Method ComputeMeasure

Common/DataModel/vtkPolygon.cxx:1220–1292

------------------------------------------------------------------------------ Different measures are supported. Historically, the measure was the ratio of triangle perimeter^2 to area (PERIMETER2_TO_AREA_RATIO). The other select for "best quality" triangles (BEST_QUALITY), and the largest dot product (DOT_PRODUCT - a measure of apex angle). The measure is used in a priority queue to select the

// positive numbers are selected first. Note that concave vertices, or zero
// area vertices, return a negative measure.
double vtkPolyVertexList::ComputeMeasure(vtkLocalPolyVertex* vtx)
{
  double v1[3], v2[3], v3[3], v4[3], area, perimeter;

  for (int i = 0; i < 3; i++)
  {
    v1[i] = vtx->x[i] - vtx->previous->x[i];
    v2[i] = vtx->next->x[i] - vtx->x[i];
    v3[i] = vtx->previous->x[i] - vtx->next->x[i];
  }
  vtkMath::Cross(v1, v2, v4); //|v4| is twice the area
  if ((area = vtkMath::Dot(v4, this->Normal)) < 0.0)
  {
    return (vtx->measure = -1.0); // concave or bad triangle
  }
  else if (area == 0.0)
  {
    return (vtx->measure = -VTK_DOUBLE_MAX); // concave or bad triangle
  }

  // If here, the vertex is convex and the area of the triangle is positive.
  // Compute the specified measure.
  if (this->Measure == vtkPolygon::PERIMETER2_TO_AREA_RATIO)
  {
    // This measure sucks as triangles become "needle-like" but works fine
    // when the triangle is more flattened.
    perimeter = vtkMath::Norm(v1) + vtkMath::Norm(v2) + vtkMath::Norm(v3);
    return (vtx->measure = perimeter * perimeter / area);
  }
  else if (this->Measure == vtkPolygon::DOT_PRODUCT)
  {
    vtkMath::Normalize(v1);
    vtkMath::Normalize(v2);
    return (vtx->measure = (1.0 + vtkMath::Dot(v1, v2)));
  }
  else if (this->Measure == vtkPolygon::BEST_QUALITY)
  {
    // Best quality: ratio of maximum edge length to height.
    // This is a greedy triangulation algorithm, so it may
    // not produce the mesh with the best total quality. However,
    // in greedy fashion it will select the next triangle with the
    // best quality. It is an expensive operation.
    double l1 = vtkMath::Norm(v1);
    double l2 = vtkMath::Norm(v2);
    double l3 = vtkMath::Norm(v3);
    // NOLINTNEXTLINE(readability-avoid-nested-conditional-operator)
    int longestEdge = (l1 > l2 ? (l1 > l3 ? 1 : 3) : (l2 > l3 ? 2 : 3));
    double shortest, longest;
    if (longestEdge == 1)
    {
      longest = l1;
      shortest = vtkLine::DistanceToLine(vtx->next->x, vtx->x, vtx->previous->x);
    }
    else if (longestEdge == 2)
    {
      longest = l2;
      shortest = vtkLine::DistanceToLine(vtx->previous->x, vtx->x, vtx->next->x);
    }