0.0, normal[3];
  const vtkIdType* facePts = nullptr;
  vtkIdType numFacePts;
  for (vtkIdType i = 0; i < numFaces; ++i)
  {
    this->Faces->GetCellAtId(i, numFacePts, facePts);
    // compute centroid of the face
    double faceCentroid[3];
    vtkPolygon::ComputeCentroid(this->Points, numFacePts, facePts, faceCentroid);
    // compute area and normal of the face
    const double faceArea = vtkPolygon::ComputeArea(this->Points, numFacePts, facePts, normal);
    // compute barycenter of the face
    double baryCenter[3] = { (0.75 * faceCentroid[0]) + (0.25 * apexCentroid[0]),
      (0.75 * faceCentroid[1]) + (0.25 * apexCentroid[1]),
      (0.75 * faceCentroid[2]) + (0.25 * apexCentroid[2]) };
    // compute the volume of the pyramid formed by the face and the apex
    double centerDiff[3];
    vtkMath::Subtract(apexCentroid, faceCentroid, centerDiff);
    // projection along normal that is signed to handle non-convex polyhedra
    const double height = vtkMath::Dot(centerDiff, normal);
    const double volume = faceArea * height / 3.0;
    totalVolume += volume;
    // accumulate the weighted barycenter and volume
    vtkMath::MultiplyScalar(baryCenter, volume);
    vtkMath::Add(centroid, baryCenter, centroid);
  }
  if (std::abs(totalVolume) > 1e-12)
  {
    vtkMath::MultiplyScalar(centroid, 1.0 / totalVolume);
    return true;
  }
  else
  {
    std::copy_n(apexCentroid, 3, centroid);
    return false;
  }
}

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int vtkPolyhedron::GetParametricCenter(double pcoords[3])